Bayesian Workflow in the 0-inflated model

Monks who drink: the Zero-Inflated Poisson Model
First model: just do a poisson
Some proper workflow
A second model: 0 inflated poisson

%matplotlib inline
import numpy as np
import scipy as sp
import matplotlib as mpl
import matplotlib.cm as cm
import matplotlib.pyplot as plt
import pandas as pd
pd.set_option('display.width', 500)
pd.set_option('display.max_columns', 100)
pd.set_option('display.notebook_repr_html', True)
import seaborn as sns
sns.set_style("whitegrid")
sns.set_context("poster")
import pymc3 as pm

Monks who drink: the Zero-Inflated Poisson Model

From McElreath:

Now imagine that the monks take breaks on some days. On those days, no manuscripts are completed. Instead, the wine cellar is opened and more earthly delights are practiced. As the monastery owner, you’d like to know how often the monks drink. The obstacle for inference is that there will be zeros on honest non-drinking days, as well, just by chance. So how can you estimate the number of days spent drinking?

The kind of model used to solve this problem is called a Mixture Model. We’ll see these in more detail next week, but here is a simple version that arises in Poisson regression.

Let $p$ be the probability that the monks spend the day drinking, and $\lambda$ be the mean number of manuscripts completed, when they work.

Likelihood

The likelihood of observing 0 manuscripts produced is is:

$\cal{L}(y=0) = p + (1-p) e^{-\lambda},$

since the Poisson likelihood of $y$ is $ \lambda^y exp(–\lambda)/y!$

Likelihood of a non-zero $y$ is:

$\cal{L}(y \ne 0) = (1-p) \frac{\lambda^y e^{-\lambda}}{y!}$

This model can be described by this diagram, taken from Mc-Elreath

Generating the data

We’re throwing bernoullis for whether a given day in the year is a drinking day or not…

from scipy.stats import binom
p_drink=0.2
rate_work=1
N=365
drink=binom.rvs(n=1, p=p_drink, size=N)
drink

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
       0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0,
       0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0,
       0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
       1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
       0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0,
       1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
       0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
       1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0])

On days we dont drink, we produce some work…though it might be 0 work…

from scipy.stats import poisson
y = ( 1 - drink)*poisson.rvs(mu=rate_work, size=N)
y

array([1, 2, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 3, 2, 3,
       2, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 0, 0, 0, 4, 0, 1, 5, 2, 3, 0, 0, 1,
       2, 0, 0, 0, 1, 3, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0,
       1, 0, 0, 0, 1, 1, 1, 3, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0,
       2, 1, 1, 1, 0, 1, 1, 2, 1, 0, 0, 1, 2, 0, 3, 3, 0, 0, 0, 1, 1, 2, 0,
       0, 1, 1, 0, 0, 1, 2, 1, 3, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0,
       0, 1, 1, 2, 2, 0, 2, 1, 1, 1, 1, 4, 2, 0, 1, 0, 1, 3, 0, 1, 1, 0, 1,
       0, 1, 0, 1, 3, 1, 0, 0, 0, 2, 1, 0, 1, 2, 2, 0, 3, 0, 1, 2, 1, 0, 0,
       0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 1, 1, 1,
       0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 2, 1, 1, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 1, 1, 1, 2, 1, 2, 0, 1, 0, 1,
       0, 2, 1, 0, 4, 2, 0, 0, 0, 0, 1, 2, 2, 2, 4, 0, 1, 3, 1, 0, 0, 3, 1,
       1, 1, 1, 0, 1, 1, 3, 0, 0, 1, 0, 1, 1, 2, 2, 1, 0, 1, 2, 1, 0, 1, 0,
       0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 0, 1, 1, 0, 1, 4, 1, 3, 1, 0, 1,
       0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0,
       0, 0, 1, 1, 1, 0, 0, 2, 4, 2, 1, 0, 0, 2, 1, 0, 0, 0, 3, 0])

Lets manufacture a histogram of manuscripts produced in a day.

zeros_drink=np.sum(drink)
a=drink==0
b=y==0
zeros_work=np.sum(a & b)
zeros_drink, zeros_work, np.sum(b)

(69, 103, 172)

plt.hist(zeros_work*[0], bins=np.arange(10))
plt.hist(y, bins=np.arange(10), alpha=0.5)

(array([ 172.,  117.,   49.,   20.,    6.,    1.,    0.,    0.,    0.]),
 array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),
 <a list of 9 Patch objects>)

png

Lets throw in some domain expertise

A survey of Abbey Heads has told us, that the most a monk could produce, ever, was 10 manuscripts in a day.

First model: just do a poisson

import theano.tensor as t

def model_poisson(data):
    with pm.Model() as model1:
        alpha=pm.Normal("alpha", 0,100)
        logmu = alpha
        like = pm.Poisson("obsv", mu=t.exp(logmu), observed=data)
        lambda0 = pm.Deterministic("lambda0", t.exp(alpha))
    return model1
model1 = model_poisson(y)

with model1:
    trace1=pm.sample(3000, tune=1000)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [alpha]
100%|██████████| 4000/4000 [00:02<00:00, 1799.36it/s]

pm.traceplot(trace1)

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x115817588>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x11586df98>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x115820e80>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x114bf5eb8>]], dtype=object)

png

pm.summary(trace1)

	mean	sd	mc_error	hpd_2.5	hpd_97.5	n_eff	Rhat
alpha	-0.184371	0.057111	0.001032	-0.297168	-0.075473	2562.0	1.000351
lambda0	0.832983	0.047501	0.000864	0.742139	0.926474	2554.0	1.000351

Some proper workflow

Notice the prior specification though: at the 2$\sigma$ level, $\lambda$ could range from exp(-200) to exp(200), ie from 0 to an extremely large number to an extremely large “mean” of counts. Not possible. Indeed, the max count is around 10. For a poisson, since the variance is equal to the mean, this means that (at 3$\sigma):

$max(\lambda + 3\sqrt{\lambda}) < 10$

Any prior should only take us marginally outside this range:

5+3*np.sqrt(5)

11.708203932499369

Limiting the prior

Thus a prior should mainly limit $\lambda$ to values upto 5. To so this consider:

from scipy.stats import halfnorm
halfnorm.ppf(0.99, loc=0,scale=4)

10.303317214195602

Simulating the Bayesian Joint distribution

This should be way enough!, So lets go again:

First we create a decorator using code from https://github.com/ColCarroll/sampled

class ObserverModel(pm.Model):
    """Stores observed variables until the model is created."""
    def __init__(self, observed):
        self.observed = observed
        super(ObserverModel, self).__init__()

    def Var(self, name, dist, data=None, total_size=None):
        return super(ObserverModel, self).Var(name, dist,
                                              data=self.observed.get(name, data),
                                              total_size=total_size)


def sampled(f):
    """Decorator to delay initializing pymc3 model until data is passed in."""
    def wrapped_f(**observed):
        try:
            with ObserverModel(observed) as model:
                f(**observed)
        except TypeError:
            with ObserverModel(observed) as model:
                f()
        return model
    return wrapped_f

@sampled
def model_poisson1(verbose=0):
    mu = pm.HalfNormal("mu", 3)
    like = pm.Poisson("obsv", mu=mu)

with model_poisson1():
    t_nodata = pm.sample(1000, chains=1)

Sequential sampling (1 chains in 1 job)
CompoundStep
>NUTS: [mu_log__]
>Metropolis: [obsv]
 93%|█████████▎| 1395/1500 [00:01<00:00, 1255.15it/s]//anaconda/envs/py3l/lib/python3.6/site-packages/numpy/core/fromnumeric.py:2909: RuntimeWarning: Mean of empty slice.
  out=out, **kwargs)
100%|██████████| 1500/1500 [00:01<00:00, 1251.33it/s]
Tuning was enabled throughout the whole trace.
Only one chain was sampled, this makes it impossible to run some convergence checks

pm.traceplot(t_nodata);

png

plt.hist(t_nodata['obsv'], bins=np.arange(0,20,1));

png

mus = t_nodata.get_values('mu')
mus.shape

Simulating replicate prior predictives

replicate_pp = np.empty((200,200))

for i,mu in enumerate(mus):
    if i%10==0:
        print("iter", i)
    with model_poisson1(mu=mu):
        temp_nodata = pm.sample(200, progressbar=False, chains=1)
    replicate_pp[i,:] = temp_nodata.get_values('obsv')

iter 0


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 10


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 20


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 30


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 40


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 50


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 60


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 70


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 80


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 90


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 100


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 110


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 120


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 130


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 140


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 150


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 160


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 170


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 180


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 190


Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks
Sequential sampling (1 chains in 1 job)
Metropolis: [obsv]
Only one chain was sampled, this makes it impossible to run some convergence checks

with model_poisson1(obsv=replicate_pp[0,:]):
    tpost = pm.sample(1000)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
100%|██████████| 1500/1500 [00:00<00:00, 1585.16it/s]
The acceptance probability does not match the target. It is 0.884204635079, but should be close to 0.8. Try to increase the number of tuning steps.

pm.traceplot(tpost)

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x120cf1be0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12274be48>]], dtype=object)

png

mus[0]

2.807525696673618

np.std(tpost['mu'])

0.12507126731431462

pm.summary(tpost)

	mean	sd	mc_error	hpd_2.5	hpd_97.5	n_eff	Rhat
mu	3.12099	0.125071	0.003999	2.864898	3.354582	758.0	1.000367

replicate_post=np.empty((200, 200))
for i,mu in enumerate(mus):
    if i%10==0:
        print("iter", i)
    with model_poisson1(obsv=replicate_pp[i,:]):
        temp_simdata = pm.sample(200, progressbar=False, chains=1)
    replicate_post[i,:] = temp_simdata.get_values('mu')

iter 0


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 10


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.913442678494, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 20


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.87983360042, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.8798054762, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.883090611023, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 30


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.883655862554, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.885589551766, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.887472349455, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 40


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.886364831976, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.898397173883, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.890151740575, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 50


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.883216060125, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.880730904944, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.903233566383, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 60


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.883250058495, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 70


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.89484935899, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.880906634377, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.891896368942, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 80


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.88641777936, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.889773855712, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.88772798345, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.885735307491, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 90


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.881200503138, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.889514484054, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.896001171371, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.880424753311, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 100


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.883662729512, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 110


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.903203993268, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.882559193625, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.892503081624, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.881423005449, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.885596967831, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 120


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.891550853837, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.889622475199, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 130


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.900029511311, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.892799779832, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 140


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.89354336552, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.890826366551, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.880590800162, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 150


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.903762471064, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
There were 1 divergences after tuning. Increase `target_accept` or reparameterize.
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 160


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 170


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.888955373819, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 180


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.883810916393, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks


iter 190


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.883053604825, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.881493785607, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
Only one chain was sampled, this makes it impossible to run some convergence checks
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [mu_log__]
Only 200 samples in chain.
The acceptance probability does not match the target. It is 0.890479598195, but should be close to 0.8. Try to increase the number of tuning steps.
Only one chain was sampled, this makes it impossible to run some convergence checks

replicate_post.shape

(200, 200)

I found this to be painfully slow in pymc3, so just simulated replicates from scipy.stats. The reason for this in pymc3 is that it will want to use NUTS for this.

mus = halfnorm(scale=4).rvs(300)
plt.hist(mus);

png

Simulate replicate predictives directly

from scipy.stats import poisson

y.shape

(365,)

replicate_pp = np.zeros((300,365))
for i,mu in enumerate(mus):
    if i%100==0:
        print("iter", i)
    replicate_pp[i,:] = poisson(mu).rvs(365)

iter 0
iter 100
iter 200

replicate_pp[3,:]

array([ 0.,  1.,  1.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  1.,  0.,  1.,
        0.,  0.,  1.,  1.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        1.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  1.,  0.,
        1.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  1.,  1.,  1.,  1.,  0.,
        1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,
        0.,  1.,  0.,  0.,  0.,  1.,  1.,  0.,  0.,  0.,  0.,  0.,  1.,
        1.,  1.,  2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  0.,  1.,  1.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  1.,  0.,
        1.,  1.,  1.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  1.,  1.,  0.,
        0.,  1.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        1.,  0.,  1.,  0.,  0.,  0.,  0.,  1.,  0.,  1.,  0.,  0.,  0.,
        0.,  1.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.,  0.,  1.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.,  2.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,
        0.,  0.,  0.,  0.,  2.,  1.,  0.,  0.,  1.,  0.,  0.,  0.,  2.,
        0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,
        0.,  0.,  0.,  1.,  0.,  0.,  1.,  0.,  0.,  0.,  2.,  0.,  0.,
        0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  1.,
        1.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,
        0.,  0.,  0.,  2.,  1.,  0.,  0.,  2.,  1.,  2.,  0.,  1.,  0.,
        0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  1.,  1.,  1.,  0.,  0.,
        0.,  0.,  0.,  0.,  1.,  1.,  0.,  1.,  0.,  0.,  0.,  1.,  2.,
        0.,  1.,  0.,  0.,  0.,  1.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,
        0.,  1.,  2.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,
        1.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  1.,  0.,  1.,  0.,  0.,
        0.,  0.,  1.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  1.,  0.,  0.,
        1.,  0.,  2.,  0.,  0.,  0.,  1.,  1.,  1.,  0.,  0.,  0.,  1.,  0.])

Simulating replicate posteriors

replicate_post=np.empty((300, 2000))
for i,mu in enumerate(mus):
    if i%30==0:
        print("iter", i)
    with model_poisson1(obsv=replicate_pp[i,:]):
        temp_simdata = pm.sample(1000, tune=1000, progressbar=False)
    replicate_post[i,:] = temp_simdata.get_values('mu')

iter 0


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.883342812173, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]


iter 30


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.886002157963, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The number of effective samples is smaller than 25% for some parameters.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.894084884845, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.899187012185, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.886911937841, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.879794148759, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]


iter 60


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.885474429987, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.888380537416, but should be close to 0.8. Try to increase the number of tuning steps.
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]


iter 90


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.712667601545, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.88947428108, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.887087941922, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.891767169364, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]


iter 120


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The number of effective samples is smaller than 25% for some parameters.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The number of effective samples is smaller than 25% for some parameters.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.87907924255, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.905429105167, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]


iter 150


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.886311372445, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]


iter 180


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.881796219178, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.881608506348, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.879968438331, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.880073746673, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]


iter 210


Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.879071395441, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
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NUTS: [mu_log__]


iter 240


Auto-assigning NUTS sampler...
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NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.90230643238, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.886455310721, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.883103326168, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.895292599169, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
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NUTS: [mu_log__]


iter 270


Auto-assigning NUTS sampler...
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NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.879569995307, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
INFO (theano.gof.compilelock): Refreshing lock /Users/rahul/.theano/compiledir_Darwin-16.1.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.890719860616, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.898114471665, but should be close to 0.8. Try to increase the number of tuning steps.
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
The acceptance probability does not match the target. It is 0.879331114624, but should be close to 0.8. Try to increase the number of tuning steps.

Calculating simulated posterior statistics

def sbc_rank(source_param, param_post):
    return np.sum(source_param < param_post)
def z_scores(source_param, param_post):
    mean_param = np.mean(param_post)
    std_param = np.std(param_post)
    zs = np.abs(mean_param - source_param)/std_param
    return zs
def shrinkages(std_source, source_param, param_post):
    std_param = np.std(param_post)
    zs = 1. - (std_param*std_param)/(std_source*std_source)
    return zs    

ranks=np.empty(300, dtype='int')
for i, mu in enumerate(mus):
    ranks[i] = sbc_rank(mus[i], replicate_post[i,:])
ranks

array([1149,  563,  203,  424, 1904,    7,   50,  946, 1637,  286,  222,
        237,  336,  433, 1659, 1913,  887, 1732,  947,  972,  163,  435,
        447, 1876,  191, 1656, 1303, 1373,  262,  318,  558,  878,  690,
        545, 1380, 1062, 1291, 1095,  911, 1251,  502, 1827, 1864, 1552,
       1263, 1663, 1783,  479,  465,  891,  210,   20, 1159, 1661, 1685,
        107,  600, 1958, 1982, 1129, 1412,  602, 1752,  913,   64,   84,
        278,  329,  985, 1144,  344,  345, 1996,  655,  984,  749,  247,
        985,  921, 1091, 1589,  691,  831,  199, 1015, 1055, 1038,  487,
       1631,  680, 1757,  658, 1957,  809, 1689, 1135, 1143, 1118, 1137,
       1695, 1500,  851,  560,  174, 1723,  941, 1577,  536,  278,  148,
        842,  853,  949,  739,  695, 1489, 1387,  575,   62, 1608,  631,
       1105,  677,  503, 1164,  112, 1413, 1638, 1017, 1376,  409, 1181,
       1167, 1618,  710, 1087, 1397,  238, 1028, 1011,  372,  849, 1091,
        389, 1341, 1354, 1930,  644,  241,   48,  897, 1444,   81,  384,
       1167,  765,  375, 1793, 1581, 1816,  401,  678, 1842,  292,  468,
       1562, 1622,   77,  340,  357, 1324, 1822,  254, 1902, 1227,  645,
        698,   75,  353,  602, 1626,  838,  614,  752,  309,  459,  696,
        349, 1598, 1228, 1293,  939,  356, 1941, 1584,  186, 1133,  424,
       1830,  267, 1820, 1978,  887,  909,  476, 1563, 1901,  474, 1900,
        198, 1564, 1991, 1419,  407,  829,  718, 1067,  735, 1069, 1427,
        388,  752,   20,  443, 1210, 1565,  948, 1522, 1381, 1336, 1878,
       1314, 1430, 1898,  739, 1233,  536,   43, 1983, 1139,  455,   24,
        952, 1709, 1141, 1306, 1162, 1187,  735, 1583,  961,  585, 1866,
       1067, 1842,  218,  794,  678,  447, 1296,   92, 1904,  239,   15,
       1780, 1611,  825,  271, 1053,  867,  769, 1274,  574,   30, 1747,
        823,  821, 1593, 1982, 1423,   60,  170, 1950,  971,  478, 1053,
       1454, 1318, 1150, 1430,  251, 1858, 1402,  841,  123, 1653, 1095,
        252, 1454, 1331])

plt.hist(ranks, bins=20);

png

zs=np.empty(300)
for i, mu in enumerate(mus):
    zs[i] = z_scores(mus[i], replicate_post[i,:])
zs

array([ 0.20875485,  0.6016904 ,  1.30960137,  0.78702808,  1.61928975,
        2.72716747,  1.92635271,  0.06241117,  0.93301711,  1.07425741,
        1.2487615 ,  1.16310945,  0.95943601,  0.80353487,  0.93391784,
        1.70004167,  0.09650991,  1.12731801,  0.01417322,  0.02712168,
        1.39434016,  0.77834144,  0.73487566,  1.46121666,  1.3120801 ,
        0.93363934,  0.41220237,  0.46541861,  1.09927987,  1.01407185,
        0.5912949 ,  0.14615846,  0.43049123,  0.60427031,  0.51333796,
        0.06269162,  0.35575461,  0.13648075,  0.07075337,  0.31533356,
        0.62646438,  1.36797655,  1.51295293,  0.75373567,  0.3587438 ,
        0.97089641,  1.24595026,  0.705806  ,  0.73371445,  0.10486241,
        1.29165145,  2.24159285,  0.22603826,  0.98767204,  1.00203528,
        1.62795917,  0.51463461,  1.92874092,  2.33878002,  0.20150074,
        0.54585983,  0.49362192,  1.1776072 ,  0.0998092 ,  1.85516996,
        1.73873001,  1.10442061,  0.94528093,  0.00685128,  0.16762791,
        0.89380005,  0.92498372,  2.66013776,  0.43001692,  0.01887145,
        0.27556404,  1.21043763,  0.00664065,  0.06259851,  0.10718859,
        0.79789518,  0.39236966,  0.18769305,  1.28916629,  0.03402082,
        0.09216981,  0.07075202,  0.68210809,  0.88387212,  0.40234211,
        1.19168411,  0.44753407,  2.07081453,  0.21609071,  0.98654428,
        0.25436728,  0.20371194,  0.14700343,  0.1606457 ,  1.05883812,
        0.67714738,  0.18197943,  0.57752559,  1.34163628,  1.09768093,
        0.06688782,  0.81177843,  0.65437409,  1.10100921,  1.43003988,
        0.24361329,  0.13448844,  0.03061459,  0.31948667,  0.36295879,
        0.65131722,  0.5338194 ,  0.56830677,  1.96553328,  0.82910981,
        0.47197781,  0.17999585,  0.415339  ,  0.66622149,  0.20862327,
        1.63827921,  0.53869752,  0.89706166,  0.05718172,  0.50802267,
        0.85201784,  0.22964725,  0.24619877,  0.89072976,  0.35939367,
        0.0983755 ,  0.54449807,  1.16235277,  0.06288202,  0.0395065 ,
        0.91237329,  0.17301441,  0.15188504,  0.83369612,  0.45482876,
        0.49037451,  1.79006236,  0.43690133,  1.11908655,  2.09209412,
        0.11579875,  0.62858649,  1.7834343 ,  0.87472903,  0.21791388,
        0.27672538,  0.88353047,  1.19541132,  0.79253429,  1.3423345 ,
        0.81820488,  0.42601122,  1.40125068,  1.0798831 ,  0.73333241,
        0.7756078 ,  0.92665724,  1.77770312,  0.95193246,  0.93897834,
        0.42090601,  1.35259294,  1.11255789,  1.66007719,  0.31153483,
        0.5066361 ,  0.37838736,  1.79521268,  0.96432111,  0.51187318,
        0.90052143,  0.19316422,  0.48848618,  0.31839763,  1.0412067 ,
        0.71013068,  0.38763803,  0.92243532,  0.82072053,  0.31276889,
        0.36107007,  0.05373277,  0.96404458,  1.78332887,  0.83191757,
        1.39002052,  0.19324279,  0.80054279,  1.33909815,  1.1280094 ,
        1.3258022 ,  2.14297087,  0.14802282,  0.0532837 ,  0.67471852,
        0.71767772,  1.52585087,  0.68867836,  1.58922037,  1.31577878,
        0.74382568,  2.40009952,  0.56679843,  0.78642716,  0.20372789,
        0.31762528,  0.12118858,  0.30448752,  0.11392841,  0.59999142,
        0.84905492,  0.3126218 ,  2.35455518,  0.75832952,  0.29850165,
        0.77609667,  0.09257672,  0.70504988,  0.51029465,  0.41373034,
        1.52622856,  0.40828562,  0.57369712,  1.61118788,  0.3253966 ,
        0.26536607,  0.59199269,  2.02381439,  2.41717773,  0.20783751,
        0.75954152,  2.23609789,  0.05381934,  1.03857446,  0.15128711,
        0.4205374 ,  0.20824507,  0.23621713,  0.31825574,  0.81370616,
        0.0480646 ,  0.52075214,  1.48752778,  0.1101137 ,  1.41047692,
        1.24667734,  0.26215521,  0.4022564 ,  0.75993891,  0.42946829,
        1.71284736,  1.64781401,  1.16095486,  2.56294249,  1.23681047,
        0.87069596,  0.17116752,  1.13531338,  0.08766663,  0.19648858,
        0.27723119,  0.40023848,  0.54533924,  2.24327419,  1.18696125,
        0.2314685 ,  0.21705051,  0.83111355,  2.3128497 ,  0.54563585,
        1.92711888,  1.37108809,  1.95848512,  0.0328257 ,  0.68839201,
        0.03419648,  0.58140161,  0.39057566,  0.1791572 ,  0.58330552,
        1.12205262,  1.47521508,  0.54123031,  0.194957  ,  1.60156986,
        0.90647313,  0.14091793,  1.14610422,  0.63244525,  0.43186317])

shrinks=np.empty(300)
for i, mu in enumerate(mus):
    shrinks[i] = shrinkages(3, mus[i], replicate_post[i,:])
shrinks

array([ 0.99977506,  0.99896202,  0.99900691,  0.99990726,  0.99797211,
        0.99813254,  0.99961598,  0.9991045 ,  0.99871173,  0.99895253,
        0.9984847 ,  0.99985669,  0.99952059,  0.99988587,  0.99899191,
        0.99941079,  0.99768422,  0.99902108,  0.99925125,  0.99893121,
        0.99973892,  0.99839893,  0.99867078,  0.99989354,  0.99947806,
        0.99866525,  0.99940548,  0.999391  ,  0.99922751,  0.99795002,
        0.99943871,  0.99817535,  0.99834013,  0.99937265,  0.99899361,
        0.99833735,  0.99897109,  0.99816391,  0.99991506,  0.998935  ,
        0.99994518,  0.99923426,  0.99970918,  0.99933279,  0.99976849,
        0.99810943,  0.99742328,  0.99996801,  0.99782177,  0.99866496,
        0.99962818,  0.99799427,  0.99976425,  0.99746803,  0.99951758,
        0.99957197,  0.99740765,  0.99993072,  0.99920324,  0.9982549 ,
        0.99917911,  0.99978575,  0.99804508,  0.99943873,  0.99944222,
        0.99957388,  0.99957655,  0.99975464,  0.99995165,  0.99967886,
        0.99973034,  0.99862781,  0.99847049,  0.99899268,  0.99882597,
        0.99983466,  0.99972088,  0.99975927,  0.99914425,  0.99886315,
        0.99971745,  0.99897043,  0.9998607 ,  0.99923503,  0.99909198,
        0.99844385,  0.99863446,  0.99952735,  0.99954988,  0.99969543,
        0.99884294,  0.99992219,  0.99958101,  0.99945533,  0.99823404,
        0.99998864,  0.99983447,  0.99964773,  0.9985266 ,  0.99933629,
        0.99851382,  0.99894904,  0.9998073 ,  0.99927112,  0.99976369,
        0.99813454,  0.99843751,  0.9993373 ,  0.99995068,  0.99910101,
        0.99927561,  0.99965261,  0.99996983,  0.99976094,  0.99868009,
        0.99775858,  0.99623435,  0.99937242,  0.99821987,  0.999706  ,
        0.9996397 ,  0.99751527,  0.99863857,  0.99913201,  0.99993183,
        0.9985371 ,  0.99789617,  0.99969111,  0.99946761,  0.99839626,
        0.99988724,  0.99797016,  0.999533  ,  0.99937455,  0.99818778,
        0.99933874,  0.99984532,  0.99967278,  0.99979515,  0.99890828,
        0.99994165,  0.99720212,  0.99964609,  0.99994657,  0.99990982,
        0.99895797,  0.9990955 ,  0.99854   ,  0.99931861,  0.99874773,
        0.99764101,  0.99983512,  0.99864291,  0.99987332,  0.99889449,
        0.99869404,  0.99839361,  0.99954914,  0.99958074,  0.99873551,
        0.99879395,  0.99827394,  0.99973792,  0.9976794 ,  0.99765033,
        0.99884994,  0.9976025 ,  0.99909832,  0.99930909,  0.99886186,
        0.99871204,  0.99762024,  0.9994201 ,  0.99800757,  0.99952869,
        0.99853194,  0.99848643,  0.99974908,  0.99930897,  0.99834262,
        0.99962509,  0.99837292,  0.99826715,  0.99927357,  0.99803775,
        0.99898646,  0.99767628,  0.99894606,  0.99967097,  0.99836621,
        0.99960743,  0.99950068,  0.9996865 ,  0.99775952,  0.99874261,
        0.99911063,  0.99972301,  0.99925549,  0.99971507,  0.99840182,
        0.99944096,  0.99909362,  0.99853356,  0.99982637,  0.99889355,
        0.99971078,  0.99996136,  0.99947856,  0.99890129,  0.99900323,
        0.99929062,  0.99921268,  0.99809608,  0.9978801 ,  0.99975814,
        0.99996862,  0.99650213,  0.99904628,  0.99856243,  0.9996639 ,
        0.99997151,  0.99939094,  0.99849445,  0.99934602,  0.99946495,
        0.99819081,  0.9987231 ,  0.99978873,  0.99978931,  0.99939787,
        0.99976264,  0.99975234,  0.99977944,  0.99977032,  0.99872433,
        0.99927031,  0.99945793,  0.99883735,  0.99880764,  0.99914335,
        0.99968435,  0.99783409,  0.99810953,  0.99872469,  0.99769568,
        0.9987453 ,  0.99991734,  0.9992987 ,  0.99965624,  0.99912328,
        0.99872834,  0.99940822,  0.99897567,  0.99840587,  0.99912349,
        0.99834478,  0.99872549,  0.99990934,  0.99765548,  0.9986538 ,
        0.9982166 ,  0.99917476,  0.9997153 ,  0.99946964,  0.99973684,
        0.99930153,  0.99987499,  0.99849411,  0.99824761,  0.9983117 ,
        0.99858787,  0.99963123,  0.99960197,  0.99711376,  0.99936327,
        0.99952705,  0.99891724,  0.99912691,  0.99869404,  0.99895025,
        0.99882399,  0.99825011,  0.99892287,  0.99745931,  0.99953974,
        0.99897533,  0.99799003,  0.99968414,  0.99867478,  0.99811734,
        0.99896973,  0.99928803,  0.99884256,  0.99891604,  0.9995332 ,
        0.9998689 ,  0.99824226,  0.99690782,  0.99966623,  0.99837936])

plt.plot(shrinks, zs, '.');
plt.xlim([0,1]);

png

mpo = model_poisson1(obsv=y)
with mpo:
    samples = pm.sample(2000, tune=1000)
posterior = samples.get_values('mu')

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [mu_log__]
100%|██████████| 3000/3000 [00:01<00:00, 1696.50it/s]

pm.traceplot(samples)

array([[<matplotlib.axes._subplots.AxesSubplot object at 0x127a5fe48>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x129060dd8>]], dtype=object)

png

with mpo:
    samples_ppc = pm.sample_ppc(samples)

100%|██████████| 2000/2000 [00:00<00:00, 5438.02it/s]

plt.hist(y,  normed=True, histtype='step', lw=3, label="y");
plt.hist(samples_ppc['obsv'],  normed=True, histtype='step', lw=3, label="pp")
plt.legend();

png

A second model: 0 inflated poisson

The likelihood that combines the two cases considered above is called the Zero Inflated poisson. It has two arguments, the Poisson rate parameter, and the proportion of poisson variates (theta and psi in pymc).

def tinvlogit(x):
    return t.exp(x) / (1 + t.exp(x))

with pm.Model() as model2:
    alphalam=pm.Normal("alphalam", 0,10)
    alphap=pm.Normal("alphap", 0,1)
    #regression models with intercept only
    logmu = alphalam
    logitp = alphap
    like = pm.ZeroInflatedPoisson("obsv", theta=t.exp(logmu), psi=tinvlogit(logitp), observed=y)
    lam = pm.Deterministic("lam", t.exp(logmu))
    p = pm.Deterministic("p", tinvlogit(logitp))

with model2:
    trace2=pm.sample(3000, tune=1000)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [alphap, alphalam]
100%|██████████| 4000/4000 [00:04<00:00, 814.49it/s]

pm.traceplot(trace2);

png

pm.summary(trace2)

	mean	sd	mc_error	hpd_2.5	hpd_97.5	n_eff	Rhat
alphalam	0.008825	0.080045	0.001699	-0.149465	0.168037	2226.0	1.000092
alphap	1.560670	0.371543	0.008146	0.911753	2.296434	2046.0	1.000071
lam	1.012106	0.081300	0.001713	0.845978	1.166795	2234.0	1.000102
p	0.820273	0.050259	0.001066	0.723801	0.917328	2257.0	0.999963

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