{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dirichlet process mixtures for density estimation\n",
    "Author: [Austin Rochford](https://github.com/AustinRochford/)\n",
    "\n",
    "## Dirichlet processes\n",
    "\n",
    "The [Dirichlet process](https://en.wikipedia.org/wiki/Dirichlet_process) is a flexible probability distribution over the space of distributions.  Most generally, a probability distribution, $P$, on a set $\\Omega$ is a [measure](https://en.wikipedia.org/wiki/Measure_(mathematics%29) that assigns measure one to the entire space ($P(\\Omega) = 1$).  A Dirichlet process $P \\sim \\textrm{DP}(\\alpha, P_0)$ is a measure that has the property that, for every finite [disjoint](https://en.wikipedia.org/wiki/Disjoint_sets) partition $S_1, \\ldots, S_n$ of $\\Omega$,\n",
    "\n",
    "$$(P(S_1), \\ldots, P(S_n)) \\sim \\textrm{Dir}(\\alpha P_0(S_1), \\ldots, \\alpha P_0(S_n)).$$\n",
    "\n",
    "Here $P_0$ is the base probability measure on the space $\\Omega$.  The precision parameter $\\alpha > 0$ controls how close samples from the Dirichlet process are to the base measure, $P_0$.  As $\\alpha \\to \\infty$, samples from the Dirichlet process approach the base measure $P_0$.\n",
    "\n",
    "Dirichlet processes have several properties that make then quite suitable to [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) simulation.\n",
    "\n",
    "1.  The posterior given [i.i.d.](https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables) observations $\\omega_1, \\ldots, \\omega_n$ from a Dirichlet process $P \\sim \\textrm{DP}(\\alpha, P_0)$ is also a Dirichlet process with\n",
    "\n",
    "    $$P\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\textrm{DP}\\left(\\alpha + n, \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}\\right),$$\n",
    "    \n",
    " where $\\delta$ is the [Dirac delta measure](https://en.wikipedia.org/wiki/Dirac_delta_function)\n",
    " \n",
    " $$\\begin{align*}\n",
    "     \\delta_{\\omega}(S)\n",
    "         & = \\begin{cases}\n",
    "                 1 & \\textrm{if } \\omega \\in S \\\\\n",
    "                 0 & \\textrm{if } \\omega \\not \\in S\n",
    "             \\end{cases}\n",
    " \\end{align*}.$$\n",
    "\n",
    "2. The posterior predictive distribution of a new observation is a compromise between the base measure and the observations,\n",
    "\n",
    "    $$\\omega\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}.$$\n",
    "\n",
    " We see that the prior precision $\\alpha$ can naturally be interpreted as a prior sample size.  The form of this posterior predictive distribution also lends itself to Gibbs sampling.\n",
    "    \n",
    "2. Samples, $P \\sim \\textrm{DP}(\\alpha, P_0)$, from a Dirichlet process are discrete with probability one.  That is, there are elements $\\omega_1, \\omega_2, \\ldots$ in $\\Omega$ and weights $w_1, w_2, \\ldots$ with $\\sum_{i = 1}^{\\infty} w_i = 1$ such that\n",
    "\n",
    "    $$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i}.$$\n",
    "\n",
    "3. The [stick-breaking process](https://en.wikipedia.org/wiki/Dirichlet_process#The_stick-breaking_process) gives an explicit construction of the weights $w_i$ and samples $\\omega_i$ above that is straightforward to sample from.  If $\\beta_1, \\beta_2, \\ldots \\sim \\textrm{Beta}(1, \\alpha)$, then $w_i = \\beta_i \\prod_{j = 1}^{j - 1} (1 - \\beta_j)$.  The relationship between this representation and stick breaking may be illustrated as follows:\n",
    "    1. Start with a stick of length one.\n",
    "    2. Break the stick into two portions, the first of proportion $w_1 = \\beta_1$ and the second of proportion $1 - w_1$.\n",
    "    3. Further break the second portion into two portions, the first of proportion $\\beta_2$ and the second of proportion $1 - \\beta_2$.  The length of the first portion of this stick is $\\beta_2 (1 - \\beta_1)$; the length of the second portion is $(1 - \\beta_1) (1 - \\beta_2)$.\n",
    "    4. Continue breaking the second portion from the previous break in this manner forever.  If $\\omega_1, \\omega_2, \\ldots \\sim P_0$, then\n",
    "\n",
    "    $$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i} \\sim \\textrm{DP}(\\alpha, P_0).$$\n",
    "\n",
    "We can use the stick-breaking process above to easily sample from a Dirichlet process in Python.  For this example, $\\alpha = 2$ and the base distribution is $N(0, 1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "from theano import tensor as tt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "blue, *_ = sns.color_palette()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "SEED = 5132290 # from random.org\n",
    "\n",
    "np.random.seed(SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 20\n",
    "K = 30\n",
    "\n",
    "alpha = 2.\n",
    "P0 = sp.stats.norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We draw and plot samples from the stick-breaking process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
    "w = np.empty_like(beta)\n",
    "w[:, 0] = beta[:, 0]\n",
    "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
    "\n",
    "omega = P0.rvs(size=(N, K))\n",
    "\n",
    "x_plot = np.linspace(-3, 3, 200)\n",
    "\n",
    "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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79+/HYrGwcuXKoC9YtemDugbscrl45513OH78OPn5+SxYsCAh9+jmzZux2+0s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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca5d2baf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
    "        label='DP sample CDFs');\n",
    "ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
    "ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
    "\n",
    "ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As stated above, as $\\alpha \\to \\infty$, samples from the Dirichlet process converge to the base distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OHJYvXz7m98btdgOc1UR/ol2wSem3v/1tfVT0bKmoqOCpp54a8ZhAIEBFRQXB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\nfj1nz54lGAxy5swZAoEAkiSRzWbRdZ2ysjIsFguHDx+ms7OT559/Hq/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rDA0N8d577+Ut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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca5a9cf5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (l_ax, r_ax) = plt.subplots(ncols=2, sharex=True, sharey=True, figsize=(16, 6))\n",
    "\n",
    "K = 50\n",
    "alpha = 10.\n",
    "\n",
    "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
    "w = np.empty_like(beta)\n",
    "w[:, 0] = beta[:, 0]\n",
    "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
    "\n",
    "omega = P0.rvs(size=(N, K))\n",
    "\n",
    "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)\n",
    "\n",
    "l_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
    "          label='DP sample CDFs');\n",
    "l_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
    "l_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
    "\n",
    "l_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
    "l_ax.legend(loc=2);\n",
    "\n",
    "K = 200\n",
    "alpha = 50.\n",
    "\n",
    "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
    "w = np.empty_like(beta)\n",
    "w[:, 0] = beta[:, 0]\n",
    "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
    "\n",
    "omega = P0.rvs(size=(N, K))\n",
    "\n",
    "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)\n",
    "\n",
    "r_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n",
    "          label='DP sample CDFs');\n",
    "r_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n",
    "r_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n",
    "\n",
    "r_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n",
    "r_ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dirichlet process mixtures\n",
    "\n",
    "For the task of density estimation, the (almost sure) discreteness of samples from the Dirichlet process is a significant drawback.  This problem can be solved with another level of indirection by using Dirichlet process mixtures for density estimation.  A Dirichlet process mixture uses component densities from a parametric family $\\mathcal{F} = \\{f_{\\theta}\\ |\\ \\theta \\in \\Theta\\}$ and represents the mixture weights as a Dirichlet process.  If $P_0$ is a probability measure on the parameter space $\\Theta$, a Dirichlet process mixture is the hierarchical model\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    x_i\\ |\\ \\theta_i\n",
    "        & \\sim f_{\\theta_i} \\\\\n",
    "    \\theta_1, \\ldots, \\theta_n\n",
    "        & \\sim P \\\\\n",
    "    P\n",
    "        & \\sim \\textrm{DP}(\\alpha, P_0).\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "To illustrate this model, we simulate draws from a Dirichlet process mixture with $\\alpha = 2$, $\\theta \\sim N(0, 1)$, $x\\ |\\ \\theta \\sim N(\\theta, (0.3)^2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 5\n",
    "K = 30\n",
    "\n",
    "alpha = 2\n",
    "P0 = sp.stats.norm\n",
    "f = lambda x, theta: sp.stats.norm.pdf(x, theta, 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n",
    "w = np.empty_like(beta)\n",
    "w[:, 0] = beta[:, 0]\n",
    "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n",
    "\n",
    "theta = P0.rvs(size=(N, K))\n",
    "\n",
    "dpm_pdf_components = f(x_plot[np.newaxis, np.newaxis, :], theta[..., np.newaxis])\n",
    "dpm_pdfs = (w[..., np.newaxis] * dpm_pdf_components).sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HL/MxxcsdzC1EmMpkMnR0dGBiYmLfEZxer8fy8jJisdiOv49Go/jiiy/Q0NCA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\nwUgYY8rAwMDAwGAkjDFlYGBgYGAwkv8fa/wVIqkOAbwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca5a849438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(x_plot, dpm_pdfs.T, c='gray');\n",
    "\n",
    "ax.set_yticklabels([]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now focus on a single mixture and decompose it into its individual (weighted) mixture components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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k5pWNb775BnPnzkVwcDBiYmLqfZVDm8/wsJdeegmjR4/G0KFDcePGDQwZMgQhISF45pln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\nIRH11kL6nqAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca5a86b860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ix = 1\n",
    "\n",
    "ax.plot(x_plot, dpm_pdfs[ix], c='k', label='Density');\n",
    "ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix, 0],\n",
    "        '--', c='k', label='Mixture components (weighted)');\n",
    "ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix].T,\n",
    "        '--', c='k');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from these stochastic processes is fun, but these ideas become truly useful when we fit them to data.  The discreteness of samples and the stick-breaking representation of the Dirichlet process lend themselves nicely to Markov chain Monte Carlo simulation of posterior distributions.  We will perform this sampling using `PyMC3`.\n",
    "\n",
    "Our first example uses a Dirichlet process mixture to estimate the density of waiting times between eruptions of the [Old Faithful](https://en.wikipedia.org/wiki/Old_Faithful) geyser in [Yellowstone National Park](https://en.wikipedia.org/wiki/Yellowstone_National_Park)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "old_faithful_df = pd.read_csv(pm.get_data('old_faithful.csv'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience in specifying the prior, we standardize the waiting time between eruptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "old_faithful_df['std_waiting'] = (old_faithful_df.waiting - old_faithful_df.waiting.mean()) / old_faithful_df.waiting.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>eruptions</th>\n",
       "      <th>waiting</th>\n",
       "      <th>std_waiting</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.600</td>\n",
       "      <td>79</td>\n",
       "      <td>0.596025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.800</td>\n",
       "      <td>54</td>\n",
       "      <td>-1.242890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.333</td>\n",
       "      <td>74</td>\n",
       "      <td>0.228242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.283</td>\n",
       "      <td>62</td>\n",
       "      <td>-0.654437</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.533</td>\n",
       "      <td>85</td>\n",
       "      <td>1.037364</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   eruptions  waiting  std_waiting\n",
       "0      3.600       79     0.596025\n",
       "1      1.800       54    -1.242890\n",
       "2      3.333       74     0.228242\n",
       "3      2.283       62    -0.654437\n",
       "4      4.533       85     1.037364"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_faithful_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PBJ5K13b0sXTbYzPgT/vXDwOeXlWn93/47LaYmoGf93+cwIBttkg3jAzfPPL8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca5abcfc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "n_bins = 20\n",
    "ax.hist(old_faithful_df.std_waiting, bins=n_bins, color=blue, lw=0, alpha=0.5);\n",
    "\n",
    "ax.set_xlabel('Standardized waiting time between eruptions');\n",
    "ax.set_ylabel('Number of eruptions');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observant readers will have noted that we have not been continuing the stick-breaking process indefinitely as indicated by its definition, but rather have been truncating this process after a finite number of breaks.  Obviously, when computing with Dirichlet processes, it is necessary to only store a finite number of its point masses and weights in memory.  This restriction is not terribly onerous, since with a finite number of observations, it seems quite likely that the number of mixture components that contribute non-neglible mass to the mixture will grow slower than the number of samples.  This intuition can be formalized to show that the (expected) number of components that contribute non-negligible mass to the mixture approaches $\\alpha \\log N$, where $N$ is the sample size.\n",
    "\n",
    "There are various clever [Gibbs sampling](https://en.wikipedia.org/wiki/Gibbs_sampling) techniques for Dirichlet processes that allow the number of components stored to grow as needed.  [Stochastic memoization](http://danroy.org/papers/RoyManGooTen-ICMLNPB-2008.pdf) is another powerful technique for simulating Dirichlet processes while only storing finitely many components in memory.  In this introductory example, we take the much less sophistocated approach of simply truncating the Dirichlet process components that are stored after a fixed number, $K$, of components.  [Ohlssen, et al.](http://fisher.osu.edu/~schroeder.9/AMIS900/Ohlssen2006.pdf) provide justification for truncation, showing that $K > 5 \\alpha + 2$ is most likely sufficient to capture almost all of the mixture weight ($\\sum_{i = 1}^{K} w_i > 0.99$).  In practice, we can verify the suitability of our truncated approximation to the Dirichlet process by checking the number of components that contribute non-negligible mass to the mixture.  If, in our simulations, all components contribute non-negligible mass to the mixture, we have truncated the Dirichlet process too early.\n",
    "\n",
    "Our (truncated) Dirichlet process mixture model for the standardized waiting times is\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\alpha\n",
    "        & \\sim \\textrm{Gamma}(1, 1) \\\\\n",
    "    \\beta_1, \\ldots, \\beta_K\n",
    "        & \\sim \\textrm{Beta}(1, \\alpha) \\\\\n",
    "    w_i\n",
    "        & = \\beta_i \\prod_{j = i - 1}^i (1 - \\beta_j) \\\\\n",
    "    \\\\\n",
    "    \\lambda_1, \\ldots, \\lambda_K\n",
    "        & \\sim U(0, 5) \\\\\n",
    "    \\tau_1, \\ldots, \\tau_K\n",
    "        & \\sim \\textrm{Gamma}(1, 1) \\\\\n",
    "    \\mu_i\\ |\\ \\lambda_i, \\tau_i\n",
    "        & \\sim N\\left(0, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n",
    "    \\\\\n",
    "    x\\ |\\ w_i, \\lambda_i, \\tau_i, \\mu_i\n",
    "        & \\sim \\sum_{i = 1}^K w_i\\ N(\\mu_i, (\\lambda_i \\tau_i)^{-1})\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Note that instead of fixing a value of $\\alpha$, as in our previous simulations, we specify a prior on $\\alpha$, so that we may learn its posterior distribution from the observations.\n",
    "\n",
    "We now construct this model using `pymc3`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = old_faithful_df.shape[0]\n",
    "\n",
    "K = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def stick_breaking(beta):\n",
    "    portion_remaining = tt.concatenate([[1], tt.extra_ops.cumprod(1 - beta)[:-1]])\n",
    "\n",
    "    return beta * portion_remaining"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    alpha = pm.Gamma('alpha', 1., 1.)\n",
    "    beta = pm.Beta('beta', 1., alpha, shape=K)\n",
    "    w = pm.Deterministic('w', stick_breaking(beta))\n",
    "\n",
    "    tau = pm.Gamma('tau', 1., 1., shape=K)\n",
    "    lambda_ = pm.Uniform('lambda', 0, 5, shape=K)\n",
    "    mu = pm.Normal('mu', 0, tau=lambda_ * tau, shape=K)\n",
    "    obs = pm.NormalMixture('obs', w, mu, tau=lambda_ * tau,\n",
    "                           observed=old_faithful_df.std_waiting.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We sample from the model 1,000 times using NUTS initialized with ADVI."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1500/1500 [01:55<00:00, 15.42it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(1000, random_seed=SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distribution of $\\alpha$ is highly concentrated between 0.25 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DZsdV2oOOvuOfkDsKpnwk+fYBJlRXR7A2Vly3p1ij/hK5Z1r9/S+iLCJRxQrA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fOWjgQvHSpTqHhBR3RtTmY/v2UXAUMjGbmV3lf+nmw+h6EJtrfEzzGwzuA3DDbXbqZ3yv0Nt0Xb\n6KnrwXZeBKLc2JViqjFJPH2C53vdgX2tb7FB9nBPEz5jfnmJmdpGTe8HzBTKzNT0kIt0sLOpjmMV\nL8DJEuHE26Jtiz7HfDHubL0TQywYshs+wAe6CckNAETMCO3r7qF/8jCMH4F4Kw3JzdTip3f6I97J\nnKQQa6ahcTumrmHqGrXBWnY2dlAoRNnvBS1JhEwe2/ok087znJyay2zK4z2bMI1uNKGhaTq0387m\n8X56R9Ikpj+kLuLHMvz05CawSgX0mQgJvcRwoANH97kRNTGh404ML7BJcEHOKiEETeF6Qn6Dna0t\nnEyXqVgOhZoh3kyH6QmvI29lGCRLW2SIZMnHMbN5zsiKtGxhZ1MNHTUpTo2ajKSLxLwk2XNr/Oq3\nLKn7q4WY96KoDnbt2iXffffd1a6G4hqgbDkcHJrl7ZNjvNb/Dh/NvkdB/wjNP4zQXBcLKTWElUB3\n6mhwTHZWRri9eIx1VoGoE+ak/3YOhfdwInITjhl2/3gMjYChk4oHaK4J0pIIsq42RCKswsWvBaSU\nFD74gOlvf4fMj36ErFQI7dpF/Mknif7cz6nk2CuMEOI9KeWu1a7HhbgS/dLp6TyDRz6gp6uNGaK8\nN5hnR2sNHXXzv7fpXJmK49AQDTCVK9M/mWNzKkbAW5vhOJIf7h+iPupnT/f8QHj2+X8CIHzHHmZf\n/ylHZioUMjmkphEyBFtTcfonc0zuvpd7NtYjhMCRzqKoewspWw4vHhimPupnZ3uC1wZexyrFebCt\nA/+Jl91CPf8KB42RdJGmmJtUdyZfmQtYMFI4zp0baump64GJPgjVIoMJ3joxxejc+i6Trc0x9g7M\nkC7lOJU7SN5yB303NxmI2dPuoEm4SWOlhMe6Hr2gu++x8Szh9BQNTUl3ptpx4MiL7qxA+575dbzn\nO4dVguF9kLrRDcrhj0C06SLanecHe10D7rbOJLomqI9eOGfPyGyR09N5dnXMp544Pnuc3sle7m27\nl5AZYt/4PqJmlK6axQGw3u8fw3Y0MkWbuoifmXyFsF/n9HSBXR21tNScycNl8+ODI+SsWWbL4/xK\ndJZYMATrH8R2bE6mT9IZ7zzv72E5lCybkuV4A22XSn6GFz7K0BgPsbvLNQZtR/L8/vl1Nk01gtPT\neQyxOM+hEIJP7mhe9J3uetdwPJtybgbR9xJmy41Qt+GidX3h+AvUBmvZndoNQL6Sd0PoewaB5Vgc\nGDtKwteKhs4HAzNIKemqi7C99dzrH/nJ06SLFvaWJ7m1K4kQgjcG32Cm5Bo1Pt1HxakgpeSOljuI\n+WKX5bKer+QJGkHyVt41kh2HD0beZbjortfaktxCZ7zznO8dH8+iGSUaIkFCZggpJd8/8jz9k3na\ngrfwCzedG2CN3AS5wz/BchzinvvivoFpKo6kq7mRWrPCYOoBopHIIt0vRdkuY2gGmtAYyAzw4fiH\nc8fSxQoRs4ayTFOxHaLZfrLZNLPB+5iaeQeA33/kd+fKFyu263p4HoP6clluv6SMLMV1RaFsc3wi\nzduDh/lw/BCjhQGmSiOkrVHychSLxdnLTSlpsixSlk3YiiCtZtLl9RwvbGeg0MRCX+nGmJ8tqdjc\na2sqRlddeC4fiOL6w5qaYubZZ5l55rtUBgYQgQDR++8n9tijhPfsUQmOV4C1YmSdzVi6SEMscPGC\nZ1Eo2/gNbdH/kp3NInQdYZpkXnkFWS5zaChNYucONu/q+Vj1q9gOhibOHQyWsq4L23kGidmSxbGx\nLEGfzsbGpdNuFCs2Fdsh4jfmzi+lJFMq8M33X2Fnqod4NEfIDNE72YsmXBfH5nAzW5Ir+6T6Uvlo\nJMNsocKtnZeXr89yrLlZqyvBWLrIz467bmaf6GnEZ+grso55KlcmGjAw9XkD7vBwmlOTOXqa47TV\nurmk9g3McHIyR33Ez6amKH5Tn1svCGDZjhtI4wrUuWAVMDXzkuQ7kS2RCM0nGF5IdmaC0WyF7tb5\nWS/Lsag4FXKVHHXBOqSUVJwKPv3qPMzNlDOumyawu3k3tYHl/f5GciPkynnaoh2LZuiWxLHh4D94\nbZH4dA2aboD6S4/gazs2vdO9mJpJ33Tf3P5EIMGO+h28PfI2uowwNZXCMEv0pGJ01K5coDNlZCkU\nS5Cv5BnKDjGUG2I4O8xQpp/h8YMMzpygvzzNjJi/HxKOpEOEaTYbiGjtZMrdHJpaz+FxYy4yVtin\ns7U5Rk9znG0tcba3xOmuD2Po1ReNUnF+pJQU9u5l9rnnyLzwIvbsLCIQILxnD5H77iWyZw9mi8q7\ndTVYDSNLCPEI8GeADvyllPKPL1S+mvolp1hEVirYU1OYbW1VGTl3IReacVNcGrmSxWi6SNdccIrV\nQ0p5jsFUsZ1Fxpji0hjNjVKwCnTEO67eRWwLrIK7HlJokOy+rNMVrAKv9rv574QQ3N9+P/4F4f1H\n00XqIv4ljduryTVhZF2soxLuHfRnwKO4qyI/L6V8/0LnrKbOTFFdSCmZTA/Qd+In9A29Rd/0UY4W\nJziq2RQWDESabUm39NEsI8TtBHa+jonpODNWiAwhSlqIxvo6uhvjrG+M0dkQpzUZIRrwu08G5+45\neebCiz9rphucwwyDppEupzmdOc3pzGkGs4PMlmbJlDNkvPwdhjAwNIOYL0YymCQZTNIQaqA53ExT\nuOmqPRlbq8hymfy775J55VUyr7yMNeSuEzDb2gjvvo3gTTsJbOvB39WFMNSy18tlpY0sIYQOHAEe\nAk4D7wC/JKU8dL7vqH5JoVAorg5Fq8hkcZKWyLXzIHPVjazldFRCiEdxw+k+CtwG/JmU8rYLnVd1\nZoqVxqkUGBx8i6ODb9I3eZCj2dMcrcxyUlawvYcnhpS0WBatFct9tyxaKhb1tk3ccYjZDnHHYaFH\nsgTyQpDVNGZ0jWHdYMjQGTHc99OmyYBpkD7rSbOBICZMIrofhIYtoCIls3aBklPhbOr8NTQH6kmF\n6kkF60kFG2gO1VPnTxAww/gDCcxADEtoVJwKlmPNuTKceVmORcWusKl2E82R5nOusVaRUlI6epT8\nW2+Te+tN8m+/g5N214yIQIDApk34urrwdXXi7+zESKUw6usxkslVTWK+FNKycPJ5nGwWJ5fDzmZx\ncnmcXG5unyyXkJUKsmJ57xWk5W1bFbAspHMm6blD4IYbSH7+85dVr1Uwsm4H/khK+bD3+Q8ApJT/\n7XzfUf2SQqFQrB2W2y9dzcestwJ9UsrjXoW+AzwBLHwa+ATwN14OkzeFEDVCiJSUcvjc0ykUq4Nm\nBmnruJe2jnu5f8H+sl3mxOwJjk4cpG/iIAOZAU7nhjhQGGfWyi99LnlmfQFIIc9Oj+GV0YjZfuqc\nANvLBilb0GpL2q0yHeUCSStLyJ4g4OQWfU8COSGY1HVGDZ1hz1gbNrIMG8P0Ggav6gbly5hW/6P6\nO/nXDbdAIA7+OPhCIHQ3SqOmz287NjgV13XAqbiLys9s25VFx6RdQQoN58bPYkt38bojJY50FzTL\nBdsV28GyJRXHmdsue++W7cxtV2yHiuPua4wFuGP91fHVFkIQ2LiRwMaN1H72M0jHoXzyJMWDByke\nOEDxcC+5n/6U2X/4h8Vf1DSMZBKjvh69Jo4IhdBCIbSg9+69hGkiTGNRsnQMwzXQpEQ6DjgSHHvO\nuJGOjSwUXbewYgGnUMQpFub2OYU8Ml/AzrmGk5NzDStZLF5a403Tq5+JMAz3XdfdugoBQqAnqzIZ\neAswsODzadyHgIsQQnwJ+BJAe3v7ytRMoVAoFFXD1TSyltNRLVWmBVBGluKax6f72FS7iU21m2Dj\nk4uOZcoZBrODTBWmmC3PMluaZaY0Q8kuIaXEchyKFXBsP5Wyn3LZj12pQVYSFIoBMrZNulThWNnm\nowXGheVIbMdBAho2EbJEyRGTOaJk0R0LYUlEyUEgETgI6RAEOh2HThwsvUTRzFPRS6BVMLUShigR\nlDZBKoSkRZgyEVkmRpG4LBKjSI0s0nbqO+B864rKUQAZGeSG716dAfkDmxuumpF1NkLT8Hd14e/q\nIv7zPz+3385kKJ88SWVkBGt83H2NjWGNj+OkMzgTk+4sUj6PUyggC4ULXOVSKiQQwSBaIIAWCLjb\n3mezoREtHEaLRNz3cAh9bjt81jHvFQi4LpCGcUUWmFczUsqvA18HdyZrlaujUCgUimuMqlgwsPCJ\nIZAVQnx0nqJ1wMTK1Oqqo9pybXI9tQWumfakgccv9yRLtuVp4OkvXO6pV5xrRC9XhMtty7orVZFl\nMggsTFTTynw63yV57733JoQQpy7zuteTzq8kSi7nomRyLkomS6Pkci5XQibL6peuppG1nI5qWZ3Z\nwieGF0II8e61Hup3uai2XJtcT22B66s9qi3XJlXYlneADUKITtz+6Cngly/0BSll/eVetArltCIo\nuZyLksm5KJksjZLLuaykTK5mLMy5jkoI4cPtqJ47q8xzwOeEy25gVq3HUigUCsVqIaW0gN8Gfgwc\nBp6RUh5c3VopFAqFotq4ajNZUkpLCHGmo9KBp6WUB4UQv+kd/wvgBdzIgn24Idyrz6lHoVAoFNcV\nUsoXcPsnhUKhUCg+Fld1TdZSHZVnXJ3ZlsCXr+AlL+pSWEWotlybXE9tgeurPaot1ybXU1uuJkpO\nS6Pkci5KJueiZLI0Si7nsmIyuarJiBUKhUKhUCgUCoVirXE112QpFAqFQqFQKBQKxZqj6owsIcQj\nQoiPhBB9QoivLHFcCCH+3Du+XwixczXquVyW0Z57hRCzQoi93us/r0Y9L4YQ4mkhxJgQ4sB5jleb\nXi7WnmrRS5sQ4lUhxCEhxEEhxO8uUaZqdLPM9lSLbgJCiLeFEPu8tvyXJcpUhW6W2Zaq0MtqcLF+\n4HrlfPezEKJWCPGSEOKo955Y8J0/8OT0kRDi4dWr/dVFCKELIT4QQjzvfVYyEaJGCPE9IUSvEOKw\nEOL2tS4XIcR/8O6dA0KIb3v/xWtKJkuN1z6ODIQQNwshPvSO/bkQVyAZpJSyal64ATSOAV2AD9gH\nbD2rzKPAi7g5TncDb612vS+zPfcCz692XZfRlruBncCB8xyvGr0ssz3VopcUsNPbjgJHqvyeWU57\nqkU3Aoh42ybwFrC7GnWzzLZUhV5WQXYX7Qeu19f57mfgvwNf8fZ/BfgTb3urJx8/0OnJTV/tdlwl\n2fxH4Ftn7hklEwnwTeDXvW0fULOW5QK0ACeAoPf5GeDza00mLDFe+zgyAN72+lnh9bufuNy6VdtM\n1q1An5TyuJSyDHwHeOKsMk8AfyNd3gRqhBCpla7oMllOe6oCKeX/A6YuUKSa9LKc9lQFUsphKeX7\n3nYGNyR1y1nFqkY3y2xPVeDJO+t9NL3X2Ytkq0I3y2yLYmmum37gUrnA/fwE7oAa7/1T3vYTwHek\nlCUp5QncyMS3rmytrz5CiFbgMeAvF+xe6zKJ4w6m/wpASlmWUs6wxuWCG8AuKIQwgBAwxBqTyXnG\na5ckA69fjUkp35SuxfU3C77zsak2I6sFGFjw+TTnDrCWU+ZaYbl13eO5Cr0ohOhZmapdcapJL8ul\nqvQihOgAbsKdZVhIVermAu2BKtGN5xK0FxgDXpJSVq1ultEWqBK9rDBVo+OryVn3c6Ocz5k5AjR6\n22tFVv8L+D3AWbBvrcukExgHvuG5Uf6lECLMGpaLlHIQ+B9APzCMm2v2n1nDMlnApcqgxds+e/9l\nUW1G1lrkfaBdSnkD8L+Bf1zl+ihcqkovQogI8Czw76WU6dWuz+VykfZUjW6klLaU8kagFfdp2rbV\nrtPHZRltqRq9KFaWC93P3lPlNTMrKoR4HBiTUr53vjJrTSYeBq5L2P+RUt4E5HDdwOZYa3Lx1hk9\ngWuANgNhIcRnFpZZazJZitWUQbUZWYNA24LPrd6+Sy1zrXDRukop02fccKSbd8wUQtStXBWvGNWk\nl4tSTXoRQpi4A5i/l1J+f4kiVaWbi7WnmnRzBs/t5VXgkbMOVZVu4PxtqUa9rGEcbwUAAAKNSURB\nVBBVp+MryXnu59EzbrHe+5i3fy3I6g7gk0KIk7iuo/cLIf6OtS0TcGcWTi+YIf8ertG1luXyIHBC\nSjkupawA3wf2sLZlcoZLlcGgt332/sui2oysd4ANQohOIYQPeAp47qwyzwGfEy67cadPh88+0TXC\nRdsjhGg6E+FECHErrs4mV7yml0816eWiVItevDr+FXBYSvk/z1OsanSznPZUkW7qhRA13nYQeAjo\nPatYVehmOW2pFr2sAsvp165LLnA/Pwf8qrf9q8APFux/SgjhF0J0AhtwF6tfN0gp/0BK2Sql7MD9\nLbwipfwMa1gmAFLKEWBACLHJ2/UAcIi1LZd+YLcQIuTdSw/grmtcyzI5wyXJwOtX00KI3Z4sP7fg\nOx8b43JPsJJIKS0hxG8DP8aNyPS0lPKgEOI3veN/AbyAG5GrD8gDX1it+l6MZbbnF4DfEkJYQAF4\nypv6vKYQQnwbN3pYnRDiNPBV3MXvVacXWFZ7qkIvuE9FPwt86K2XAfhDoB2qUjfLaU+16CYFfFMI\noeMaHM9IKZ+v0v+z5bSlWvSyopyvH1jlaq0U57uf/xh4Rgjxa8Ap4N8AeP3jM7iDawv4spTSXvlq\nrwpKJvA7wN97DyOO4/4faqxRuUgp3xJCfA/XFdsCPgC+DkRYQzI5z3jt49wv/w74ayCIG13wxcuu\nm+rjFAqFQqFQKBQKheLKUW3uggqFQqFQKBQKhUJxTaOMLIVCoVAoFAqFQqG4gigjS6FQKBQKhUKh\nUCiuIMrIUigUCoVCoVAoFIoriDKyFAqFQqFQKBQKheIKoowshUKhUCgUCoVCobiCKCNLoVAoFAqF\nQqFQKK4gyshSKBQKhUKhUCgUiivI/we5L5mCJGk/qgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca1ddf7f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['alpha']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify that truncation is not biasing our results, we plot the posterior expected mixture weight of each component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6DmuSJEljatNF/9fAx5O8kcFEM0cymBNekiRNqDZd9JckOQn4JHAj8Niq+lbnlUmSpJG1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\nudVNXlwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca1dcf5278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "plot_w = np.arange(K) + 1\n",
    "\n",
    "ax.bar(plot_w - 0.5, trace['w'].mean(axis=0), width=1., lw=0);\n",
    "\n",
    "ax.set_xlim(0.5, K);\n",
    "ax.set_xlabel('Component');\n",
    "\n",
    "ax.set_ylabel('Posterior expected mixture weight');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that only three mixture components have appreciable posterior expected weights, so we conclude that truncating the Dirichlet process to forty components has not appreciably affected our estimates.\n",
    "\n",
    "We now compute and plot our posterior density estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_pdf_contribs = sp.stats.norm.pdf(np.atleast_3d(x_plot),\n",
    "                                      trace['mu'][:, np.newaxis, :],\n",
    "                                      1. / np.sqrt(trace['lambda'] * trace['tau'])[:, np.newaxis, :])\n",
    "post_pdfs = (trace['w'][:, np.newaxis, :] * post_pdf_contribs).sum(axis=-1)\n",
    "\n",
    "post_pdf_low, post_pdf_high = np.percentile(post_pdfs, [2.5, 97.5], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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57W9/C8C//du/zfkelrvF43333cf999/P9u3bKSgoOOf1xcLr6OigpqYG0zSB+PZKJBJJ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\nCP8LlRbLQSkNUTIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca1dbde780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "n_bins = 20\n",
    "ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, normed=True,\n",
    "        color=blue, lw=0, alpha=0.5);\n",
    "\n",
    "ax.fill_between(x_plot, post_pdf_low, post_pdf_high,\n",
    "                color='gray', alpha=0.45);\n",
    "ax.plot(x_plot, post_pdfs[0],\n",
    "        c='gray', label='Posterior sample densities');\n",
    "ax.plot(x_plot, post_pdfs[::100].T, c='gray');\n",
    "ax.plot(x_plot, post_pdfs.mean(axis=0),\n",
    "        c='k', label='Posterior expected density');\n",
    "\n",
    "ax.set_xlabel('Standardized waiting time between eruptions');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "ax.set_ylabel('Density');\n",
    "\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As above, we can decompose this density estimate into its (weighted) mixture components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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i8tSFDoAQ0rPUVt1FWdEtDBo3XSHzrT+WqZB5rOydEXP8H1RXlEHPyEQhcxKi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\ngiCoEf4HUzvYg5VIAvQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca17f84a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "n_bins = 20\n",
    "ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, normed=True,\n",
    "        color=blue, lw=0, alpha=0.5);\n",
    "\n",
    "ax.plot(x_plot, post_pdfs.mean(axis=0),\n",
    "        c='k', label='Posterior expected density');\n",
    "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0)[:, 0],\n",
    "        '--', c='k', label='Posterior expected mixture\\ncomponents\\n(weighted)');\n",
    "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0),\n",
    "        '--', c='k');\n",
    "\n",
    "ax.set_xlabel('Standardized waiting time between eruptions');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "ax.set_ylabel('Density');\n",
    "\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Dirichlet process mixture model is incredibly flexible in terms of the family of parametric component distributions $\\{f_{\\theta}\\ |\\ f_{\\theta} \\in \\Theta\\}$.  We illustrate this flexibility below by using Poisson component distributions to estimate the density of sunspots per year. This dataset can be downloaded from http://www.sidc.be/silso/datafiles. Source: WDC-SILSO, Royal Observatory of Belgium, Brussels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sunspot_df = pd.read_csv(pm.get_data('sunspot.csv'), sep=';', names=['time', 'sunspot.year'], usecols=[0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>sunspot.year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1700.5</td>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1701.5</td>\n",
       "      <td>18.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1702.5</td>\n",
       "      <td>26.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1703.5</td>\n",
       "      <td>38.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1704.5</td>\n",
       "      <td>60.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     time  sunspot.year\n",
       "0  1700.5           8.3\n",
       "1  1701.5          18.3\n",
       "2  1702.5          26.7\n",
       "3  1703.5          38.3\n",
       "4  1704.5          60.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sunspot_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, the model is\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\alpha\n",
    "        & \\sim \\textrm{Gamma}(1, 1) \\\\\n",
    "    \\beta_1, \\ldots, \\beta_K\n",
    "        & \\sim \\textrm{Beta}(1, \\alpha) \\\\\n",
    "    w_i\n",
    "        & = \\beta_i \\prod_{j = i - 1}^i (1 - \\beta_j) \\\\\n",
    "    \\\\\n",
    "    \\lambda_i, \\ldots, \\lambda_K\n",
    "        & \\sim U(0, 300)\n",
    "    \\\\\n",
    "    x\\ |\\ w_i, \\lambda_i\n",
    "        & \\sim \\sum_{i = 1}^K w_i\\ \\textrm{Poisson}(\\lambda_i).\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "K = 50\n",
    "N = sunspot_df.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    alpha = pm.Gamma('alpha', 1., 1.)\n",
    "    beta = pm.Beta('beta', 1, alpha, shape=K)\n",
    "    w = pm.Deterministic('w', stick_breaking(beta))\n",
    "    \n",
    "    mu = pm.Uniform('mu', 0., 300., shape=K)\n",
    "    obs = pm.Mixture('obs', w, pm.Poisson.dist(mu), observed=sunspot_df['sunspot.year'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1500/1500 [00:12<00:00, 127.34it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(1000, step=step, random_seed=SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the sunspot model, the posterior distribution of $\\alpha$ is concentrated between 0.6 and 1.2, indicating that we should expect more components to contribute non-negligible amounts to the mixture than for the Old Faithful waiting time model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tZcXwsQyGPr2Pem89ASNAd6Cb2q7ahOOyij7Hu26xxmdN9K3JcbzJdyLvZp4n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\nLi4uLi4uLi4uZ5H/DxT5IWkB17pUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feacc3e2470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['alpha']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, we see that between ten and fifteen mixture components have appreciable posterior expected weight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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z7TnOBr8kST3ipX5JknrE4JckqUcMfkmSesTglySpRwx+SZJ6xOCXdlFJnp7k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\nI1g7MQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feacc0f6828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "plot_w = np.arange(K) + 1\n",
    "\n",
    "ax.bar(plot_w - 0.5, trace['w'].mean(axis=0), width=1., lw=0);\n",
    "\n",
    "ax.set_xlim(0.5, K);\n",
    "ax.set_xlabel('Component');\n",
    "\n",
    "ax.set_ylabel('Posterior expected mixture weight');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now calculate and plot the fitted density estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_plot = np.arange(250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_pmf_contribs = sp.stats.poisson.pmf(np.atleast_3d(x_plot),\n",
    "                                         trace['mu'][:, np.newaxis, :])\n",
    "post_pmfs = (trace['w'][:, np.newaxis, :] * post_pmf_contribs).sum(axis=-1)\n",
    "\n",
    "post_pmf_low, post_pmf_high = np.percentile(post_pmfs, [2.5, 97.5], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RlSaRVXtU2+WXX466ujrcddddo37eE+GCGcF26NAhtLW1IRaLAXC+uWUyGSxfvhx79uzB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1KpeFmYaZqcPn2aU6dOecIM4HrFZjIZTp06xdzcHI899pg3e2qzbTFH9XwTapyMXk/ckUgi1hYK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\najQajUZzj+hkqtFoNBrNPfL/AV/fg2fowCU4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feacc0f6e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.hist(sunspot_df['sunspot.year'].values, bins=40, normed=True, lw=0, alpha=0.75);\n",
    "\n",
    "ax.fill_between(x_plot, post_pmf_low, post_pmf_high,\n",
    "                 color='gray', alpha=0.45)\n",
    "ax.plot(x_plot, post_pmfs[0],\n",
    "        c='gray', label='Posterior sample densities');\n",
    "ax.plot(x_plot, post_pmfs[::200].T, c='gray');\n",
    "ax.plot(x_plot, post_pmfs.mean(axis=0),\n",
    "        c='k', label='Posterior expected density');\n",
    "\n",
    "ax.set_xlabel('Yearly sunspot count');\n",
    "ax.set_yticklabels([]);\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we can decompose the posterior expected density into weighted mixture densities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4gg5TS41MbaSOUCnqwDQas9+LEEJI9yPoMLXUyFRi7wAAUDXUm/1ehBBCuh/B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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feacc2d2358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.hist(sunspot_df['sunspot.year'].values, bins=40, normed=True, lw=0, alpha=0.75);\n",
    "ax.plot(x_plot, post_pmfs.mean(axis=0),\n",
    "        c='k', label='Posterior expected density');\n",
    "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0)[:, 0],\n",
    "        '--', c='k', label='Posterior expected\\nmixture components\\n(weighted)');\n",
    "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0),\n",
    "        '--', c='k');\n",
    "\n",
    "ax.set_xlabel('Yearly sunspot count');\n",
    "ax.set_yticklabels([]);\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An earlier version of this example first appeared [here](http://austinrochford.com/posts/2016-02-25-density-estimation-dpm.html)."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
