{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Poisson and 0-inflated\n", "\n", "##### Keywords: glm, regression, poisson regression, link-function, zero-inflated, mixture model" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "//anaconda/envs/py35/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n", " warnings.warn(self.msg_depr % (key, alt_key))\n" ] } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib as mpl\n", "import matplotlib.cm as cm\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "pd.set_option('display.width', 500)\n", "pd.set_option('display.max_columns', 100)\n", "pd.set_option('display.notebook_repr_html', True)\n", "import seaborn as sns\n", "sns.set_style(\"whitegrid\")\n", "sns.set_context(\"poster\")\n", "import pymc3 as pm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Monks with different exposure times" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "y_i \\sim Poisson(\\lambda_i)\\\\\n", "log(\\lambda_i) = \\alpha + \\beta x_i\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "y_i \\sim Poisson(\\lambda_i)\\\\\n", "log(\\lambda_i) = log(\\frac{\\mu_i}{\\tau_i}) = \\alpha + \\beta x_i\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "y_i \\sim Poisson(\\mu_i)\\\\\n", "log(\\mu_i) = log(\\tau_i) + \\alpha + \\beta x_i\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.stats import poisson\n", "num_days=30\n", "y=poisson.rvs(mu=1.5, size=30)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 0, 4, 2, 4, 1, 2, 1, 1, 1, 0, 1, 1,\n", " 1, 0, 1, 2, 1, 1, 3])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([5, 0, 3, 3])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "num_weeks=4\n", "y_new = poisson.rvs(mu=0.5*7, size=num_weeks)#per week\n", "y_new" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", " | days | \n", "monastery | \n", "y | \n", "
---|---|---|---|
0 | \n", "1 | \n", "0 | \n", "1 | \n", "
1 | \n", "1 | \n", "0 | \n", "2 | \n", "
2 | \n", "1 | \n", "0 | \n", "1 | \n", "
3 | \n", "1 | \n", "0 | \n", "3 | \n", "
4 | \n", "1 | \n", "0 | \n", "1 | \n", "
5 | \n", "1 | \n", "0 | \n", "1 | \n", "
6 | \n", "1 | \n", "0 | \n", "1 | \n", "
7 | \n", "1 | \n", "0 | \n", "1 | \n", "
8 | \n", "1 | \n", "0 | \n", "1 | \n", "
9 | \n", "1 | \n", "0 | \n", "1 | \n", "
10 | \n", "1 | \n", "0 | \n", "1 | \n", "
11 | \n", "1 | \n", "0 | \n", "0 | \n", "
12 | \n", "1 | \n", "0 | \n", "4 | \n", "
13 | \n", "1 | \n", "0 | \n", "2 | \n", "
14 | \n", "1 | \n", "0 | \n", "4 | \n", "
15 | \n", "1 | \n", "0 | \n", "1 | \n", "
16 | \n", "1 | \n", "0 | \n", "2 | \n", "
17 | \n", "1 | \n", "0 | \n", "1 | \n", "
18 | \n", "1 | \n", "0 | \n", "1 | \n", "
19 | \n", "1 | \n", "0 | \n", "1 | \n", "
20 | \n", "1 | \n", "0 | \n", "0 | \n", "
21 | \n", "1 | \n", "0 | \n", "1 | \n", "
22 | \n", "1 | \n", "0 | \n", "1 | \n", "
23 | \n", "1 | \n", "0 | \n", "1 | \n", "
24 | \n", "1 | \n", "0 | \n", "0 | \n", "
25 | \n", "1 | \n", "0 | \n", "1 | \n", "
26 | \n", "1 | \n", "0 | \n", "2 | \n", "
27 | \n", "1 | \n", "0 | \n", "1 | \n", "
28 | \n", "1 | \n", "0 | \n", "1 | \n", "
29 | \n", "1 | \n", "0 | \n", "3 | \n", "
30 | \n", "7 | \n", "1 | \n", "5 | \n", "
31 | \n", "7 | \n", "1 | \n", "0 | \n", "
32 | \n", "7 | \n", "1 | \n", "3 | \n", "
33 | \n", "7 | \n", "1 | \n", "3 | \n", "