{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Mixtures and MCMC\n",
"\n",
"##### Keywords: supervised learning, semi-supervised learning, unsupervised learning, mixture model, gaussian mixture model, pymc3, label-switching, identifiability, normal distribution, pymc3 potentials\n",
"\n",
"We now do a study of learning mixture models with MCMC. We have already done this in the case of the Zero-Inflated Poisson Model, and will stick to Gaussian Mixture models for now."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"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\n",
"import theano.tensor as tt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mixture of 2 Gaussians, the old faithful data\n",
"\n",
"We start by considering waiting times from the Old-Faithful Geyser at Yellowstone National Park."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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