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Density Estimation with Dirichlet Process Mixtures using PyMC3
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"---\n",
"title: Density Estimation with Dirichlet Process Mixtures using PyMC3\n",
"tags: PyMC3, Dirichlet Processes, Bayesian Nonparametric Statistics, Bayesian Statistics, Nonparametric Statistics\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I have been intrigued by the flexibility of [nonparametric statistics](https://en.wikipedia.org/wiki/Nonparametric_statistics) for many years. As I have developed an understanding and appreciation of Bayesian modeling both personally and professionally over the last two or three years, I naturally developed an interest in Bayesian nonparametric statistics. I am pleased to begin a planned series of posts on Bayesian nonparametrics with this post on Dirichlet process mixtures for density estimation.\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": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/maikel/.local/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
" warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
]
}
],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import division"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Couldn't import dot_parser, loading of dot files will not be possible.\n"
]
}
],
"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 statsmodels.datasets import get_rdataset\n",
"from theano import tensor as T"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"blue = sns.color_palette()[0]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"np.random.seed(462233) # from random.org"
]
},
{
"cell_type": "code",
"execution_count": 6,
"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": false
},
"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": {
"collapsed": false
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"outputs": [
{
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vo7u7C4DsOZg8eQrOPHMZJk2ahLw8B84//xLk5dH4+9//gYKC7F8cPB4PJElCUVExAKjR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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4127fc81d0>"
]
},
"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": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Xfea0zvHJJ//IoUNt3Hjj/z2m8X/60+M8/PD/4nA40DSNj37041x88aVs376N2267lfr6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\n5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0QijQwNDdDS0oqmafj9forFIl/60tO43W7e//4PsHr1Wsf0LxQKMzU1gWHojk+DHR31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\n5CylUpHu7tXs3n0zp0+fYHZ2muPHD5NMzmPbNrquI0kSknQpT9QwTGzbwv/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MYRg4HE5u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"text/plain": [
"<matplotlib.figure.Figure at 0x7f4127fc8e90>"
]
},
"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": false
},
"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": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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V3G4PotFwT8+rsg8bFKqkHyhUT5lkMg6e59u+2kspGsdqTtcS8IMHD8BxHGZm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\nKhERkUj+An3JHL+6UCM5AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4127ea3d90>"
]
},
"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": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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5XE6L9vsZZkpfVUVKDDc3NwBARgYtqyHCQ0lVYJjE019GqgBVbPZX8fGxMDQ0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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4122a8c110>"
]
},
"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`](https://pymc-devs.github.io/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": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"old_faithful_df = get_rdataset('faithful', cache=True).data[['waiting']]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For convenience in specifying the prior, we standardize the waiting time between eruptions."
]
},
{
"cell_type": "code",
"execution_count": 15,
"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": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>waiting</th>\n",
" <th>std_waiting</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>79</td>\n",
" <td>0.596025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>54</td>\n",
" <td>-1.242890</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>74</td>\n",
" <td>0.228242</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>62</td>\n",
" <td>-0.654437</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>85</td>\n",
" <td>1.037364</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" waiting std_waiting\n",
"0 79 0.596025\n",
"1 54 -1.242890\n",
"2 74 0.228242\n",
"3 62 -0.654437\n",
"4 85 1.037364"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"old_faithful_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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5HI4itzNNLAAANUuJoR4XF6dNmzbp1KlT+vbbb4vcTqgDAFCzlBjqPXr0UI8ePZSQkKCo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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4122910850>"
]
},
"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 post, we take the much less sophistocated approach of simple truncating the Dirichlet process components that are stored after a fixed number, $K$, of components. Importantly, this approach is compatible with some of `pymc3`'s (current) technical limitations. [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 weights ($\\sum_{i = 1}^{K} w_i > 0.99$). We can practically 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 our Dirichlet process too early.\n",
"\n",
"Our Dirichlet process mixture model for the standardized waiting times is\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" x_i\\ |\\ \\mu_i, \\lambda_i, \\tau_i\n",
" & \\sim N\\left(\\mu, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n",
" \\mu_i\\ |\\ \\lambda_i, \\tau_i\n",
" & \\sim N\\left(0, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n",
" (\\lambda_1, \\tau_1), (\\lambda_2, \\tau_2), \\ldots\n",
" & \\sim P \\\\\n",
" P\n",
" & \\sim \\textrm{DP}(\\alpha, U(0, 5) \\times \\textrm{Gamma}(1, 1)) \\\\\n",
" \\alpha\n",
" & \\sim \\textrm{Gamma}(1, 1).\n",
"\\end{align*}\n",
"$$\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. This model is therefore actually a mixture of Dirichlet process mixtures, since each fixed value of $\\alpha$ results in a Dirichlet process mixture.\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": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to alpha and added transformed alpha_log_ to model.\n",
"Applied logodds-transform to beta and added transformed beta_logodds_ to model.\n",
"Applied log-transform to tau and added transformed tau_log_ to model.\n",
"Applied interval-transform to lambda and added transformed lambda_interval_ to model.\n"
]
}
],
"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', beta * T.concatenate([[1], T.extra_ops.cumprod(1 - beta)[:-1]]))\n",
" component = pm.Categorical('component', w, shape=N)\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, lambda_ * tau, shape=K)\n",
" obs = pm.Normal('obs', mu[component], lambda_[component] * tau[component],\n",
" observed=old_faithful_df.std_waiting.values)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We sample from the posterior distribution 20,000 times, burn the first 10,000 samples, and thin to every tenth sample."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 20000 of 20000 complete in 183.1 sec"
]
}
],
"source": [
"with model:\n",
" step1 = pm.Metropolis(vars=[alpha, beta, w, lambda_, tau, mu, obs])\n",
" step2 = pm.ElemwiseCategorical([component], np.arange(K))\n",
" \n",
" trace_ = pm.sample(20000, [step1, step2])\n",
"\n",
"trace = trace_[10000::10]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The posterior distribution of $\\alpha$ is concentrated between 0.4 and 1.75."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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V45vX107rvXSEkOS+973vJfyeeOSRR8axNeE8EXtCLQ5/1r08tb9jE6/dTMh+\nKr1Whp4BZ/A2x/Nwe3wYsLlgyJFHHWt1+utLCQXsmEelBTFSDwaWMYYmuhgvTR3+vgYFVGQqaOm0\nwOb0oLnDgpoZsQcn4pVMmFWsgUCQoNTC0Gc/MMBitrkpoBpHKQVUAoEg7PacOXNw9913Z6RB083B\nU53geB6rFhZluylZc92KGTjd0o8jZ7oxu0SLzy8pyXaTCCET2BVXXDHm52hoaMBdd92F2267DV/9\n6lfD7jt48CB27doFgUCA1atXY/v27WN+vcCSvnip0gUJAsR+iysYYMmlIihlIrg9Pjhcw9n9PN5A\nQDW2dsbqsE2WxEE8z+Nilw25GmnCkXxCsiUwoJKozly8Jb7JBhU+a+rFotnTMxfBRJBSQBXvYsIN\nbYxjaePoqPA8jw+Od0AoYLG8Nj/bzckaAcvi3zbNw4//cAR73j2HikI1Zhaps90sQsgE9aUvfSn4\n74aGBpw/fx4Mw6CqqgqVlckT3KRSdP6ZZ56BwWDA1q1bsXHjxpSeN5FgJylO4BS696lUrwyboQrd\nhM7xPLw+Dieb+8KPH3p+3xiDH5Eg+nru843fXox4AWEqmYAHbG509NnR0WfH8pqCDLQusc4+ByQi\nwZQvfUJGx+nyYmCoDlyifZFjKep97FwPFgztgSTjK6VIaMGCBaitrY36r6amBrW1tZlu45R1vs2M\nzj4HlszRB7MqTVc5KgnuvL4WHMfjt3/5LGHtFUIIAYCf//zn+Na3voV3330X+/fvxze/+U089thj\nSY/LVNH5HGX8jjQXYw9VqEBGO5VcDLFIgKoSbczH8TzwydluuCP2anl9PFp7bDCP8bszVkcvdIbK\n6+PAcf4liKPl8vjiLk2M15X0Jgjq7IMenGjszfp140KnJW7CADJyXh8Hx6An+QMnifqW4fdGvOQ1\nQOxBBQbxBxPYiC+VQXfsz2b3gBOf1HdP60LeLrcvYzPuKc1Q3XXXXZg1axZWrFgBhmHw3nvvobm5\nGXfddVdGGjVdfHDcX3tq1TRLRhFP7QwdNq2qwF8+aMZ/v/IZvrflEoiEguQHEkKmpcOHD+Nvf/sb\nRCL/gJTb7caWLVuSLkkfadH5VOsuikXD31c6lRR9Q0V2Q8XrFuWoJKgq0UKj9Lcr3mxMvBkoh8uL\n1p6xF0qP1ZkL7YD4fDxOXuzDoNuLS6sNI05tPmBzof5iP0r1ShTrw5OIeLw+GLtj5473+ri4WXBP\nNfeB4/mgIfhHAAAgAElEQVS49brGA2VUS79zxgGYHW7Mn5k7JQad3SGBTJzM52jptKKjz5+QQikV\ngeMBh8sTVbMu9LtFJGDhCnnvd/cPz26Hzuw2tfuLA/dbB2PuxZwOjp3vAcswWDY3/avCUgqoDh06\nhH/7t38L3r7mmmtw6623UkA1Bk6XF3X13cjTSFFdTunCA669YgbaTXYcOdONZ/bW487raihJBSEk\npry8vLBCviKRCCUlY9uDOZai8/l6FZxe//ErFpfgYqcFze3hCZz0ehVU8tjBnF4/nJhIKBGhYyA6\nIINQALUqei9Fn90T8+epMuTI0d3vgNPLgxULkauRQa3yd8DkCjF8jD+YUWvlEHfZIJaIoNMpw4LI\nVATa6eaZsN8XAM4Z++P+Ds3ddiyaY4BaEX3ulEZ/OxUyEexDWQIjnzvTOI6HWmVJy2tnqu0Wuxu9\nZicqiiZHKvrTRjPUKhnEUjH0+ugMnuP9Nx4rtdocHLAQCKLf/8Dw7wwA1TN0yFFJcKqpFzOLNdAM\nzYBrc+Q4eKIjeEyeVgZTaBIbIPgcPTYPaoeWAAY+zzk6BfR52c+IOt78n1H/ecnEeyelgGpgYADv\nv/8+Lr30UgBAXV0d+vtpWnssDp3qhMvjwzULyqKma6czlmFwxxfmos/iwuHTXdBrpbhhNRX9JYRE\ny8nJwY033ojly5eD53nU1dWhtLQ0mJl2x44dI37OsRSdt1mdsFj9HZueHits1sHg7YC+XhsG7clH\n2802V9SxAGL+LFR+jhxdMQqCJjOrQInzQ8998J+tWFKlD76W2+XBoNufAOP9T1qCx5hM1hGtIsjL\nU6K71z+LxnlF6OkZno1yuryobzIlPP70+W5UxggGgu0c9GDQ429n6HOPB47jw/72o6XXqzLW9kOn\nOwEAvMcbN6ifSALns6tbAFHEYtBMnqdYfBw35kLTFstgcK8kyzAwtvWjzWRHeb4KwqG9i6Gf74F+\nO1ifDyU6GdxON3pCsmxWl6hx5EwXAEAjFcT8XlCrZGgy9sGgEoc9d1+vCKJpOKPq9XExP6PpCq5S\nenf89Kc/xe9+9zusXLkSK1euxG9/+1vs3LkzLQ2Yjniex3vH2iBgGayextn94hEJBfjWjfNh0Mrw\nxsEWvH7wQrabRAiZgEpLS7Fu3TrI5XIoFAqsXbsWlZWVEAgEUdlpUxVadN7r9eLAgQNYuXJlSsdG\nztaIYy5RS20ATSUXQ6+RxUwSkUjkAN2SqvBgcFaRJma65shZuE8bhoPKeEkpRtonC91sL4zonAbS\noyeSaB8J4O/0ZstIii9n2xhyHoyrwHskshTBePP6ONTVd6PBODCq4wfd3qh9OxzP48yFfvQMOP17\nIj0+2CP2iyWaGWcZBgtm5mFWgnpWAZGfi8n0Xk2F0+XFodOd6E4ykJTpZbkpzVAtWLAAzz///IiW\nPpD4GtssaO2xY2m1ITiFS8Kp5WL855ZL8Mjzx/DqP5rA8zyuX1GR7WYRQiaQb33rW6M6LlNF5zUK\nMQp1Ckgl/sAq1p6fVC+hLMugsliDMy39MA9lBktFjkoS3IPhb8NwkDejQI08rSyseG4q7fL4Yu9N\nGnFAFXJAZPDJp9DLT3bustnxnmJ91IzgOB49A07kaqTBGRnA39F1unyQS8O7pAIBAy+XOIHDeAgk\neYi1JzIZr4/DP8+bIBVHd7dD9z2dazNH7Y+MV2IhQC4VQi4VwpygKDgAuD0cWGbqvkFNZv/fpbnD\nGnNvmGPQA4ZhUv7uHa2UAqr6+nrce++9cDgceOutt/DEE09gxYoVWLhwYWZbN0W9d6wNAPC5S2h2\nKhG9Vobvf2URfv78Mfzlg2a4PD7cuKaSlkgSQgAAv/vd7/D000/DavUv3wgM+p05cybhcZkqOs8w\nTFiB9ljL4Ub89ZWkp16gk2PA6sagxwupSAiVPP5ywsAIbWhHbUmVAQyDsE3vqYo30u31cRh0+8Jq\nQXl9XNjMSOR5YEbx+tnQb3VBKGBiLJmbuh3WsbA5PTDbXCjWK9FusqPVZIPF4cbskCyWxm4b2nvt\nqCrRQqeWBn8enJGcxKfW7fEHSYEls/G43L6oz2CqExipDDScvjBcZmGyzFAGOF1eOF3esPdGLHzE\nG6W5w4Je82Cw7MSCmXkZayOQ4pK/+++/Hw899FBwHfnVV1+Nhx9+OKMNm6psTg/q6ruRr5NTMooU\n5Gll+P5XF8GgleHNQxfx3y+dgGMw8RcTIWR6+Otf/4pXX30VJ0+exMmTJ3Hq1CmcPHky280KEsYo\nkjvSVR6x+j55GhnmVeRi2dx8zChQBwOXZKtIhkthDT9GJGQhFLBpHag60diLk829aDPZ0dpjQ1O7\nBZ+c7YYz5Ls7MhYb6e4Um9ODjl7/TFyipYCtPbZRL9WKxPE8zhr7cSqkc9pvdeGzpl54vJOsl5oh\n/VYXmkOWb55s7oWxxx9EBWZ67INecByPjl472nps6Oj1L9Xqt0XMxIb8WTt67Tja0DOhikz7uORp\n3VNtr4/jYybESUXoZ1fAstBHFAD2eCLaMMmmU483mtDQOhD3XMb79Hf1O8Jq+IUufczE8r+UvsOE\nQiGqq6uDtysqKsIyK5HUfXiiA14fh89dUkTLJ1OUp5Hh//vaUtTOyMHxxl48+KdP0NI5vhuOCSET\nz6xZs1BQUBDcMzWWvVOZEPiOD90HNdKJmFjX/VnFGihlomBHSij0/z/e0ii5xB9wxUs7PlqBTknk\nTFWgRpax24rWHhu6B/wd5uPnhvdluSLqWI30eniquQ8tXVZYHO6oEXpxyMxga49tVEu1YnHFqO9z\n1tgP+6AHJnNIlrUJ3mGNd6Z5PrpTnwqny4uuPv/f+KyxH139Djhd4QOfNsdw4MFzPI7Ud6Glywpj\njy04s8BH9JcD7TRZnGjpssLt9cHqmDh1qeovDuBEU2/cQV6O5zEQGSTG4eO4Uc/EKUKWSsolQlQW\nhyduiVwKO8HfnnEF9mCaba7g+8vm9ASX/IWKNSMYOhDS0mXFmZZ+/PNc4kQ4I5FSVCQUCmE0GoNf\neO+//z7VXBgFjuPx3rFWiIQsrphPtadGQikT4e7NC/Hn9xqxv86I+/+3DhsuLcUXV86ERDxxOlCE\nkPHzxS9+Eddffz1qa2vDAqlsrKBYsbAI/SF7lwKWVecDDIIZuVJNShGQq5HC6ky8RyIQWMXryFeX\nadFndSFP418yE1haFDmzs6TKgE8bulNuG8f7OylWhxvLawrA8zwa25InlwAAs92F1m4bHC4vbE5P\nSsVGQwOnQCfc7vSAZZiw3z3WaUg+e5d8j3i8gqmxnivjGzYy4GhDD0RCARZU5ob93GR2ot/qwqxi\nTdQ5sg968FlTL4DwfXGRf4M2kx05Kv+ecVecemGR799Yp9DfUR7fvefx+ruBQtKDbm/U/i8AaGqz\nwGRJnJUzVOh5KdQpUt5jzzAMNHJx3KLekUW4XV4fbE5P2JLcyWDA7oZWIcaZi/4s48trCnCyuTfs\nMT6OA8Mw+Of5xIFS59AAQDpn5lMKqL7//e9j+/btaG5uxpIlS1BcXIxHHnkkbY2YLo6d60HPwCDW\nXFI06d7IE4GAZbHl87MxvzIXf3rrLPYdMeLImW5sXFaG1QsLY276JIRMXQ8//DA2bdqE/Pz0F2kc\nKWGcbHzR+yJG9rwFOjn6ra6EiSkCrxHZIc0f2qAtFglQoBverC0RCTC3LCcqO5hIyEIkEMRNQhGJ\n5/lgp5LjeQy6vCPqQLaaxl6I2BsjA6HH50ObyY7iPEVIW2Of+0AgdbyxFxIhi7kxMiAOv9Zw0NfY\nbsaMkP1yoaee44ARJmccV/GGwz0+LmZij/Nt/vpFJXpl1HumrWd4EOGscbicDsfz8HEcpCIhBj1e\nsEzy9370DGv0AU6XL+p97vFyaO6woNQQ3b50CH21fqsLDANo4wQ7nX0OuD3+/YMj+SxECt2LOSJD\np2xmkQYmq/+z2d4bPtDTM+BEz4ATy+bmjymgaDfZoVaIoZSJ4BwqLD6jQJ32mfCApnZzWHtjLeWt\nq++GZgQlAeL9HUcjpXdeTk4OXn/9dfT19UEsFkOpTL0g2MMPP4zjx4+DYRjce++9mD9/fvC+devW\noaioaCj7BoNHH30UBoNh5L/FJLHviBEAsOHS0iy3ZHKrnaHD/Xcsw+sHL+DtT4zY8+45vP5RM1bM\nL8SyufmoKFTRckpCpoGysrJRZ/obb4tn6+Hy+OIGXolIxQKYoye/guJ1iioK1XGPiTf6LRKywYCq\nolAdth8mUugSmu5+Z9jSo0ywxVju1RYnKDN2W8MCKo7nwUZ00M9c6IN90Ivq8hwMur0YjBjg53ke\nRxtM0CjEwfpWAYFOaUBo7a+JvuQv1hRe5CyMY9ALs92VdOYwXjKTyJkDnk+e9j50maDbEx04AUD3\ngAMcx8MQUjsosKxz0O3Fgsr0Jx4IbUYgaFxeUxD82cUuWzBhwoXO1GZoM82glUGfp8ThE21xH+Pz\n8WCFo+srNXdYgu/55TUFONdqhsPlgUjIYkZB/O+dsQp9T8Rbyhtvpi6STiVN+B05Uil9+333u9/F\nH//4R+h08UduYqmrq0NLSwv27NmDxsZG/PCHPwzLnMQwDHbv3g2pNHHmjqmgsc2M821mLKjMRWGu\nIvkBJCGxSIAb11Ri47IyvPtpK979tBX764zYX2dErlqK2godqsu0qCrVJs0MQwiZnBYuXIjf/OY3\nWLx4cdiSv8svvzyLrYpNLBJEpQofjVJD9Mh1rlqKi91WVAx1ZBZW5o165FmnlsDR4w9c8nPkCQOq\nUBc6LZCk4fdLVJjYNuiB18eNKih1e6KPM4cs2YqlvdcBj8+X0kxDaEePG8c0ahzHw9htgyFHFjU7\n4/VxaGq3oESvDNuc73T7MNBpRbFeETwnkbNDpy/0hR0D+JMDzCrWIC8k6UGqbzMvxyUNNN1eH042\n9cLl4RLOkposTpy50Aef24tctSTY9kylV0+2xWXQ48Wg24sTjb0JH5eITCyEM0kmwJFK9h3g4ziI\nwILjeHT1O5CnkYXNLnEcD6vTA7GQhc3pgV7r/7ubzM6oz2gg5fto/wZOlxfHG01Qy8WYW56TsUHx\n0OXBKrkorbNpKQVUFRUVuOeee7Bo0SKIRMNL1W666aaEx3388cdYv349AKCyshIWiwV2ux0KhT+g\nGO0GyMlof51/dmojzU6llVImwqaVFbhmeTlONffhSH0Xjp834R/H2/GP4+0AAI1SjJmFalQUqjGz\nSI0ZBeqY650JIZNLXV1d2P8B/0DdRAyo0kEkYMNmXQIkYkHYiPlYlj1JEwRFyWasIhNNjEZRrgJy\nqTDu6/jTsafWCQosVQOAE00mLJ1jiBmMuTzh2b8YhoHXx8HYPbrkR+NZN6mr34GOPjv6rS5cMjsv\n7OeBcxg5kh+YRZFJBMG6PZFBYGQwFdDT7wwGVKYBJ7wp7H0LCE3cEaBTScPaZ0uSNS+0HRarE939\nIkgj9lHzPA8fx48q8I4lVoAcORPV0esY08ykSMgiyVbJEUsW2DtdPjBgYHa40dJlRUuXFQtm5gX7\nRxc6rcGEMoB/mWt5vgqOiIQjnX0OeLnAnkZv8LXbTHaYBpyYWayBRpF4GV6gsLfF4Ua/1ZWxgXCh\ngA0mzUn7cye6s76+HtXV1XC73RAIBHj//feRkzOc6jtZQGUymTBv3rzg7ZycHJhMpmBABQA7d+5E\na2srli5dGiykONWYhiphlxqUlCo9Q0RCFpfMzsMls/Pg4zhc7LKh/mI/zreacaHTimPnTDg2lM2F\nAVCWr8LcGTmonaHDnDJt2r54CSHjJ1YtqX379mWhJVOHeqjjkx+jQKZoHL4nGSbxzJjD5U15Jiyy\nA98z4IRKLo7awxw6Q8XxPAQMEzNzWKoiC7TGY3N6wPN8jJpW8bWb7OgZcGL+zFywLAPf0B6yyCWJ\nqcwsBjqxhhx5VDAcmegjwD6U0c5id+N8uznq/pFSykRjysLocHngcPmDsMCSwotdNnT02TGrWIPO\nXgdml2jHlLwqVpwUSGoQMNZZSa1SAovDDZZhUF2Wnn5inlaG/Bw5+iyDMffGBZYvloXMep9oMqGi\nQI18nRz9Mf4uLV3WqD1KocGlw+VBg3EANqcnGLicaekLG/CJJTSDZuiARKwi5COhUUhg0Mpwrs2/\n30qQwXp3CQOqhx56CH/84x+DGZNuvfVWPPnkkyk/eayc+qHTeDt27MCqVaug1Wqxfft27N+/Hxs2\nbBhJ+yeFN49cBM/7907R3p7ME7AsKoZmpHCZ/2f9Vhea2i1o6jCjsc2CpnYzWrqseOvwRcglQlwy\nOw+X1eSjdoZuVAUuCSHjr729Hf/3f/+H/n5/x8DtduPw4cPYuHFj0mNpf29sYpEAy6rzYy7lGo+B\np8hrZGT2MmOXFcJRfke3dPlnnJbXFKDfOpzkI7ROj9nmhtPtC/ZfGDBRBUOTSXWGKrDPKFlnM9TF\noVkzq8MNlVw85tkwY7cdYpEA9ReHE0okWjkUWLqX6ii/RCSAxxt/uV86O7iDHi8+PdsdDB4CM5St\nPbaoVOLxdPU5IBSwyFFJgn2BVFZSpfp3yM+RQ6eSwGx3Q8Ay0KokGHT5kKuRIlcjTcuy2QCWZVBR\nqEZ5vgpH6rviPi5yn1xzpwWGHFmcRyffozTSAHnQ7Y16P/lXsEXvxRuJPI0Ms4b+7v02GfqtLuRq\npGjtGXsynFgSBlRjXY6Xn58Pk2k4dWF3dzfy8oanpDdt2hT89+rVq9HQ0DDlAqpe8yD+8c92GLQy\nXFaT/UxU01WOSoIlc/RYMsdfnNrl8eF8qxnHG0349GwPDp7sxMGTnchVS7ByQRHWXFKU1uwvhJD0\nu+eee7B69Wq899572Lp1K959992UMtDS/t7EYg0qleqVkEuFkEuEcHm4sCKZ6RSIpwKBTGQ/1ePj\n0NAau1CvRCiA28slDYDaemwwhnSqQkfvA8+tU/n/9jq1BL2W6A6iSMDGHPUHgNYeO6RiAfptbuTn\nyGIGosn6V14fh8+aelGgk8fcd30mJAAKdfpCHxTS1LMIe3w+nGsNn2ni+cS1iprbU9tXJ5cIMac0\nB8fO98R9jE4tgdurRK5aCmO3Nbq47wjF+pvE+13MNhccLm/w/PZZBtE8NNsiZFksrtKjtceWUtCX\nKIgoz1ehpcuKEr0SJXp/UrfQpDCBv1c6g6lQyQaJYy3VHc9lq6cvhL+XuwecaIwz+6mUimDIkQVn\nVxMJ/bvNKtYEJ3UCe8MCe8LSJeFwU+RI0UgDrBUrVgSXX5w+fRr5+fmQy/3LCGw2G+644w54PP7p\nvLq6OsyePXtEzz8ZvPHxBfg4HtetmEHLyiYQiUiA2godvrK+Cr/YfgXu3bYEay4pgm3Qi79+2Izv\nPXEQu984jYtdVECYkIlKIBDgzjvvRF5eHr761a/it7/9LZ577rmkx8Xb3xswUff3ZrNJxXolhAIW\nCyrzgvWsxkIqFkIdY6lbsFixwP//kezLWlSlh1iU/DprjBihtsfYtxPomIe2sSgksEmUYMTh8uBE\nUy+M3VacHwpWBmwuf+Y8mz9zntkef5Tf6+NgH/TC5fGhpcsKl9sXllEwHtOAExaHGx0x6qElEhkc\nczyfMCjtMTvRE2M/VKRcjSzpUjuWZVBq8Afr6e7gBnA8D6+Pg2nACcegB91D5/LMxX60dFnB8Twc\ng56wQN3LcThS34X2XnvU+2UkGDAozFVg6RxDMJjKhLICFSRCAcrzR55uPdZnLN2JVfpCBiW6+hxh\ny2wjZ6esCWbASg3KhEtkJSFFvSOTcgRimrJ8FWpn6NLeJx/RztWRLldbtGgRamtrsWXLFggEAtx3\n33149dVXoVKpsH79eqxduxa33HILpFIpampqUlqmMZn0DDjx4YkO5OfIsLyWZqcmKpZhMKtYg1nF\nGtyybhYOne7C23XG4KzVvJk6fGF5OapKtbRkk5AJxOVyobOzEwzDwGg0oqioCG1t8dMEB0y2/b3Z\n/NpZWJkXY/n+6J9vblkO1AoxGIaByewPAEIFfldhxAyQRCSI6vgV5ymj0qYrpKK0JMcILIMKzQKm\nUUqCNX1yVBIIWSbp8ieHywuO48OW1Klk4rBizZHbIT45G15c+bOmXng5LukMRjr2NAH+Ar+xJMrA\nGIsyheRPoZ1enVqK6rKcsHMFAFUl2mCwM39mLhRSEc51pD7Y2WcdhKvFFxY4SyKy2VlipORPh0Bg\nmukBdYVUhEVV+lEdG2tAwT7ojTsDOxoNrQNQDs3E2QY9ELIsllaPfBk1j+hASaeSwurwwOPzweX1\nIUcpQb/NFdwPOl4SvtuPHTuGtWvXBm/39vZi7dq1wQ//gQMHkr5A5IVozpw5wX9v27YN27ZtG1mL\nJ5HXD/pnp65fWQEBS7NTk4FULMTaS4qxemERTjb14q3DF3GyqQ8nm/ows0iNqy8rw6LZetpnRcgE\n8C//8i/4+OOPcccdd2DTpk0QCAS49tprkx432fb3yoey9mmU49tBAGJnDIw1exHZ2VZIRTE7aqFL\nncTC6AAh8HdQK8Rwur3I00ihkIqgVojwaURHv9SgRIlegaYOS3CJXkWhekxJDgLcQ0GZMKTjLRQw\nqChQw9htQ36OHCV6JQZsrqgAIBTPxxiBj0jn5s9Ix6Df6oJaG50MJJBxL5VlTukQb79Teb4KOrUU\nXi8X3OQfT1WJNvi3rihQo7nTAqVUBLeXCzsfkYOUWqUkKiFGaFbewPK4JXPzceFiX9zln5Ei34uh\nM4Q+jg8r2jwSNeU6nG7pS/7ALAssOwSAGQXqqCyFkQW9Q4s0j0RRriKqkHBAaAZHL8fB6+PCkqeI\nhYKke/N4HojsTssl/tnNs8Z+SMVCzC7VwuX2ZaTIcyIJX+2tt94ar3ZMOe0mOw5+1onCXDkum0uz\nU5MNyzBYUJmHBZV5aGwzY++hFhw7Z8L/vHoShhwZ1i8pwYr5heP+gSWEDAss2wOAI0eOwG63Q6NJ\nvvk8U/t79fqRL7dJRV6eEgX5amiVEggmwNLxXrsHroh+z6Xzi/CPY8Ozg2IRC4Eo/PuxdmYu8kKW\ndanUXrT2hS8dC5zD3FwluvsdMOTIgwNYcqUMx8/5g6rZZVro8/xLqAyG8OKcI5m9CJWnlcEUsbSu\nMF+N1l7/zwoLNJCIBJg3Z/ianpenhFgmRlevI6wwbaiBQR/UqvjL2axuDvk6KTqMZvTauxI+ViwZ\n3h+lkosTLo8KVWxQoq17dEvXxCIW5QVq5OuVCPzmXZb4e52EQhZzKodnS/R6FWqrDGAYBi2dFlwY\n2oO16pLimIOT2nZrWIBTkK+GussefK6AOZV6dJpHt+fK6eOD51mnU8DFAerB1GY2VXIxKorUkEmF\n8Hq5qPdwpEx9L6Qi8Np6vQr9Dv/7c/6cfPACFv0Rf8NUF1wqZCKoFWJ0mKIDpyXzimA72hr2s1yN\nFL0xsmY2tFsBMFCrZFApxFg8x4APj7cFM1fGUpCvhkwihLrD/14u0isws1gLActArZFBo5RkrV+W\n8FWLi4vHqx1TCs/zeO7tBnA8j5vWVNJsxiRXWazBv9+4AB29duw7chEHT3bi+XfO4eV/NOGKeQVY\ntaAQ5fkqWg5IyDix2Wx46aWXcNtttwEA9uzZgxdeeAHl5eW47777woKjWFasWIHHH38cmzdvjrm/\nd8eOHXjyySchEolQV1eHq666KqV29fRkds9lX196C3+Olt02CIvVn4Lc5vCgWK+AyWRDVZEKTe0W\nWB1uKDQymKz+juayuflg4A9YQs8Rz/OwDD1m0Sw9vBwXdr8AQG9veBAQeLx5QAxRnJmUwGNGgmUY\nVJeo0WQMn20wDziCzzfQb49ZLFUuYCAVAF1WJ/RaWdR+p2TtsVidON/CwsdxUKtkKbdfCB6WJLNx\n/sHBXEhELM6M4LwsnWMILj30ZyHkw/42xToZzgzNzMwt18Hl8aGn3wmr043yfFXcz4KI5+HzeFFq\nUEb9bQMsFmdYHaz+Prv//SYTB59Xr/e/Rui5ijXzkoqmi33o6nMG068nIhMLUVyshtflgdXlgcvt\nC7ZhTmkOPD4OTRFLLzP9vRBP4BwFWKxOiAQsenqsEIZ89kaqptQ/aNXLhpcmCPzdKwwKdPQ6gjWs\nVBJB0tdifD709Fgx06DEpw3dUfcvrMyD3emBy+GCc+j7J9CWvqH3kQCAzeLESIcN0hXw0vB6BtTV\nd+NMSz8WVOaGFdojk1thrgK3XT0XN6yuxD+Ot+O9Y21476j/v+I8BZbX5mNxlT5mRiZCSPrcd999\nwQG/5uZm/OpXv8Jjjz2GlpYWPPjgg9i1a1fC46f7/t6xKtYrIBSw0GtlYXuMhAIWVaVaAIBj0IuO\nPjtUMnHMIATwL/cKbA6XiAWQIPUsZ+leRq+UicAyDC6tNqCufrhDF9r2eL8HABTo5FDKRFDKRMGA\nSi4RRhVBjWckWRMDS+JiDdb66w65gsu3FDIRpOLUunpzSnOCS72S7fnRKMRYMDMXXo4PJu7Qa6Rw\nuryQJ8gyKBKymD8zN+FzBwYn5RIRZpdowAz9XWKd/1K9Mpg0IrTAb0meEq2m2F3rPI0sLBBIVrMr\ndLlczYycsPMuCkmCIhULIPCFtzFdNaXS4dJqQ/Dc6rUySESC4HJFIcvGLeYcz8xCNdRyESx2D0wW\nZzBZhEwixMwidTCgEguTf1YDM+8iIYvFs/Uw291hmf5kEmFw5mmijl1TQJVmTpcXe949B6GAxVfW\nz6ZZiylIrRDj2itm4OrlZfisqQ8HP+vAP8+b8PL7TXj5/SYU5sqxoDIXtTN0mF2qzVgqVEKmK6PR\niF/96lcA/IV8r7rqKlxxxRW44oorsHfv3pSeYzrv7x0rAcuiKC/xwJFcKsT8mblhndxYRlLUFhhO\n6JDoeZVSUdh+jVgCG9cDZpf4A0EBy0ItFweTZaS6woRhmODvsrAyDz6Ox4DVBYcrvFMvEwvhdI9t\npq5n6bQAABNwSURBVDGwvyhWR7VAJ0dFoRpOlxfn28yYWTi8HDJWwofaGTqcuuDvVGuVYiypMqSc\n4TIycGIYJmEwlarAKVdIhzvR8QLofJ0cxh4bWIYJe08U5MpjBlQigSC4JzGWS6sNaOuxB/cBqeRi\nFOYqggFV5PshNMgTClhIxQIYhvbB+Thu3BMjJBJ5DkPbtnBWbtQexWRYloEhR448LY8SgyIqcF9Y\nmQf7oCcsOI+3Tyo0TbtYJIBeKwMPRM32ASNPkDdeKKBKs9c+asaAzY3rrpgBQ4xK82TqELAsLpmV\nh0tm5cHm9OD4eROONvTgZHMf9h0xYt8Ro38Tc6EaVaVazC7RorJYPaIaIYSQaIHleYC/5MaNN94Y\nvD1RL7bTUSa+6+bOyIHPx4fNjEWqqdDhyJn4hUzL81XIVUvRP7Qfy6CVhz1fVak2LNPe0jmGEY2K\nB4IAqVgQ1akXCllcUpaH821myMTClNKPh9LIxRh0+7OZxQoMAunmZRJh1EyQO6SA69yyHIhFAsgk\nQiyszIPby4FhGIiE2f/8yKVCuGy+hKnpA4QC/4yXWMhClCBlNgDMq8iFXCJMmKlQwLIozFXA7eWQ\nq5YiR+VPrFEzQweny5twZlQg8BcCn1mkjvuYiaYkTwmn2wuRUIAlVXpwvD/DJcf5Z0DlUiHaTf66\nalaHB7kxSib4g9no92JgVik0k2dthQ71Lf1RgwraGAl3DFoZ8tTSuElSJhoKqNLo1IU+7D9ihF4r\nxTWXl2e7OWQcKWUirJhfiBXzC+H2+AslnrrQhzMX+nG+zTxUOLEFAFCYK0flUJr2ymINCnPlCZeS\nEELC+Xw+9Pb2wm634+jRo8HZKrvdDqdzdPsCyOTAMgzYJJ1+lvEPZLWb7CjRK4NLhxj4S2QEOoWL\nZuvR2etAiSF8ti1yudtoU14LBSzmluWEFeENdD7nVeTCNBC/npNKJkZVqRZOtxenLwzv61LJxZhR\nKEWf1YVcjRQiIQtjty04I5eowx9IY16oU4RlW/R3fKMfn63lajOLNOgecKJAl1qahNDAvShXAceg\nN+bMokIqBMMwcZMWiAT+gEwkZDGrODy5jVoujlk3DfBnMXS4vJPyOl5iGK6NFQhII1fVBOpn5WlG\nVycs9LxIRAIsnJWHU819sDrdELIsZpdowt6PYceyDFhEn1e9RpZwUCUbKKBKE7Pdjd2vnwbLMvjm\n9fNomdc0Jh4qGlxboQOA4NKL861mnG8zo6nDgo4THfjwRAcA/zr7ymINZpVoUFWiQUWhOqWROUKm\nq2984xu45pprMDg4iLvuugsajQaDg4P4yle+gs2bN2e7eWQCyM+RI39olQgDf40mQ44sbIRdIhKg\nvCD2hvR5Fblhy5BGSyETQciykEuFcHs5FOUOz66GdiIVUhHmz8zFaaM/+CsvUEEkZCESinHZ3Hz0\nW11oardAn+Pf+1IcTKUvgUohDs7IJVqiKJeKsKTKkHJHVBunk5tpIiGL4iRLSuMpCylsK4qoZRaY\nvdYqJZhTmgOlTITmDgv6rIMQsiwWVY1uz3u+jlYjJRKYNRWGBPuVxWqcazWjskg9qmWilcXJs7mO\nN4afiOXg48hWppRkOJ7HrheP41RzHzZ/bhauuqws200iExjH8WjtsaGx3YLzrWY0tpvR3T88Silg\n/aOrc8q0qCrVYlaxhtKzk0ktE2mDPR4PXC4XlMrhEdYPP/wQK1euTPtrpWqiXqMmisisY+PJ5vRA\nLhVmZRaB43kwiL0c1T7owTmjGXPKtJBJhPAyLFra+lFZNLIOY8+AE24vN+pAZLJJ5b3E8Ty8Xg5H\nh5Z2+rMVhvP6ODS1W1CiV6Rl/9dEks3PWySz3Q2ZWDAhB4vTdX2igCoNXjrQiL2HWrCgMhf/cdOC\nSTntS7LLbHfjfKsZ51oH0GAcQEuXFYFPpn/5igpzynJQXabFrBJNylmbCJkIslmHZTxN1GvURDGR\nOngTFZ2j1KR6nniex+Gh2btYAdVURu+l1FDa9Anibx9fwN5DLcjPkeGOL8ylYIqMikYhxpI5eiyZ\n4y+G6HR50dhmRv3FAZy92I/mDisa2y3Ye6gFLMOgvECFqlINqkq0mFmsgWYCZRIihBBCJgKGYVCU\nq0iabZKQsaKAagze+cSIl99vQq5agu9uWTTi9K+ExCOTCDFvZi7mDWVpCgRYZ40DqG/px4VOK5o7\nLNh3xAgAyNNIMbNIjfJ8FcryVSgxKKGWiyjjGSGEkGktdF8VIZlCAdUoOQa9eOHdc9AoxPjulxfF\nTCVJSLpEBlgujw9N7Racbx1AY7sFjW1mHDnTjSNnhlP9KqRCFOYqYMiRwaCVQa+VQaeWQKeWQquU\nTLgMOYQQQgghkxEFVKMklwrxL1+oQWWJBgbt6FJJEjJaEpEAc8tzMLfcn9aW53mYzINo6bSipcuK\ndpMd7b0Of9DVFl0YD/Cnes9RSaBRiKFRiqFVSqBW+P+vUYihUYihVoghFQtoposQQgghJI6MB1QP\nP/wwjh8/DoZhcO+992L+/PnB+w4ePIhdu3ZBIBBg9erV2L59e6abk1aXz5teGxzJxMUwDPRDs1BL\nqw3Bn3t9HHotg+jpd6LHPIg+i/+/AZsbAzYXegacMHZHV5MPJRaxUMuHAyy1wl+PQx0SdFHwRSab\nqXxtIoQQMr4yGlDV1dWhpaUFe/bsQWNjI374wx9iz549wfsffPBBPPPMMzAYDNi6dSs2btyIysrK\nTDaJkGlFKGDD6rHE4nL7MGB3wWxzw2z3B1oWuzt422J3w2x34UKnNWldFrGIHZrdkkCjFA/Nfkmg\nVYbMfCklUMlFlMCFZA1dmwghhKRTRgOqjz/+GOvXrwcAVFZWwmKxwG63Q6FQwGg0QqvVIj8/HwCw\nZs0aHDp0iC5ahIwziViAfHHioAvw1/RwDHphtrthtQ8HWxZHSOBlc2PA7i9AySWoyMAyDFQKEbQK\nCVQKETRyMVQKMVRyEVQyMZRyEZRSERQyIeQSIWQSIURClma/SFrQtYkQQkg6ZTSgMplMmDdvXvB2\nTk4OTCYTFAoFTCYTdDpd8D6dTgej0ZjJ5hBCxoBlGChlIihlIiBJ8UiO42FzejBgcwVnvcy24YDL\nbHfDbHOho9eOli4u4XMFCFgGEpEAErEAYiELoZCFUMBCyDJgWAYswyA03OJ5Hjzg/4/nwfNAvBiP\nZfzLJpmh/0fe/n/t3V9M1fUfx/HnOUdDJSbSgfMb0GpLZcvUWVtq/FNGyLStrVxuFo6tzRa0qLaU\naWLzBjV2XJu11uCmbC2paFwJs6bVUEEpN2PLMbdmMjlIUnEO/w7n87s4cYTj6Rwk4XuE1+OGne8H\nznnz+r7P53s+53zPOTYb2Aj+HBO+tBv7vbGsgjXB+hX/Y/VS56T+R5kZOjaJiMjdNK0LqvDvDDbG\nhJ5hjjYmIvc2u90Wer9VLIPD/n9e6Rrhb98wf/tG8A6M0D8Y/OkbGmVgyM/gkJ+hkVGGRkYZHB7F\nPzDCyGiAQMAwGjARF0s2xi+MglvCp5ng3xkCATBEvp7/Yr7DrgVVnNGxSURE7qZpXVC5XC5u3LgR\nuuzxeHA6naGxnp6e0Fh3dzepqalRr+9ufZuxiIjMXXf72DRGx6jYlFFsymhylFNsymjmTOsX0WRn\nZ9PU1ARAR0cHLpeLRYuC79PIyMjA6/XS1dWF3+/n1KlT5OTkTGc5IiIiOjaJiMhdZTPh5zfcZW63\nm9bWVhwOB1VVVXR0dJCUlERhYSHnz5+npqYGgOLiYkpLS6ezFBEREUDHJhERuXumfUElIiIiIiIy\nW03rKX8iIiIiIiKzmRZUIiIiIiIiU6QFlYiIiIiIyBRN68em/xfV1dVcvHgRm83Gnj17WLlyZWis\npaWFI0eO4HA4yMvLo6yszMJKrRMto4KCAtLT0//5Dh4bNTU1pKWlWVitdS5fvkx5eTmlpaW8+OKL\nE8bUS0HRMlIvBR0+fJj29nZGR0fZuXMnTz/9dGhMfXRLtJxmYy9Fm4fnovD9v3LlSt5++22MMaSm\npnL48GHmz59PY2Mjn3zyCQ6HgxdeeIHnn3/e6tJn1NDQEFu2bOG1115j3bp1yiiCxsZG6urqmDdv\nHhUVFSxfvlw5jePz+di9ezd9fX34/X7Ky8txOp28++672O12srKy2L9/PwC1tbU0NTVht9spKysj\nPz/f4uqnX/jjmuvXr0+6f/x+P5WVlXR1deFwOKiuriYzMzP6DZo41Nraal555RVjjDGdnZ1m27Zt\nE8Y3b95srl+/bgKBgNm+fbvp7Oy0okxLxcqooKDADAwMWFFaXPH5fKakpMTs27fPHDt27LZx9VLs\njNRLxpw9e9bs3LnTGGPMzZs3zYYNGyaMq4+CYuU023op1jw810Ta/5WVlebEiRPGGGPcbrf5/PPP\njc/nM5s2bTL9/f1mcHDQPPPMM+bPP/+0svQZ53a7zdatW01DQ4OprKw0TU1Noe3KKNg/RUVFxufz\nmZ6eHrNv3z7lFObYsWPG7XYbY4zxeDymuLjY7Nixw1y6dMkYY8xbb71lvv/+e3P16lXz3HPPGb/f\nb3p7e01xcbEJBAJWlj7tIj2uuZP+aWhoMAcOHDDGGPPjjz+aN954I+ZtxuUpf2fOnKGwsBCARx55\nhL/++guv1wvA1atXSU5OxuVyYbPZyM/P5+zZs1aWa4loGQEYYzD6AEcSEhKora2N+Cy4eikoWkag\nXgJ48sknef/99wFYvHgxAwMDoUzUR7dEywlmXy/FmofnmvD97/P5aGtro6CgAICNGzfS0tLCxYsX\nWbVqFYmJiSQkJPD444/T3t5uZekz6sqVK1y5coX8/HyMMbS1tbFx40ZAGY1paWkhOzubhQsX4nQ6\nOXDgAK2trcppnCVLlnDz5k0A+vr6SE5O5vfff2fFihVA8IyAlpYWzp07R15eHg6Hg5SUFDIyMujs\n7LSy9GkX6XHNZPvnwoULE+b2p556alI9FZcLqhs3bpCSkhK6vGTJktC32oePpaSk4PF4ZrxGq0XL\naMz+/fvZvn07brd7psuLG3a7nfvuuy/imHopKFpGY+Z6L9lsNhYsWADA8ePHyc/Px2azAeqj8aLl\nNGY29dJk5uG5ZPz+r6+vZ8OGDQwMDDB//nwAHnjgATweD729vbfdZ3p6eiyp2QqHDh2isrIydFkZ\n3e7atWsMDAzw6quv8tJLL3HmzBkGBweV0zibN2+mq6uLoqIiSkpK2LVrF4sXLw6Njx2L5mJGkR7X\n3Mn9bPzcbrPZsNvt+P3+qLcZl++hCn8G0xgTOihHG5tLYuVQUVFBbm4uycnJlJWV0dzcTFFR0UyX\nGdfUS5OjXrrl5MmTfP3119TV1YW2qY9uFyknmH29pH0f2cmTJ/nqq6+oq6tj06ZNoe1j+UTKba74\n5ptvWLNmDRkZGaFt43tGGQUZY+jr6+ODDz7g2rVr7NixQzmFaWxsJD09ndraWn799Vdef/11EhMT\nJ/zOv2U0F+epyfZPpGwCgUDMzOLyFSqXyzXhWT6Px4PT6QyNjV9Zd3d3k5qaOuM1Wi1aRgDPPvss\nKSkp2O128vLyuHz5shVlxjX10uSol4J++OEHPv74Y2pra7n//vtD29VHE/1bTjD7einWPDwXhe//\nRYsWMTw8DATvG2lpaRHvM/f6h5NM1unTp/n222/Ztm0bX375JR9++CELFy5URmGcTidr1qzBbrfz\n4IMPkpiYqJzCtLe3k5ubC0BWVhZer3fCfBQto7l4jLqTuSgtLS2U5dgrUw6HI+r1x+WCKjs7m6am\nJgA6OjpwuVwsWrQIgIyMDLxeL11dXfj9fk6dOkVOTo6V5VoiWkb9/f28/PLLjIyMANDW1sayZcss\nqzVeqZdiUy8F9ff389577/HRRx+RlJQ0YUx9dEu0nGZjL0Wbh+eiSPt//fr1oYyamprIzc1l1apV\nXLp0if7+frxeLz/99BNPPPGElaXPmCNHjlBfX88XX3zB1q1bKS8vZ/369Zw4cQJQRmOys7M5d+4c\nxhj++OMPfD6fcgrz0EMP8fPPPwPBUyQTExNZtmwZFy5cAKC5uZnc3FzWrl3L6dOn8fv9dHd34/F4\nWLp0qZWlW+JO5qLs7OxQr3333XesXbs25vXbTJy+Pup2u2ltbcXhcFBVVUVHRwdJSUkUFhZy/vx5\nampqACguLqa0tNTaYi0SLaNPP/2UhoYGFixYwKOPPso777xjdbmW+OWXXzh48CBdXV3MmzcPl8tF\nQUEBmZmZ6qV/xMpIvRR8P9DRo0d5+OGHQ6cErFu3juXLl6uPxomV02zspfB5OCsry+qSLBNp/x86\ndIi9e/cyPDxMeno61dXVOBwOmpubqa2txW63U1JSwpYtW6wuf8YdPXqUzMxMcnJy2LVrlzIKc/z4\ncerr67HZbJSVlfHYY48pp3F8Ph979uyht7eX0dFRKioqcDqdVFVVYYxh9erV7N69G4DPPvuMxsZG\nbDYbb7755qQWCPeySI9rampqqKysnFT/BAIB9u7dy2+//UZCQgIHDx7E5XJFvc24XVCJiIiIiIjE\nu7g85U9EREREROReoAWViIiIiIjIFGlBJSIiIiIiMkVaUImIiIiIiEyRFlQiIiIiIiJTpAWViIiI\niIjIFGlBJSIiIiIiMkVaUImIiIiIiEzR/wHytvNZEQ5j2wAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4127f5e350>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace, varnames=['alpha']);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To verify that our truncation point is not biasing our results, we plot the distribution of the number of mixture components used."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_components_used = np.apply_along_axis(lambda x: np.unique(x).size, 1, trace['component'])"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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WDodDNptNffv21YYNGyRJhmF4siwAACzLo8FeUlKiwMBA53JAQIBKSkouuC4w\nMFBFRUWSpPz8fE2YMEFxcXHKzs72ZIkAAFiKR6fif7rnbRiGbDZbves6deqkxMRExcTEqKCgQAkJ\nCVqzZo28vbl0PAAA7ng0LR0Oh3MPXZKKiooUFBTkXFdcXOxcV1hYqODgYIWEhCgmJkaS1KFDBwUF\nBamwsFDt27d32U9AgJ+8ve0eGsWFBQf7m9aXj4/5H2qao0+zWHlsEuO71DG+pmHme3Rz9nkhHn2E\no6KilJGRoeHDh2vnzp1yOBzy8/OTJLVv314VFRU6dOiQQkJC9Pnnn2vBggVauXKliouLNX78eBUX\nF6u0tFQOh6Pefo4cOenJYZwnONhfxcXHTevPrKNIzzLzyFWzWXlsEuO71DG+pmPme7Rkfi7U9yHC\no8EeGRmpiIgIxcbGym63Ky0tTVlZWfL391d0dLRmzpyp5ORkSdLdd9+tjh07KigoSJMmTdLatWtV\nU1Oj9PR0puEBAGggm2GBQ9Ct/snMyr81NZuVxyYxvksd42s6Zv+O/WLaY+fMcwAAWAjBDgCAhRDs\nAABYCMEOAICFEOwAAFgIwQ4AgIUQ7AAAWAjBDgCAhRDsAABYCMEOAICFEOwAAFgIwQ4AgIUQ7AAA\nWAjBDgCAhRDsAABYCMEOAICFEOwAAFgIwQ4AgIUQ7AAAWAjBDgCAhRDsAABYCMEOAICFEOwAAFgI\nwQ4AgIUQ7AAAWAjBDgCAhRDsAABYCMEOAICFEOwAAFgIwQ4AgIUQ7AAAWAjBDgCAhRDsAABYiLen\nO5gzZ462bt0qm82mlJQUdevWzbkuOztbL7zwgux2u/r06aMJEya4bQMAAFzzaLDn5eVp3759yszM\nVH5+vlJTU5WZmelcP3v2bL3++usKCQnR6NGjNXDgQJWVldXbBgAAuObRYM/JyVF0dLQkKTQ0VOXl\n5aqoqFCrVq1UUFCgtm3byuFwSJL69u2rnJwclZWVuWwDAADq59Hv2EtKShQYGOhcDggIUElJyQXX\nBQYGqri4uN42AACgfh4NdsMwzlu22Wwu17naxtk2AACgfh6dinc4HHX2touKihQUFORcV1xc7FxX\nWFiokJAQ+fj4uGzjSnCwfxNX7p6ZfT6b1Ne0vgAAP09zZNGFeHSPPSoqSh999JEkaefOnXI4HPLz\n85MktW/fXhUVFTp06JBqamr0+eefq3fv3vW2AQAA9bMZrubAm8jzzz+v3Nxc2e12paWlaefOnfL3\n91d0dLQ7ls4oAAAPqklEQVS+/PJLPffcc5Kku+66S2PHjr1gm7CwME+WCACAZXg82AEAgHk48xwA\nABZCsAMAYCEEOwAAFuLxc8Vbyfz587Vp0yadPn1aDz30kO68887mLqnJnDp1StOmTVNpaamqqqr0\nyCOPqF+/fs1dVpP78ccfNXjwYCUmJmrIkCHNXU6Tyc3NVVJSkq6//noZhqGwsDDNmDGjuctqUitW\nrNCSJUvk7e2tpKQk9enTp7lLahLvvfee/v73v8tms8kwDH399dfatGlTc5fVZE6ePKmpU6fq6NGj\nqqmp0aOPPqrevXs3d1lNxjAMzZw5U99++618fX2Vnp6uzp07N2tNBHsDbdy4Ufn5+crMzNTRo0d1\n7733WirYP/30U3Xr1k0PPPCADh06pHHjxlky2F9++WUFBAQ0dxke0atXLy1cuLC5y/CIo0ePatGi\nRfrggw9UUVGhP//5z5YJ9vvvv1/333+/pDPX11i9enUzV9S0srKydO211+rxxx9XUVGRxowZo1Wr\nVjV3WU1m7dq1OnHihDIzM1VQUKDZs2dr8eLFzVoTwd5AvXr1Uvfu3SVJbdq0UWVlpaXOijdo0CDn\n34cOHdKVV17ZjNV4xnfffafvvvtOffta84Q/Vv6BS3Z2tqKionTZZZfpsssu09NPP93cJXnEokWL\ntGDBguYuo0kFBARo9+7dkqRjx47VOWW4Fezdu1c33nijJKlDhw46ePBgs2cD37E3kM1mU8uWLSVJ\n7777rvr27WuZUD9XbGyspkyZopSUlOYupcnNmzdP06ZNa+4yPCY/P18TJkxQXFycsrOzm7ucJnXw\n4EFVVlbqkUce0ejRo5WTk9PcJTW57du368orr9QVV1zR3KU0qUGDBunQoUMaMGCA4uPjNXXq1OYu\nqUl16dJFX3zxhWpra/Xdd9/pwIEDOnLkSLPWxB57I33yySdavny5lixZ0tyleERmZqa++eYbPfHE\nE1qxYkVzl9NkPvjgA0VGRqp9+/aSrLd327FjRyUmJiomJkYFBQVKSEjQmjVr5O1tjZe4YRg6evSo\nXn75ZR04cEAJCQn67LPPmrusJrVs2TLdd999zV1Gk1uxYoWuuuoqvfbaa/rmm280Y8YMvffee81d\nVpPp06ePNm/erNGjRyssLEyhoaHN/v5ijVe9Sb744gu9+uqrWrJkiVq3bt3c5TSpr7/+WldccYXa\ntWun8PBwnT59WmVlZZaZNlu3bp0OHDigzz77TIcPH1aLFi3Url073Xbbbc1dWpNwOByKiYmRdGY6\nMCgoSIWFhc4PMpe6oKAgRUZGymazqUOHDmrVqpWlnp/SmQMg09LSmruMJrdp0yb99re/lSSFh4er\nsLBQtbW18vKyzoRxUlKS8+8777yz2WddrPPIetiJEyf07LPPavHixfL3vzhO9N+U8vLy9Prrr0s6\nc0ndyspKS71pvvDCC1q2bJn++7//W8OGDdOECRMsE+qStHLlSue/X3FxsUpLS+VwOJq5qqYTFRWl\njRs3yjAMlZWV6eTJk5Z6fhYVFalVq1aWmWE5V8eOHbVlyxZJZ75SadWqlaVC/ZtvvnF+dbl+/XpF\nREQ0c0XssTfYhx9+qKNHj2rixInOAyPmz5+vdu3aNXdpTWLkyJFKSUlRXFycfvzxR82cObO5S0Ij\n9O/fX5MmTdLatWtVU1Oj9PR0S4WEw+HQwIEDNXz4cNlsNsvt2RYXFzf7Xp6njBgxQikpKYqPj9fp\n06ctd+BjWFiYDMPQ8OHD1aJFC+f1T5oT54oHAMBCrDMfAgAACHYAAKyEYAcAwEIIdgAALIRgBwDA\nQgh2AAAshGCHJR08eFDh4eH6xz/+Uef2/v37N8n2w8PDVVtb2yTbcuXjjz9WdHS03n///Ua3zcrK\nqrfdqVOntGbNml9S3q/C5s2bdeDAgWatoW/fvjp06FCz1oBLC8EOy+rUqZMyMjJ08uRJ521NdeEe\nMy4AtG7dOv3hD3/Q0KFDG9323nvvrbfd119/rY8//viXlPersHz5chUUFDRrDVa82BQ8yzqnpgJ+\nIjg4WL/97W+1aNEiTZ48uc66rKwsZWdn69lnn5UkxcfHa8KECbLb7Vq8eLEcDod27Nih7t27Kyws\nTGvWrNGxY8f06quvyuFwyDAMLV68WDk5OaqoqND8+fN13XXXaffu3Zo3b55qampUU1OjtLQ0hYeH\nKz4+XjfccIN27dqlpUuX1nmz/vzzz/Xyyy87L0manp6uLVu2aN26ddq0aZPsdruGDRvmvH98fLxu\nueUWbd26Vfv379f06dP1wQcfaM+ePfr973+vhx9+WBkZGTp9+rTuuOMOPfnkk1q+fLlOnz6toUOH\natasWZoxY4aOHz+u5557TqGhoS4fi1deeUUtWrTQgAEDdM899+jpp5/W/v37VVFRobvvvltjx46t\n87gahqFZs2Zpx44dstlsGjt2rO666y5t3bpV8+bNk4+Pj2w2m5588kmFhoY2eCwFBQU6cuSISkpK\ndOutt2rq1Kmqra3VM888ox07dsjLy0u33nqrkpKSlJubq1dffVXt2rXTnj175OPjo9dee00tWrTQ\nqlWr9Pbbb0uSAgMDNWvWLLVp00Y333yzHnnkEa1fv14lJSV68cUXtW/fPq1evVrbt2/X9OnT9c03\n32jlypXOf6dnn31Wbdq0cY49NzdXL774ov72t79JkqZPn66ePXtq0KBBmjRpko4fP66amhrdcccd\nevjhh1VeXq6ZM2fqyJEjOn78uMaNG6e7775bpaWlmjhxompra3XDDTc0+wVFcAkyAAs6cOCAER8f\nb1RXVxuDBw82vv/+e8MwDKN///6GYRjG8uXLjcmTJzvvP3r0aCM7O9vYuHGjcfPNNxvl5eXGqVOn\njBtvvNH4+9//bhiGYUybNs1YunSpYRiGERYWZnz00UeGYRjGsmXLjMcee8wwDMO4++67jf379xuG\nYRi7du0y7r33Xuf2X3zxxfPqrKysNKKioozCwkLDMAzj7bffNqZPn+7sb9myZee1GT16tLFw4ULD\nMAzjpZdeMgYNGmTU1NQYBw4cMG655Rbn7Wf7e/75542//OUvxksvvWS8/PLL542/IY+FYRjGa6+9\nZrz00kuGYRjG6dOnjaFDhxq7d++uU9sHH3xgJCUlGYZhGOXl5cbDDz9snD592hg4cKCxY8cOwzAM\n47PPPjPi4+MbNZZ7773XqK2tNaqqqow777zT2L17t/GPf/zDePjhh531DBs2zMjLy3PWXVZWZhiG\nYcTHxxtr1qwxfvjhB+N3v/udUVVVZRiGYbz55pvG3Llznf+eX3zxhbO/2bNnO+vLyckxDMMwevbs\naZSWlhqGYRj//Oc/jW+//bbO2Ddu3GiMGjXKuXz232/NmjXGgw8+aBiGYdTW1hpLly41amtrjfT0\ndGP58uWGYRjGyZMnjTvvvNMoKysznn/+eeO5554zDMMwvv76ayM8PNw4ePDgec8DwBX22GFp3t7e\nmjx5smbNmqXXXnutQXs/oaGhzgv9tG3bVpGRkZLOnK+8vLzceb/bb79dkhQZGak33nhDZWVl+v77\n75Wamurs5+TJk86/z27nXHv37lVwcLBCQkIkSb169VJmZqbbGm+66SZnTREREbLb7WrXrp2OHz9+\n3n0TExMVFxcnb29v595qQ3Xu3Nn5WGzcuFGFhYXauHGjJKmqqkr79+9Xly5dnPfftm2bevXqJUny\n9/fX4sWLdfz4cZWVlTkvjtGrVy8lJyc3aiy/+c1vZLPZ5OPjo27dumnPnj3aunWr89/Ay8tLPXv2\n1Pbt2xUREaHQ0FAFBARIktq3b69jx45p8+bNKi4u1gMPPCDDMFRdXa0OHTo4+zhbd/v27etMv5/9\n9xs2bJgeeOABDRw4UHfddZc6derUoMfwpptu0p///Gc9/vjj6tOnj4YNGyabzaaNGzdqx44dWr58\nuSTJ19dXBw4c0O7duxUbGytJ6tq1q+WuJAnPI9hheX379lVmZqY++eQT5xT4T7+3rK6udv5tt9vr\nrDt3+dwPBuduw2azydfXV76+vlq6dOkF6/Dx8bng7edu0/h/Fxhy59yaflrvT/3444+qqqpSVVWV\nKisr1apVqzrr63sszq3Z19dXjz76qAYMGOCyL5vNdt6Hp59u/6djbMhYzt1mbW2ty8fo7O0/3Y5h\nGPL19dWNN96oxYsXX7DduRfNudAHwKlTp+qHH37Q559/rkcffVTTpk1zXo70QuOsqqqSdGbKf8WK\nFdq8ebM++eQT3XfffcrKypKvr69mzpx5wauBnbut06dPX3CsgCscPAfLOvfNOSUlRQsWLHC+2bZu\n3Vo//PCDJKm0tFR79uxp9PZzcnIkSV999ZW6dOmi1q1b6+qrr9a6deskSd9//70WLVpU7zY6d+6s\nsrIyHT58WJKUnZ2tHj16NLqWsy4USLNnz9bYsWM1cuRIPfPMM5LOBEdNTY2khj8WPXv21KpVqySd\nCde5c+fWmcGQzsxKfPHFF5LOXOr47BWvgoODtW3btkaN8dyx5OXlyTAMVVVVafv27erSpYt69Oih\n7OxsSVJNTY1yc3PVvXt3l9vr1q2btm/frpKSEknS6tWr9emnn57X17m8vLxUU1Oj8vJyZWRkqF27\ndho5cqRGjRrlHM9ZrVu3VmFhoSSpsrLSuf5///d/9dlnnykyMlKTJ09W69atVVZWpp49e+rDDz+U\ndOZXCunp6aqtrVVoaKg2b94sSdq6dWudgz+BhmCPHZZ17l5Phw4dNHDgQP3lL3+RdOb63q+//rpi\nY2N17bXXOqeD69vGuby9vbVnzx698847Onr0qPPAs3nz5mnWrFn6z//8T9XU1Gj69On1bqdFixaa\nPXu2Jk6cKF9fX/n5+TnDtyHjcrdu3bp1Kiws1JAhQySduW77unXrdOONN2rBggVKTU3Vk08+qSVL\nlrh9LOLi4rRnzx7FxsaqtrZW/fr10+WXX17nPjExMdq8ebNiY2NlGIbGjx8vHx8fzZ07V3PnzpXd\nbpfdbld6enqjxtKhQwclJSXpwIEDuvvuuxUaGqprr71WW7Zs0ciRI2UYhgYMGKDIyEjl5uZecHsh\nISFKTU3Vww8/LD8/P7Vs2VLz5s2rt46oqCjNnDlTKSkpqqio0NChQ9WmTRv5+Pho9uzZde4bHh6u\nsLAw3Xfffbrmmmucj2Pnzp01depULVmyRF5eXrr99tt15ZVXKjExUTNmzNCoUaNUXV2t4cOHy8vL\nSwkJCZo4caLGjh2r6667Ttdcc43Lxwi4EC7bCuCidvYI/6SkpOYuBbgkMBUPAICFsMcOAICFsMcO\nAICFEOwAAFgIwQ4AgIUQ7AAAWAjBDgCAhRDsAABYyP8B+EFOHDtVOwgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f41082c9250>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"bins = np.arange(n_components_used.min(), n_components_used.max() + 1)\n",
"ax.hist(n_components_used + 1, bins=bins, normed=True, lw=0, alpha=0.75);\n",
"\n",
"ax.set_xticks(bins + 0.5);\n",
"ax.set_xticklabels(bins);\n",
"ax.set_xlim(bins.min(), bins.max() + 1);\n",
"ax.set_xlabel('Number of mixture components used');\n",
"\n",
"ax.set_ylabel('Posterior probability');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the vast majority of samples use five mixture components, and the largest number of mixture components used by any sample is eight. Since we truncated our Dirichlet process mixture at thirty components, we can be quite sure that truncation did not bias our results.\n",
"\n",
"We now compute and plot our posterior density estimate."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"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": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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FSy9tZmwsxKOP/gqAVCrF6OgoPp/P7UN7443/6p5PKUVn524GBvr47Gc/gVKKaDRKf38f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\nSYoglbJEIpFIJCnC/wcK/fOHmMF7RwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4122ab35d0>"
]
},
"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": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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NNGrkSE7WcY4fPYpz0+aXbGdvr70sm3zGLif/94xnzJcXOX0thKgVKQlRAPj4\nhzLp458Y+fBLNGnmpkiWEfc/x1PjP6LvbaMM2WR9ZWEhFOspCyEalpTEA2ht7Wjdtj1WVhrc23gr\nlsW9jTfubbxJvvBF4XDiAbr0HKxYHiEqSU9ZCGF25/NyOXksFS+/YKysLKcv4Onlj5VGw+FD0UpH\nEQKQoiyEqAWHL5we9vXvrHCSS9lobfH0CiAj7RAlJUVKxxFCirIQwvwqTxP7dAhVOMnlvDt0oqJc\nV3WblhBKkqIshDC7lIQo1FYaGjd1pbAwX+k4VSoqKrB3cAJksJewDJZzcUcIUS+VFBeRnpqAp5c/\nP379HocPRfPI/71L74EjlY7GlJfv5eSxVODiKXYhlCQ9ZSGEWR05HE9FuQ6fDp04np4MQGBoL4VT\nGbS8MALc1taO1KQYKioqFE4kGjopykIIs0pLigWglYcPxcWF2GhtFbs/+b/Ceg6selxYcJ7skxkK\nphFCirIQwszSkg1F+cypTADcWrVVMM2lQsP7A1BSWgxczCqEUqQoCyHMRq/Xk5oUS+MmrhxONIzA\n7hAYrnCqizTWNjg4OqO/cNpairJQmgz0EkKYTe7pLM7l5hDabQAF+XkAdOt7u0n2vXJ7qkn24+Ed\nQPLBSMrLdaTJbVFCYVKUhRBmU9nzbOcbxJC7n0Cn06HRWNavnXFvzUatVvPxG49y5PBBSkuKsdHa\nKh1LNFBy+loIYTapSZVFORDA4goygFpt+DXYzjeQinIdR9MSFU4kGjIpykIIs0lLjkWlVuPp3VHp\nKNfVzjcIgFS5riwUJEVZCGEWOl0Z6YcTcG/jg20jO6XjXFdlUZbrykJJUpSFEGZxPCOFstLiqlPX\nls7FzR0HpyYyAlsoSoqyEMIsKicNaebmzk9z3ictxXJ7oBUVFaxbsRCtthGns0+Qd/a00pFEAyVF\nWQhhFlWThmSfYPvG5Sz78UuFE12dWq1m5S+zOZ1zAjBMDSqEEqQoCyHMIjUpFttG9hy7MN91QHB3\nhRNdW+MmLlWPMw4nKJhENGRSlIUQJleQn0fWiSO09Qkk8/gRAMJ7D1U21HV4eHWoenzk8EEFk4iG\nTIqyEMLkjly4fuzp3YHCgjysNBpc3dwVTnVtgZ1vAcDKyoqMVCnKQhlSlIUQJlc5yEuttgKgabMW\nSsYxSpeegwHDfN1nz+Rw9kyOwolEQyRFWQhhcpUTcHh4BdCmrR+dewy8ziuU5+DojFf7YFq0bgdA\nWrIM9hLl1rUeAAAgAElEQVS1z/LmvBNC1Gl6vZ605DiaNW9FWI+BhNWBglxp0kc/Ehu5nVnTxpKa\nHE/7wB5KRxINjPSUhRAmlZN5lILzZ6tmyKprPL0DADgiPWWhACnKQgiTqrw/2at93SzKTs7NcG7a\nnLQUKcqi9klRFkKY1MWVoepmUQZDbzn3dDZnc2Wwl6hdUpSFECZ1JCUetZUGj3Ydrr+xhao8hS2T\niIjaJkVZCGEyOl0Zx9KTcPfw5uuPx/PxG49SmJ+ndKwbsunPX9j8128ApMv9yqKWyehrIYTJnDyW\nSllpCZ7eAezavJqKch22dg5Kx7oh2ZlHOX/uDADp0lMWtUx6ykIIk6ksYs1cW1FRrsPewQm1um79\nmunUtT9gWKQiXabbFLWsbv1vEUJYtPQLqyvln88FwLWlh5JxasSvYxfAcL/1udwcGewlapUUZSGE\nyaSnJmCl0ZB1PAMA7/bBCie6cWq1GnuHxuj1ekAGe4naJUVZCGESOl0Zx44k4e7hy4mjKQAEh/dT\nNlQNubXyrHosayuL2iQDvYQQJnHy6GF0ZaV4evkT0Kkn0f9urjoVXNcMu/dp0g/HsPr376WnLGqV\nFGUhhElUrkHs6R1Q5+a8/q/gsN706DOQHRtXkZ4qRVnUHjl9LYQwicoeZeXEG/WBp3eAYbDXmWyl\no4gGQoqyEMIkjhyOR6OxppWHj9JRTKbyC4bcryxqixRlIcRN05WVcTw9GXdPX6ytbZSOYzIeXv6A\nzOwlao8UZSHETTt+NAWdrqxenboGmQNb1D4pykKIm5ZxYZCXa0sPnhsVxidvP6lwopuXd+4Mbzw3\nDJVKTUZaotJxRAMhRVkIcdMqR17n5+VSUVFOaUmRwolunlPjpuh0pej1FZw9k03ehfmwhTAnKcpC\niJuWkZqAxtqGzGNpAHi1r7trKVfn1LhZ1eOjqdJbFuYnRVkIcVNKSko4lp5Ea09fjmckAxAc1lfh\nVKbhXm0kuZzCFrVBsclDXF0dlTp0nSNtZRxpJ+OYup0iI5Mo1+nw6RDElvXLAAjr0QeNpu7PTRTU\nuTsHo3cDcOJoknzGrkLaxXQU+1+Tk3NeqUPXKa6ujtJWRpB2Mo452mnz5h0ANHVtg66sjEZ2DpSU\nlFNSUm7S49Q2e3stQWED+H3hF4CKtKR4+YxdgfzfM54xX17q/ldZIYSiYmIOAOAX2IVPvv+b7JNH\nFU5kOs1btuHN6YtZ+uMXJMXv4/z5PBwdnZSOJeoxuaYshLgpBw5EobG2oWVrL5ybNqd9xzClI5lU\nW5+OtL1wv3J8fJzCaUR9J0VZCFFjxcXFJCYepE1bPzQaa6XjmE0brw4AxMZGK5xE1HdSlIUQNZaQ\nEE9ZWRme3v5KRzErj3aGohwTI0VZmJcUZSFEjUVHG64n17fpNf/LraUnNlpbYmNjlI4i6jkpykKI\nGouOjgKgSbMW9Xp5w4qKcpo0a0FSUiIlJSVKxxH1mFFFecaMGRw5csTMUYQQdU109AFsbW3Z9vdS\nJj49mP/98LnSkczizeeHk3XiCDqdjsREWTFKmI9RRdnJyYlXXnmFRx55hJUrV8o3RSFE1SCvjh2D\nOJaeBIBPh04KpzKP5i09qh7LdWVhTkYV5aeffpply5Yxbdo0srOzeeyxx5g8eTKHDx82dz4hhIU6\neDAOnU5Hp06h5J7KBKBjaE+FU5mHr3/nqscyAluY0w1dU87KyiI9PZ2CggLs7e2ZNGkSv/zyi7my\nCSEs2IEDhuvJPj6+lJWVorW1w8bGVuFU5tGpW/+qxzLYS5iTUTN6zZ49m9WrV+Pp6cn999/P+++/\nj5WVFaWlpdx7772MHj3a3DmFEBamciav3NxcAJo1b6VkHLNq09YPlUqFXq/n4ME4ysvLsbKyUjqW\nqIeMKsqnTp1iwYIFuLu7V/3s6NGjtGnThldffdVs4YQQluvAgSgaNWoEgFptRVufjgonMh+1Wo1z\nMzfyz52mqKiIlJRk/Pw6KB1L1EPXPX1dUVHB4cOHadWqFRUVFVRUVFBaWsrzzz8PQJ8+fcweUghh\nWYqKijh0KIHAwGBefXUS3/4vkkf/7z2lY5nV9O/WMXnyVECuKwvzuWZRXrNmDUOHDiUiIgJ/f38C\nAgIICAigU6dOtGzZsrYyCiEsTHx8LOXl5YSEXBxtrVbX/2kPgoIM71euKwtzuebp6+HDhzN8+HBm\nzZrF2LFjayuTEMLCVU4aEhISqnCS2hUYGIhKpZKesjCbaxblrVu30rdvX1q0aMHSpUsve/7ee+81\nWzAhhOWqnF6zU6fO19myfnFwcKRdOy9iY2PQ6/WoVCqlI4l65ppF+dChQ/Tt25f9+/df8XkpykI0\nTNHRUdjZ2ePj46t0lFoXFBTCH38s5+jRDDw8PJWOI+qZaxblZ555BoCPPvqo6lthaWkpp0+flmvK\nQjRQhYWFHDqUSHh4NxYu/B57e3us3cLRWNsoHc3skpIOkZVlmCglNjZGirIwOaNuifruu++ws7Nj\n1KhRjBw5EgcHB3r16sVLL71k7nyinlq5PbVGr7urt5eJk4gbFRcXS0VFBSEhnfjgg/coKipi1uLd\n1OPllKv8+ONC9uzZBUBs7AFuv32EwolEfWPUcMnNmzfz8MMP89dff9G/f3+WLFlCZGSkubMJISxQ\nTIxhkJefnz9FRUXY2dmhtW2kcKracdttQ6seywhsYQ5GFWWNRoNKpWLbtm0MHDgQMNy/LIRoeCqn\n1zx37hwArVu3UTJOrerVq3fVYynKwhyMKsqOjo4888wzHD58mNDQUDZv3iyjDoVooGJiDmBv70BC\nQjzQsG6LUqvVODk1BiAz8yTZ2fV3DWmhDKPXU77vvvtYtGgRADY2NkyfPt2cuYQQFqigoICkpEME\nBQVX3RY1YMCtCqeqXe3aXRzXEBcn9ysL0zKqKFdOvL5582aWLl3KyZMn2bVrl1mDCSEsz8VBXqEE\nB4fg4uLKbbfdrnSsWnX77XfQqpVhHQA5hS1MzajR12PGjEGtVl+yIAXIfcpCNDTR0YY5C0JCOnHv\nvfdXe6bhnMYdP/4V7rlnFGFhgVKUhckZVZR1Oh2//fabubMIISxc5SnrhnQd+Upat25DkyZNqpav\nFMJUjDp97ePjU7VmqhCi4TpwYD8ODo54e/soHUVRKpWKwMAQjhxJIy/vnNJxRD1iVE85MzOTwYMH\n4+3tfcnC3osXLzZbMGH5ajoBiKibzp/PIyUlmZ49b2kQK0JdT1BQMNu3byE+Po4ePXopHUfUE0YV\n5crpNoUQDVdMTDR6vb7BLUJxNcHBIYBhbWUpysJUjPq627VrVwoLC0lKSqJr1660aNGC8PBwc2cT\nQliQyklDOnYMZMCAXkyfPlXhRMrJyclh7tw5gOHLihCmYlRR/vTTT1m6dCnLly8HYPXq1Uyd2nD/\nQwrREB04YBh5nZd3jri4WFauXK5wIuU4Ojqyf/8+QG6LEqZlVFGOiIhg9uzZ2NvbA/DCCy8QHx9v\n1mBCCMsSFbWfpk2bVvUMAwODFU6kHFtb26rfh4mJBykuLlY4kagvjCrKWq32kr+Xl5dTXl5ulkBC\nCMtz5sxpMjKOEBISWtVj7tdvgMKplFU557der6+aclSIm2VUUe7cuTOTJk0iJyeHhQsX8vDDD9O1\na1dzZxNCWIjK68mhoZ1JT08HYNiw4UpGUlz1AW9yCluYilFF+Y477qBPnz5YWVmxf/9+nnzySV57\n7TVzZxNCWIjoaENRDggIoqAgH63WliZNmiqcSln9+1+c81uKsjCVa94SVVxczCuvvEJiYiKBgYG4\nubmxb98+tFotffv2xcbGprZyCiEUFBVlOGUdGBjIE088jUZjdZ1X1H+DBw9l6NDbWb/+L1mYQpjM\nNYvyN998g5ubGzNnzkSjMWxaVFTEhx9+yOeff86kSZNqJaQQQlnR0VG0aNESLy8fpk+foXQci+Dg\n4MAPP/zKgAG3EB8fh06nq/o9KURNXfP09b59+5g0adIlH7RGjRrx3nvvsXPnTrOHE0IoLysrk5Mn\nT9CpU8Oe7/pqgoKCKS4uJiUlWekooh64ZlG2srK64ilqa2trnJyczBZKCGE5Kk9dy0xeVxYUZLg1\nLDZWTmGLm3fNoqxSqa76XPU5sIUQ9VflLVDSU76ywMDK6TZlsJe4ede8ABIVFUW/fv0u+7ler5dV\no4RoICqLckiI9JSvJDAwEJVKJT1lYRLXLMrr1q2rrRxCCAuk1+uJjo7Cw6MtX389k59//oE33niX\nJ54Yo3Q0izFq1F3AxQU7rnWGUYjruWZRdnd3r60cooHKO3uavdvWkn44nmPpyahUapycm9LKw4du\nvYfh6R0gv+QUdPRoBqdPn6ZXrz5s3bqZs2flDNl/nTlzGr1ez/nzeWRkpOPp2VbpSKIOk/H7QhFn\nz2Tz59Lv2fnPH+jKSgHQ2tqhUqs5npFMQsxeNq1ZTCsPHx548nU6BMmqZEq4eD25M5s3bwJg+PA7\nlIxkcQIDg0lLM6wtHhMTLUVZ3BQpyqLWxURuY+Gsdyk4fxaX5u4MuuMROob2oqS4iNLiQpq5tiIj\nLZHdW1azf+8mPp/8ND3738F9T8gscrWtcnrNwMAgzp/Pw8bGBldXV4VTWZY+ffqxevVKAOLiohkx\n4k6FE4m6TIqyqDV6vZ4/fv2atcvmobG24YExk+h7271YWRk+hn8u/Z4/fv0agJatveg/9AH6D3uA\n3xd8wq7Nq8hITaR/yCpatmyl5NtoUA4c2I9KpSI//zyAtP0VDBs2gtdeGw/ICGxx8xQryq6ujkod\nus6x1Layt9def6ML9Ho9v8z7lLXLFtK8ZRteensmbb39L9mme5/BlJYUcDzjMAej9/DL99NwcHLm\n+YmfsH/PZjau+ZXhwwexfv16/P39LzuGpbaTpTG2nSoqKoiJOYCfnx/79+8FIDS00xVffyOfhbrk\nv+/rSu/d1dURrVZLSUkJsbHRDfJz2BDfs7koVpRzcs4rdeg6xdXV0WLbqqCgxKjt9Ho9y378gr9X\n/YiTswtqtQbHxi0ue32z5p7c/ZChx3Eu9xRb1y9h6/r/4eTcglGPT8SxsQsrFs/i1lsH8tdfm2jV\n6uJAREtuJ0tyI+2UkpJMXl4egwcP5dVX3yYoKAxfX98rvt7Yz0JdYm+vvex9Xa3t5s5dxPffz2HH\njm3ExaXg5uZWGxEtgvzfM54xX16MWiVKiJuxbcMy/l71Iw5OTcg7e4q8c6c5cfTwNV/TuIkLdzzw\nPNO+XUvzlh6oVCqGjhzDe+9N5eTJEzz44D3k5Z2rpXfQMO3b9y8AYWHh2NnZcffd9xAYGKxwKss0\ndOjtdO/eE0AWpxA3RYqyMKvDiQf4bf7HWNtoyc/LpYlLC9746Ce82gcZ9XqtttElf3/++bE89dSz\nJCQc5MknH6W8vNwcsQWwb18EAF26yMh3YwQFycxe4uZJURZmcy73FHM+fZXy8nLKSktwbdGGiR8s\nwK2VZ433qVKp+OCDjxk8eAjbtm1m5kxZschcIiMjaNSoEQEBgUpHqRMuzoEtRVnUnBRlYRZ6vZ6f\nv5tK3tlTePkG4ejUhJff+5ZmzW9u9K5er2f27C9p3twNd/fWfPLJNPbs2WWi1KJSfn4+CQnxhISE\nYm1trXScOsHdvTVNmjQhJuaA0lFEHSZFWZjF3m1riY7Ygl9gOK9NXcg7M37HpfnNzxBXXFzMihXL\n+PnnH7jzzpGoVCqee24MZ8+eNUFqUenAgf1UVFQQFhbO6dOnlI5TJ6hUKvz8AkhPPyLjHUSNSVEW\nJnf2TDa/zf8Yra0dj70wGSsrK5ybNjfJvhs1asSPP/5K06ZNmTfvWx577ElOnDjO66+/bpL9C4PI\nSMP15LCwcLp2DaFlyyYUFhYqnMqyjRv3f+zZY1hnPi4uVuE0oq6SoixM7vcFn1JYcJ57H33ZJL3j\n//Lw8OTLL7+htLSUf//dQ4cO/sydO5ddu3aY/FgNVWVRNszkdR6NRoOdnZ3CqSxb+/Ydqh7LKWxR\nU1KUhUklxv5L5O4NePkF02fwvWY7zpAhw3jwwYeJi4ulS5euqFQqXnllHMXFxWY7ZkOh1+vZty+C\n1q3bEB8fB0CrVq0VTmX5qk+vKYO9RE1JURYmU16u49d5HwPQd/B9Zl/daerUj7nvvgeZMGEiY8eO\n5fDhFL7+eqZZj9kQpKcf4dSpHMLCwtm4cT0AISGdFE5l+Tw921ZNGSs9ZVFTUpSFyWxd/z9OHjOs\nlhN/YKfZj+fo6MTs2d/RunUbPvjgA1xcXJk16wsyM0+a/dj12cXryV2qHg8YMFDJSHVG5WIdSUmH\nKCoqUjiNqIukKAuTKCrMZ9Vv3wCGJRjvffTlWj2+k5MTb775LoWFhUydOrlWj13fVB/klZ+fDxgW\nXRDX5+dnuK6s1+tJSIhXOI2oi6QoC5PYsPonCgsM89/e8cD/mWy09Y148MGHCQwMZsmSX4mKiqz1\n49cX+/b9i42NDcHBndi/P56kpAycnJyUjlUn/PTT73zxxWxAriuLmpGiLG7a+XNnWL/yBwBauLdj\nwLAHFclhZWXFBx98BMCUKe+g1+sVyVGXFRUVERcXS1BQMFqtYYUkZ2dnhVPVHba2tgQHy3Sbouak\nKIubtm7FQspKi7HR2jLykZeqBrvUtqSkQyxcOI/evfuya9cOtm7drEiOuiwmJhqdTkdYmMx3XVN+\nfv5YW1vLwhSiRqQoi5tyNjeHzet+p5lrS6bNWUtIl76KZYmI2MuqVSuqTrVOmzZFess3qPr1ZFEz\nNjY2+Pn5c/BgPDqdTuk4oo6RoixuyoZVP6ErK2XoyDE4NW5q9tugruX++0fj69uedevWMmDAIA4c\niGLt2jWK5amLKpdr7NKlq8JJ6rbg4BCKi4s5dChR6SiijlHmPKOoF/LPn2Xb3//DuWlzevS/Q+k4\naDQa3nprMo8/PhqVCtRqNdOnT2Xo0NtRq+X7pzEiIyNo3twNJ6fGzJ49k7vvHom7exulY1mMldtT\nr7tNaWkxGdmGUesLl6znloF23NXby9zRRD0hv6lEjW1a8wslxUXcdudjWFvbKB0HMCw2HxISyj//\nbGTQoCEkJiawfv1fSseqE06cOM7JkycICwtnzZo/eP/9d3joofuUjlXnnDyWxo6NKwBIS4lTOI2o\na6Qoixo5fz6Pf9YuxsHRmVsGjVQ6ThWVSsWECRNp1KgRPXr0QqVSMXPmZ3Jt2QiVp67DwsLZvHkT\nAJ07y7XlG+Xp5V91GeeIFGVxg6Qoixr5+ecfKSosQG1lRUV5udJxLjFkyDAiI+N5/vmxDB06nP37\nI9m+favSsSzevn2GQV7h4V2JjTWMHB48eIiSkeose0fDbWRH05IoLZH52IXxpCiLG1ZeXs433xjm\nmG7Z2otGdg4KJ7qUSqWiWbNmALz00gQAZs6coWSkOuHff3ej0WgIDu7E8ePHAZles6Zatm534ZGe\no2ky2EsYT4qyuGHr1q0lKysLgBH3PadwmmsLDQ2jb9/+bN++tep2H3G5goICYmKiCQnpRH5+PqWl\nJTg6OmFjYxljBeqaDoEXR6/LdWVxI6QoixtW2et09/TFN6Czwmmub/z4VwGYOfNzhZNYrv3796HT\n6ejWrSdZWSdp1cqd8HC5LaqmutwyBK2tYf3pI8lSlIXxpCiLGxITc4ADB/YDMHzUM4rel2ysnj1v\nISwsnHXr/iQh4aDScSzSnj27AOjWrQfBwZ04cCCB335brnCququle1u++nkndg5OpKXIwhTCeFKU\nxQ2ZO3cOACEhoYR2HaBwmutLTT3MnXcOxdvbG4CvvpLe8pXs2bMbgG7duiucpP5QqVS09e5ITuZR\ncnPPKB1H1BEyeYgwWlZWFitWLMXXtz3r129m1c4jSke6LhcXF+Lj4zh8OAV3Dx+Wr1hK5wGP4tqi\ntdH7qO8TP5SVlREZGUHL1l5siz8HnFM6Ur3RzjeQg9G7iYraL4PmhFGkpyyM9sMP8ykrK+Ppp/+v\nzsyQ5eTUmEceeZycnGx8OoSir6hg05+LlY5lUeLiYigsLMDHP1TpKPVOW59AAFlKVBitbvxmFYor\nLi5m0aL5NG7szKhRDygd54Y8+eTTqNVq0lLicG7anJ3/rKSwIE/pWBaj8tS1r7/lD9qra9r6dASk\nKAvjSVEWRlm5chmnTuXwyCOPY29vr3ScG+Lh4cngwUPJSE2gU9f+lBQXsX2DDGKqVDnIy9c/lF/n\nT+e7Ga9x9ky2wqnqh73b1mKlsWbfvgiZVU4YRYqyMMq3336NWq3mySefVjpKjTz11LM0buKKV/tg\ntLaN+Oev3ygvl2X1Kioq2Lt3F61audPUtSW7N68ictcG1GoZbmIKe7auoVxXxpkzpzl+/JjScUQd\nIEVZXFdMzAEOHozD2tq6zq4P27t3Xz6as5bufW+nZ/87yT2Vyf49m5SOpbjExATOnDlDr169KSku\norioAGsbLU7OTZWOVi94dwipeiynsIUxpCiL65o37zsAnJ2b4OHhqXCamlGpVGisrQG49fbRqFQq\nNqz+qcGfUty5cxsAvXr1Jmqv4UuKq5vxI9PFtXXufmvV4/37pSiL65OiLK6psLCQ5cuXAvD882Pr\nzKjra2ne0oPgLn05khxH6qFopeMoaufOHYChKEdHGBbt8PYLudZLxA3wC+wKGCbYkZ6yMEbd/w0r\nzOqPP5ZTWlqCRmPN6NGPKB3HZAaOeBiADWt+VjiJcioqKti9ewdt2njg6dmW9MOGmafCegxSOFn9\noVarcXBsDEBU1H7KLWxFNWF5ZDRHPbFye2qNX3utyTFmzzasBnXHHXfRuLFzjY9haXz9O9OmXQei\n9v7DqazjuLi5Kx2p1sXHx5Gbm8tttw0D4NbhDxMdsZUOwd0UTla/9Bt6Pwf3bSQ19TDJyUl06OCv\ndCRhwaSnLK4qOTmJ5ORDNG7szLhxE5SOYzKxkduZPP4eQrsNQF9RwT9rf1U6kiJ27doOGOYGBxg4\n/CFemTK3XlyisCR33P9/PPfci4CcwhbXJ//7xFUtXvwjAJ999iUBAR0VTmM6KrWazONp5GQexbmp\nKzs2raCoMF/pWLVu505DUb7llj4KJ6n/OncOAyAycp/CSYSlk6Isrqi0tJQlS36hadOmDBlyu9Jx\nTCogpAcuzd2J3L2BXgPuoriogF3//KF0rFpVXl7Orl078fRsS+vWbZSOU+/5+3ekUaNG7Nv3r9JR\nhIWToiyuaP36tZw6dYr77huNVqtVOo5JqdVqeg8aSWlJMdpGdljbaNm09lcqGtAgnNjYaPLyzkkv\nuZZYW1sTGhpGYuJBzp+XKV7F1UlRFlf000+LAHjooUeVDWImPfvfidpKw7/b/qJb72GcyjpGTOQ2\npWPVmi1b/gGgXz/LX36zvujSpSsVFRVyv7K4JinK4jIZGels2fIP4eHd8PProHQcs2jcxIVO4f0o\nL9fRo98IADY2oNujtmz5B5VKRe/efVmz5g/atm3Br99/pHSseis+Po5Fi+YBEBGxV+E0wpLJLVHi\nMt999zUArVrV79uEHnthMraN7FGpVASE9OBg9G4yUhPx8KqfX0Qq5efnExGxl5CQTjRt2ow1a1ZR\nWFhIcXGh0tHqLU/PtuTlGU5bS1EW1yI9ZXGJ8vJyfv3VsN5w5a0y9VUjOwdUKsNsS7cOfwigQay1\nvHv3DsrKyujXzzAF5P79hhHBoV3lVLa5ODg44OjoBEBExL9UVFQonEhYKukpi0ts2rSe/PzzWFtb\n17l1k29Gx049cWvVlogd6xj58Es0buJS9Zy5JmZRSuX15L59+wNUrV4UGNZbsUwNgZ9fB/bt+5f8\n/PMkJR2SSUTEFUlPWVziiy9mADB48BAcHBwUTlN71Go1A4c/hE5Xxtb1S5SOY1ZbtvyDnZ09Xbp0\nJTExgbKyMpo2bYpGI9/Rzan6oDo5hS2uRoqyqJKVlUVkZARAvZrBy1jd+w7HzsGJrev/R1lpidJx\nzOLo0aMkJyfRs2cvtFoty5f/D4DAwGCFk9V/1c88SVEWV6PYV2NXV0elDl3nGNNW9vY1v5e4cv/z\n5xsGeHl6ejJoUN+q663mOGZNXastrtdOV8tbWlLMqiXfU67Tceuw+1i9ZB7RERvpO3jkTWU1JlNt\nmzfvdwCGDx+Gq6sjM2ZMZ8SIoTRt2pSDWfXrfnRTMNVn3NXVEVfXEH744QdefPFFIiP/tbjPxs2o\nT+9FaYoV5Zyc80oduk5xdXU0qq0KCmres8vJOY9er2fu3O+xtbVl3brNnDp1/Wknb+aYNXW1tjCm\nna6Wt6JCz/YNf5B37jRvTv+FP5cu5M+liwjrOey6X0xqmlcpf/75JwDdu/etyhYUFA5ARGrNr53X\nR/b2WpN9xivbeujQu+na9Wc2bdpAXFwKbm5uJtm/koz9HSWM+/Iip68FALt27SAtLZURI+6iWTOX\n67+gHqk+w1dSfARhPQZxPCOZQ3ERSkczqeLiYjZs2IC3tw9eXt5Kx2mwunfvCcC//+5WOImwRFKU\nBXBxBq9HHnlc0RxKqZzha9vfyxhw+2gANq6pX7dH7dq1g4KCAgYNGqJ0lAatWzdDUd6zZ5fCSYQl\nkqIsyM09w59/rsLb24du3XooHUcRlTN8HUtPQqVS4dU+mNjIbWSdSFc6msls2LAOMIysF8oJDe2M\nVqtlzx7pKYvLSVEWLFu2hJKSEh566LGbvoZal/UeZBjYdSjuXwYOfwi9Xl9v1lrW6/Vs2LAeJyen\nqi9eu3btQKfTKZys4dFqtfj5+RMbGy2LU4jLyI2JDZxer2f6p58CKsrs2t3URBl1nX9wd6bMXEHL\n1u0oL9fRxKUFuzb/wZ0PPo+dvZPS8Yx2pX/DExkpZGSk063PEP7cc5SS4iLGPjQMW1s7vlosp1Fr\n04QJ44iJOQAYbo0aMGCQwomEJZGecgOXlhzLudwcVCpwcavfc11fj1qtpmXrdgBYWWnoP/R+SoqL\n2JwxEHoAACAASURBVLFxhcLJbl5M5HYAQrv2A2Dv9rUANHVtqVSkBqv6JCK7d8sXInEpKcoN3Npl\nhpVrfPxDcXRqonAay9J74D3YaG35Z+1vlJfX7dO8UXv/Qa22olO4Yf3k/bs3AhAQ0jDHEChp2LDh\nVZeJZLCX+C8pyg1YcVEBcVE7ARg28imF01geewcneva/gzOnTnLg381Kx6mxM6cySUuOpX3HLjg2\nNnzxSj98EIBeA+9WMlqDpNFocHV1BSAyMoLi4mKFEwlLIkW5Adu1eTUV5eXY2TviH9Jd6TgWacAw\nw+1RG1b9hF6vVzhNzUTt2QRA5+6GVaGKiwopyD+HRmONexu5X1kJoaFdANDpdFVT2woBUpQbtC0X\nFl64ZeBI1Gr5KFR3PCOFX+d9jJNzM0LC+5GaFENS/D6lY9VI5J6NqFQqQrsZrmVmHk+jkZ0DraQg\nK2bEiDuwsrICYMeObQqnEZZEfhM3UMfSk8k8lop/cHduv/dppeNYnJh9W9n812/8u/0vho58EoC1\ny+crnOrGnc3N4XDiAXw6hFYtR9nWpyMzf9rB25/9pnC6huu++0aTmJiGWq1m587tSscRFkSKcgO1\nc5NhRHHf20bRyK7hLNForKoZvjYspZ1vEB2CupIQvYcjKXFKR7shB/b+g16vp3OPgUpHEf/RuLEz\nQUEhREZGUFhYqHQcYSGkKDdAZaUl7Nn6J46NmxLcpY/ScSxS1QxfR5JIS45j6MgxAPy1fIHCyW5M\n5IVR1pXXk4Vl6dWrN2VlZbKUo6gik4c0QFF7/6Eg/xy33fU4Go210nEsVu9BI9m/ZyPbNyzj0eff\no61vIFF7/+HE0cN14nps7ukskuL34d2hE02a1f3ViOqyq03KY+XsC8CCX1eRq/a84jZ39fYyWy5h\neaSn3ABt37gcgFtuldthrsU/uDsuzd2J3LMRXVkpw+4x3DZWV3rLe7etRa/X073vcKWjiKvwDeiM\nWm3FoXgZgS0MpCg3MNknMzgUF0GL1u1wa3Xlb+bCQK1WM+alD3n/qxVY22gJDutDKw8fInasIyfz\nmNLxrkmv17N7y2o0Gmu69Bxc9fMZ7z3PH79+o2AyUd3hQ9FobRuRmhRHcVGB0nGEBZCi3MCsW74Q\nACu1lcJJ6gbvDp1wbmKY6EGtVjN05JNUVJTz9x8/KJzs2jLSEjl5LJXg8L7YOxjm7T57Jpv9ezez\ncc1PCqcTlXZsWkFRYT7oK0hOiFI6jrAAUpQbEF1ZGXt3GOY8HnL3kwqnqZu69ByMi1trdv6zkrNn\nspWOc1V7tq4BuOTU9ZZ1/4P/b+++o6Oo3gaOf7enk57Qexekt1CUDiKC9CrlR5HeCaAUUboUpQgC\nL6hgaAkiXaQLhiAIEqqAtFBDSM/Wef+IrITdUENmk9zPORyS2Tt3nr27mWfKnXuBfIVKyhKTYKvm\nOy2tP5879buMkQiOQiTlHOT4b7swGvRodU5UriVmpnkVKpWaZq17YjIZ2b7JMZ9bNpmMHDu0AzcP\nL96qEGRdfvr4AQAq1xSfvaN4q2IQCkXqbvjMn2IcbEEk5RxlR1hqB6Xqdd8Tva5fQ813W+IbkI9D\nezbx4N4tucOxcSriAPGxD6lWuylqzX+f851bVwHRwc+RKJVK60xdd25eceirL0LmEEk5h7h3+zq3\nb6Y+lvF4hCrhxVksFs7/dYzIP4+gVmt4v31/zCYTWzcskzs0G/t3rgOgXpP21mVX/z6DyWTEPZcX\nTs4ucoUm2FHqrarWn8+KS9g5nkjKOcTjx6BatO+Hr3/Onjf5VSTExTB/6gA2fTcfSZKoXqcZufMV\n4ej+n7lz6x+5w7O6ePECF85EUKpcNevc0ACeXn7UbtCaJh90kzE6wZ7673WmcPFyAJw9dVTmaAS5\niaScA5iMRo7s/QlXd0+aiQ5er8TD04cK1d7h5rWLXLlwCqVKxQedBiJZLISt+Vru8KxWrUqdH/vJ\ns2QAL58Aug+YROvOH8sRlvAM+QuVIHj6d+Ty8uPcqd+xWCxyhyTISCTlHODPY3uJj4uh1jvvo9Hq\n5A4ny3q3aQcA9u1IncihYvX6FClZnpPhv3Lp7Ak5QwMgISGBdet+xNPbj7er1pM7HOElKBQKyrxd\ng/i4GG5duyh3OIKMRFLOAQ7+sglInaJReHUlylYhT4FiHD+6h0cx91EoFLTvMQqA9avmyH6GExLy\nA/HxcdRp1EZ05MuCylSoCUDkn+ISdk4mknI2dzfqGuf/OkaJspXT3GMUXp5CoeDdZh2xmE0c3pM6\ny1aREuWpVrsp1y6f5dihHbLFZjAYWLToK1xcXHjnqUvXQtZQpnwNFAoFZ04eljsUQUYiKWdz2zel\n3mOsXuc9mSPJHqrXaU6XvhNo2KKLdVnrLkNQa7Rs+n5+6uhMMti4cR23bt2kW7ceuOfyTvOawZAi\nS0zCy3HP5U2hYm9xMfIEiQlxcocjyEQk5WzMoE8h4vBOANxzeckcTfbg5OxCvSbtcHJ2tS7z8c9D\n8w97Extzn59+XJTpMZnNZr76ai4ajYaPPx6c5rXrV88zqFMNvpzUN9PjEl7Ovu0h/PN3JCCJXtg5\nmEjK2djBXzZhMhlxdnGnfGUxb/Kb1KR1TwLyFGTfznVcu3w2U7e9ZUsYV65cpmPHLuTJk/Zxt73b\nfwTAyck5U2MSXl5g/iJIUmq/hNPHD8ocjSAXkZSzKUmS2LU5dfKJBu91RqkSE1C8SRqNls59xiNZ\nLPyw9HPMZlOmbFev1zNt2meo1WoGDRpm8/rZfzsN1WncNlPiEV5d6XLVrB30Tv9xCIvZLHNEghxE\nUs6mLp45TmzMA5RKFQ3f7/L8FYTXVrp8dWrUa8G1y2czbc7lb7/9hmvX/qF3774ULlwkzWtJSQk8\nengPpVLFWxWD0qlBcCT5CqdOFpKcGMfVS3/JHI0gB7XcAQhvxk8hqXPmlq9SFxdXD5mjyTibD12x\nu9zVVUdioj5TYzEZjZwI/5Wyb9fE1T0XAB16jeHCmQi2bliWmgjrFHlOLa/u/v37zJ07Cy8vL0aO\nHGvz+t7tawHIV7A4SqU4/s4KatZ7n38unQFSz5aLlqogc0RCZhN/qdlQTPRdLl84hV9gPtp9NFLu\ncLKtA7s3sHxeMId/DbMuc3XzoMegz7CYTaxYMIGkpKQ3tv0ZM6aSkBDPmDHj8fS07cgXdf1vIHUC\nDSFrqNOwNaAAxH3lnEok5Wxo/871SJKFZq174xeYT+5wsq0a9Vqgc3Jm7/YfMZmM1uWly1enQYsu\n3I36hxEjBiFJUoZve+/ePXz//SpKly5D9+72h07tO2IWc1bspZ64n5xlqDVapi3ZSvnKdbl1/RL3\nbl+XOyQhk4mknM0YDXoO7QnF1S0X1eo0kzucbM3VzYPaDVoTE32X47/tTvPah12HUrTk24SGbmTJ\nkoUZut2HD6MZOnQAGo2GhQuXotGkP3qXh6c3ao02Q7cvvFm+/nmpWKM+ACfD98ocjZDZRFLOZiJ+\n20VCXAx1Gn6IVuckdzjZXoMWXVAqVez+aXWaM2KNRku/0XMIDMzNZ599yq+/7n5GLS9OkiRGjx7O\n3bt3GDt2AuXKvZ0h9QqOpXyVeiiVKpGUcyCRlLMRSZLYtyMEhVJJvSbt5A4nR/D1z0vlmo24ee0i\nF85EpHnN08uPlSu/R6vV0rNnVw4ffv17hLNnT+fnnzdTvXpNBg4c+tr1CY7J3cOLEmUrc+XiaW7f\njpI7HCETiaScjVw4E8G1y2cpU74GPv555A4nx2je9n/0GzWbEmUq27xWpUo1Vq1ag8VioWvX9vz+\n+5FX3s73369izpwZFChQiOXLv0Mlnj3P1ipWT72EvX37VpkjETKTSMrZyPpVXwKgc3aROZKcJW+B\nYlSu2SjdAVrq12/E8uXfYTAYaNu2JT/++MNLb2P16pWMHj0MHx8f1q8PJSAgIN2y61bOYt3KWSTJ\nNA63kDEedx7cvv1nmSMRMpNIytnEzX8ucvOfCwC07T5c5miEpzVt2pw1azbg4uLC0KEDGD16OLGx\nj567nsFgYPTo4YwePQwvLy/WrNlAkSLF0i1vsVjYv3M9v25bi1EvJqLIyrZvTJ1M5vDhgzx48EDm\naITMIpJyNrFu5WwASpatgq9/3ueUFuTw7rsN2LVrP6VKlWb16hXUqFGRFSuW2U3OZrOZdevWEhRU\nhdWrV1C2bDl27dpPpUpVnrmNn34Kw2w24eUTQC4v3zf1VoRMUK5SbSC1r8iWLWHPKS1kF2JEr2zg\n+vVrXIhM7WTUvtcYmaMRnqVw4SLs3n2AZcsWM2/eHMaNG8WnnwZTq1YdChQogIuLC1euXOb48WM8\nevQIrVZLnz79GT9+Eq6urs+tf9my1JHcqgQ1edNvRXjDmn3Ym98PbgMgLGwjvXr1kTkiITOIpJwN\nTJ8+FYD8hUuRv1AJmaPJ2VKSkziwaz1BDVrh5u5pt4yTkxNDhoygQ4curF37Hdu3b+XgwX1pyhQq\nVJjWrdsyePBw8uXL/0Lbtlgs/PnnSQCatu75em9EkF3u/EVwcfUgKTGO8PCj3Lhxnfz5C8gdlvCG\niaScxUVHR7N9+8/k8vSlx6DP5A4nx/tt72Y2fT+fpMQ4WncZ8syyAQEBDB8+muHDR/PwYTQxMQ9J\nTEwkMDAP/v7+L73t9et/xGw24e2XG3cPMX92dvB21Xoc3Z/a0SssbBNDhoj+ItmduKecxa1YsZTk\n5GSafthLnCU7gNoNW+Ph6cPe7SHEx8W88Hre3j4ULVqc8uUrvFJCBmje/H0+/ngILdr2faX1Bcfz\nfof+1K37DiqVirCwjXKHI2QCkZSzsMTERFasWIq3tze1G7SWOxwB0Omcadq6J/qUJH7Z8n2mbtvD\nw4MpUz6ndkPxXcgufP3zsnHjFho1akJk5F+cP39O7pCEN0y2y9d+fu5ybTrLSa+t1q5dSUxMDJMn\nT8bbx/79y5zE1VUndwgANGvVhd0/rWbfjhBgBn5+fpm6/ee1g6O0U1bgCG3l5+dOz54fsXPndn7+\neSN16sySOyQbYn+ecRTSm5jC5gXcvx8vx2azHD8/d7ttlZycTPXqFYiLi+PEiTMcjIyVITrHIcd8\nys/y67a1rFs5ixkzvsz0XrPpzTkNjtdOjsxR2qpVnSLo9XrKly+BSqXm1Knzz5yEJLOlt48SbL3I\nwYu4fJ1FLVgwhzt3btO2bQe8vX3kDkd4St1GbRg55VvxGIuQIXQ6HW3atOfBg/vs2ZMxk5sIjkn0\nvs6CkpKSWLToawDKlxezBDkijVZHybeqPvOs9Vla1SnywmW3bfuZChUqkDfviz06JWRN7dt3Zvny\npaxd+x3Nmr0ndzjCGyLOlLOgOXNmoNen4OPjS9euH8kdjiAji8VCv349qVixLPfv35c7HOEN6to1\ndea33bt3cvfuHZmjEd4UkZSzmPj4OOuoTZMnT0WpFB9hTvbtt0swGAzky5c/0zuUCZmrRo0gIHXY\nzXXr1socjfCmiD16FjNp0gQMBgP+/gG0a9dJ7nCEl/Am+lQuWbIQQMytnANMmvTf4EArV36LyWSS\nMRrhTRFJOQu5e/cO69f/CMDs2fPFWXIWYTQa2PjdPFZ+9UmG1hsZeYaoqFtotTp69vxfhtYtOJ78\n+QtSqFBhAKKibrFr1w6ZIxLeBLFXz0LmzJmJwWBg4sSpoqNHFqJWa7h09gThB7dx+cKpDKt30qTx\nADRr9p44QMshnrwismLFUhkjEd4U8ZecRVy6dJEfflhF0aLF6N9/oNzhCC9BoVDQ9qMRAGxY9SUW\niyVD6m3dui0FCxZiypQvMqQ+wfF169aDAgUKEhCQm8OHD3Lu3Fm5QxIymEjKWYAkSXzyyVjMZjMT\nJ05FrRZPsmU1xUtXpFLNhly5eJrwf6fje11dunQnIuI0efKI+bNzCqVSyfHjfzFr1lwAli8XZ8vZ\njUjKDkRvNHP3YVKaf1H3E9gQ+hP79v1KjVp1qVjtHZsydx8mYbbIMjCb8BLafTQSjdaJTd/PJzkp\nQe5whCysceOmFChQiA0bfuTevXtyhyNkIHHK5UBiE/QcjUz7/KFOq2Dip2NQKlU0bTeE38/etbuu\nwWjGWSc+Tkfm45ebZh/2Iur63xiNBpyfUfZVBx0Rsp/0vgu1m3Rm7bfTGPXpND7sajtN6MsMQCM4\nDnGm7OBCVs7j4YM75M5XhDwFiskdjvCa3mvbh74jZ+GRy1vuUIQsLqj+B3h4+rB/13qSEuPkDkfI\nICIpO7B7t2+wc/N3ADRp1UPeYIQMoVAoXmv9yD+PcDHyjwyKRsjKNFodtRt9SEpSAvt3rpc7HCGD\niKTsoCRJYvHMYUiShQJFSlO9bnO5QxIcwIoFE5gzsTdn/zwqdyiCzJKSEti5aQUAv2z5npTkJJkj\nEjKCSMoO6tCeUKJuXEapVPLxmLmvfYYlZH0Hf9lEQlwMLq7ulKlQU+5wBJm5uLgRkKcQAIkJsfy6\nbY28AQkZQiRlBxQX+5B1K1MnMm/ZoR8+frlljkh4U27fvMq6lbNe6NnlsB++AuCDjuI5dSFV1/7/\njRK3I+z/SIh/JGM0QkYQSdnBSJLEmqWfYzToqVC9Pm26ih1wdrYlZDG/blvLvh0hzyy3Z+saEhNi\ncXXLxbvNO2ZSdIKjK166EgF5CgJgSEliR+hKmSMSXpdIyg7m2KHtnAzfS/Eylek/ag5KlUrukIQ3\nqNP/gnHz8CL0hwXcvnk13XJbQlJnBmv70fDMCk3IInoPnWb9+ddta4m+f1vGaITXJZKyA7l18zo/\nLp+BzsmZHgOniPGMcwAPTx+69vsEo0HPt3PHYtCn2C039NPFVA1qQlD9VpkcoeDoChUrS/U6zalc\nqzEWs4mNq+fKHZLwGsRe30EYjUbGjPyYpMR4OvQcg19gPrlDEjJJpRoNqNu4LTevXWTDqi/tlila\n8m36jJiZyZEJWUXvYdPoM3wGRUqU54+jv3D21O9yhyS8IpGUHcTYsSM59ecfVKvdlKAG4mwop2nf\nYxSFi5cjf+GScociZFFKpZJOfcahUCgIWZE6o5yQ9Yik7ABCQzfwww+rUKvVtOsxSjz+lANpdU6M\nnbaauo3byh2KkIUVLFKauo3bcufWVZYs+VrucIRXIJKyzM6ejWTgwL4AfNC6A7m8fGWOSJDLk30I\nTEZDhk3xKOQsrToNwsPTl9mzp4upHbMgkZRlFBv7iA8+aIbZbKZcufJMnDJL7pAEB7Fk9khG9HiH\nKxf/kjsUIYsxm83odE4YDAYGD+6P0WiUOyThJYikLBO9Xk+zZg2IjX2Ep6cXYWHbUInHnwQg4sgu\n/vrjEMlJ8SQlxYkzZuGlmM1G62NRp0//ybx5s2WOSHgZIinLwGKxMHTox/z99yU0Gg1bt+7GwyOX\n3GEJDiDu0UNWLkgdpalGvfdZMnMkm76fL3NUQlbi5RNAh56jrb/PmTODgwf3yxeQ8FJEUs5kkiQx\nadJ4QkM3UrVqdY4cOUGJEqLHrZBq9qc9MZuM5C9cinY9RuDjl5tftnzHto3fyh2akIW827wjVapU\ns/7et29Pbt+OkjEi4UWJpJyJJEli6tRJLF26mBIlSvL99yEULFhQ7rAEB/Hz+qXcjbqGRqtj5GfL\ncXP3ZOini/Hxz8NPPy4SQygKL2X9+s24uLgA8PBhNH369ECv18sclfA8arkDyCkkSWL69KksXDif\nYsWKs2nTVry9feQOS3AgzT7szaWzJ2jRri8uLm4A+PjlZuSUb5nz6f8IW/MVCqWCpq16yhypkBXs\nOXmPIZ8uZfm8YHLnL8qxYwf5sGM3eg+b9tzRAlvVKZJJUQpPE0k5E5jNZnr16sqOHdsoXLgIoaFb\nCQgIkDsswcGo1WpGTF5qs9zXPy8jpizjq6kDyJu/mAyRCVlVkRLlmLZkG0aDnrlT+hHx2068/QJp\n022Y3KEJ6RCXr9+w5ORkPvigGTt2bEOr1bJp01YCA8VUjMLL8Q/Mz+T5oZSrXEfuUIQsSKPVMTB4\nPgF5CrJr8yp2hK6QOyQhHSIpv0G3b0dRs2Yljh37HaVSyTffrCBfPjGmtfBq1BqN3CEIWZibuydD\nP1mMt29uwtZ8LToPOiiRlN+QAwf2U716RaKibuHs7MxPP+2gRYsP5A5LcBAXzhxn+Ed1uXbl3GvX\n9eDerQyISMgJfAPyMmjcVyhVan76cRGhP3wlnoN3MCIpZzCz2cy8ebPp0KEVKSnJ5M2bn/DwP6le\nvabcoQkOIuLILuZO7kNiQhy7Nv/fa9V17nQ4nwxsyea1CzGZxMhNwvP9um0NFrMJgJ1hK1k+Lzjd\nKUOFzCeScga6fPkSrVu/x/TpUwkMzM2IEWM4evQPcQ9ZsFq3chbffjkWSZKoWL0BfUe83tCqzi5u\nePsGsn3TcqaN7cL1K+czKFIhu+r28USKl6lk/f34kd3M/rQX9+7ckDEq4THV5MmTJ8ux4aSk7DOt\nmF6vZ9GiBfTr14t//rlKixYfsGbNeho1aopa/eId3BNTjNy4l5BmmVarxmg0P3ddk9mCRp1zj7Fe\ntJ3kNGNcd078vgeARi2789HAya9dp6e3PzXfbUlC3CPOnPyNw3s3k5yUQNGS5VFrtDbls0I7OYrs\n2lYKhYKg+h9w/+5Nbl67CEBszH0O7/0Jv8B85C1QjFIFvV64PldXXbban79Jrq6655bJuXvxDCBJ\nEj/+uIZKlcryxRdTcHNzZ8WK71i58nvxDLJgQ6tzRqVSMyB4Pu0+GpFh9bq4utN9wCSGTVyCt08A\n4Qe3Z1jdQvbVa8jndO47HoVCgYurB5LFzLdzx7J45nAx+peMFJIkSXJs+P79eDk2myEkSWLLljA+\n+SSYu3fvANCxYxc++2wanp4vfoT5tHsxSRw5cyfNMldXHYmJzx+FJ1lvwlmXcx87f9F2kpPBkEJS\nQhye3v5vbBtGg547Uf+Qv5D9oVuzQjs5ipzSVreuXUKjdUKSLHz/zWdcjPwDNzd3hgwZTt++A6yj\ngqXHz889S+/PM5Ofn/tzy4ik/BL0ej0rVizl66/nEx39AACtVsuAAUMYPXocmtd8ZEUk5VfnSDvQ\npKQEtBqt3cvHr+Ju1DUM+mQM+hSMRiMmkwGTyUj5ynXtjsy0fdNyjAY9JpMRk9GAyWjEZDLyTpN2\n5C1YELXGLU35hdOHYjTqkSwWLBYzln//HzVlhd3HsGaM647ZbEKhVKJUKFP/V6oY9uliNFrby3Nr\nln4BCtBodKg1WjRaLRqNjoYtutqt/5+/z6BWa9E5uaBzckbn5IJGq3vuKFQZzZG+U5nFYrHw297N\nbF+/iOjoaPz9Axg6dASdO3fH1dXV7joiKb+4F0nKOXcv/oIkSeKvv06xfv2PbNgQQkxMDAA6nY6e\nPfswduyEdL+sQs4Sff8261fO5mTEPmo3aE23/p+iUCjSlJEkifWr5pAYH0tiQixJifHoU5Iw6FOY\nNG8jGjuJfMrwtnZ7Vn+99ig6nbPN8m0bv8VosE0ml87+QfT927xVqTa13m1JuUp1UGs0nDv9e5ry\nCoUChVKF2WJCjW3SvHv7OiajHovF8m8ityBJFnjqvT526Ncwa2/fJzVs0dVu+VkTetp9vwvX/o5W\n52Sz/Js5o1CrNeicXHB2ccPZxQ0XV3fqNGqDWm0bvyRJNp+LkEqpVFKn4YdMHtWXgQP7snPndiZM\nGMusWdPo0eN/dO7cjcKFxRCcb5JIynaYzWaOHv2NnTu3sWPHNm7cuA6Ar68fXbp0p0SJkvTq1Red\n7vk37YWsSZIk9CnJ/ybOOBLj4yhepiIqVdo/GZPJxOejOnDvzg1Mxv86uxzeE0q7j0bg7JL2rFSh\nUHB03xaSElPPLJRKFVonZ7RaJ4wGvd2kXKdRGxQKBVqtE2qtFo1Gi0qtQam0P//24PELUSqVqDUa\n1Gotao0GCTh36neOHdzKqYj9nIrYj5uHFxWqvcOcFb+i1mhR/nvG+7yENW/V/hdowf989lUYJqMB\no9GAyaDHaDRgNOhR2ekEKUkSDVt0Ra9PTv2XnIT+36sE9s7CLWYzJ47usbvdeo3b2a1/YMdqaJ2c\nrQnc1S0Xbu6e/G/4dJvPF+D+nZu4unvg7OKeY5K5u7sHJtN/ndxiY2NZsOBLFiz4kqCgOrRs2Zr3\n3muJv/+buxWTU4nL16TuWE+cOM7mzZs4dOggV678jdGYeqTu7u5Bo0ZNeP/9VjRu3PS1L1E/i7h8\n/eqe1U5xj6KtZ6VJCXGpSTYhjqAGreyeaU4a+iH37lzHbEp7djd7+R5yefmmWbYjdCVha76y/u7k\n7ErufIXx8gmkW/9PcXW3nSc76vrf6JxccHXPhc7JJVN39K6uOs5Hnubovp8JP7gND09fJs3bkGnb\nz2iSJJGUGI9Bn0xKchLJSQkkJ8aTkpJI5ZqNbMobjQbmTelHUmL8f2WTE9FonVj04+9pyrq66nj0\nKJ6BHVOnQFSq1Li6eeDm7ol7Li9GTllu89lZLBYun/8TVzcPXN09cXXLlSVHYns8IcXOndv54ovJ\nXLhg/1G7smXL0bhxQypXrkHNmkG4u3tkZphZjrinbEds7CPOnz/PuXORnDsXydmzkUREhNuMauPp\n6cWCBYto0KAxWm3G3Bt8HpGU//P4a2kvYZ3+4yCxMQ/+TbDxJCXGYdAn0bb7SNxzeduUD+7XjIcP\nbtss/2LRVvwCbYc9nf/Zx6QkJ+Lilnp2ZNQnEx//iEHjvsLVLe1Ox2BI4YvRnalRrwWN3u+aYfeR\n35Qnv08Ws5nYRw/w8rGdHOX8XxGErJhB4eLlyFewOIF5CxOYrzBePgGZfm/3TTMZjSQlxePx1HfH\n1VVH9IOHhKycRULcIxLjH5EQ/4iE+FiUSiVfrtxrU1diQhzDP6qbZpnOyQVv30CmLAi1u+1jh3fg\n5u6Jq5sHLm65cHF1x8nF1e4BY2Z5epaoW7duMHPmNLZv38q33/4fFy9eYPfunUREhJOSkjrw07cZ\n/QAAF2NJREFUiEKhoEiRYlSsWIkyZd6iTJmylC5dhoCAwGz3nXlVOSop6/V6oqMfEB39gHPnznLt\n2j9ERUVx8+Z1bt26xYMH95EkC7GxsWnWS71kp8TDw4Ny5d6mSZPmNGv2HnnzZv4Y1VkhKUuShNlk\nwmjUo9U52b3cdzHyDxITYjEa9BgMekxGPUaDgRrvtMDdw7Z3+sqvPuHOravoU5JJSU5En5JESkoy\nk+ZuIHe+wjblPx3cirtR/9gsnzRvI3kL2M6itHH1XJKTE3F19cDZ1f3fnZ8HZSvUsrm8DKlJ+d6d\n6yTExpCSkmRdPmV+KLnzP/9+msVsxmwxo1Kp7e6MHj64g0GfgsVswmwxYzaZsFjM5C1QHJ2T7Y44\n8s8jJMbHYjabsVhMqfWbzVSu1chue/66bS0x0XexmM1YLGbM5tR13mvXl/wFC9p8n9Ys/SL1ysC/\n5S1mM3GPool99MDm3nRQ/VZE37/NnVtXUSiVKFCgUCqQJIl2PUZSpHg53Nw901xqXjZ3LHejrqFU\nKlEoFCiVKpQqFR8NmExAHtv5xDevXUhM9N3U9lOpUCpVqNRqGrfsbvcAIvzgNhIT4lLLqVLrVqk0\nlKtU2+6VimtXzmEy6K11K1UqVEoVfoH508T9+G/v8a2Gx5+nUqUCFKhUtrcPkhLj2bV5FUkJcSTE\nPyIxIY7EhEdotDqCp31nUz4m+i5j+zaxWe7h6cucFbaX5RMT4vjx22k4ubjh5OyK87//e3j6UDXI\nth6z2UTco2i0Ome0OifUas0LXZl50akbU1JS+PvvM2ze/DNffTXPbhmNRkOBAgUpUKAg+fMXJCAg\nAG9vH3x9ffH29sHHxxcfHx+8vX3e6JVIR+CwHb2aNGnCvXv3MJslzGYTZrMJkwnq129AoUIFMRpN\nqfedjEYMBgM//riGpKTEf8ta/t3RmPH19UOtVhMfH098fNxzt+vr60fDho0pXrwkpUuXoUyZshQv\nXpJBg/rz6FEMZrOFbdu2snXrVgDGjBlHrVq1bOrp2rUTMTGpva8l6b8z7ODgSdStW9emfIcOrXj4\nMBpJArP5cXmJCRMm07BhY5vyM8Z1IyE+FiyAInUbkgRtPhpO5RoNbMpPGdaW+IRYHv+pSamB0aHn\nSKrWbmZTPrhvM5KS4pAkCQmQLBaQoGOfMdRp8KFN+SFda5OSnGCzvF3PsTRq0clm+bzPBmA22R5I\nSCho3NK2c0/Eb7swWzv2KFJ3GgoFZ07+ZjcpJyXGodU5A4rH7xaFQsGlc3/aTcr7d67HYNBbyz7W\non1/Wnbob1P+7KmjNssATkYcsJuUB3cJQp+SaLO8U5/xvNu0vc3yTwa1THP/+bH2PUfTsEUXm+Vf\nTxuKxWzb8SklOZmmrT+yWb5+1ZdIFttBL7z985C/+0Cb5Qd/2ZTme/xYszZ9qBrUmNs3r3D75hXu\n3PqHYqUrcGT/z3brXzp7lPVnnZMzbu6eNHy/G8eP7AY7x/6rF0+mfJW6aLXOqNRqVCo1BYuUYnvo\nCrvlDcmJ1G7UBsW/Pb4VKMjl5cvKryYiSbbxNHi/O+80bpPm4MHF1Z3pwd3ttmeL9h9Tr3Eb6+9G\nvRazRc3IXg0wm2w/r/c7DaRug9ZplumcXNi3Yx0pyYn/9nv7969SoWD3lh+oUffpv0clzq7u6FOS\nQAIJCUmC+LgYDuzeRMXq76YpHRvzgGOHd9rEAmA0plCuYtpZxOJiHzJleFubskqVml5DP6d0uepp\nlicnxfPFmC4Mx/LvAVTqSYtGo2XOnK+oXj1t+ZSUFAYNGsSjR7Go1WpMJtsOfSVKlCQq6haXL/9t\nN+6neXh44OLigrOzC05Ozty+HYXFYsFg0P93YKRUULBgIby8vClWrDgqlRq1Wo1Go+HAgX3o9XqS\nkpJQKpWoVKkHgxUqVCEgwI98+QpYDxDVahXbtm0lOTmZpKTE1E6O/x60VKlSlcDAPOTNm9e6XKVS\n8/PPm0lISCQ5+XF5sFigZs0gAgNzkzt3blJ3YQrUag2hoRtJSkokMDAPixcveO77l+VMOSPvoRUo\nUAg3Nzd8fHzx8/PFx8eXb7/9xm5Zf/9Azpy5aGe5/fsggYGBnD6deeUfxqVw+nI07ZuUtlve08ef\nZWsP2CxPr3wuL19mL7c92u7bpkKGlPf08WfWst0vXN7LN5CZS213KOmV9/HPw/QltgNhpF8+L9OX\nbHvx8n65mf7NjhcuX6hoWcbPWvPi5Yu/xfgZP7xw+aIlKzB22qoXLl+sVEXGfGE7dnZ65UuUqcyk\nuT/YnCmnV77kW1UZOcV2JqF0vw9e/hQvU4mE+BgS4mNJiH/Eu806EPr983dEj73foT8/r7P/9yvK\nw3vt+rJtw7IXLt+oZTd+2fL9C5d/p1kH9u9Y98Lle/fuy4oVLx7Phx+2IzT0xfswqNWabDWm+4uk\nW9kuXwuCIAiCkJa4+y4IgiAIDkIkZUEQBEFwECIpC4IgCIKDEElZEARBEByESMqCIAiC4CBEUhYE\nQRAEByFLUn748CF9+vShe/fudO7cmdOnT8sRhsMzm80EBwfTpUsXOnbsyIkTJ+QOyaEdO3aMWrVq\nceCA7bPcAkyfPp2OHTvSqVMn/vrrL7nDcWgXL16kUaNGrFlj+1y68J9Zs2bRsWNH2rVrxy+//CJ3\nOA4pJSWFYcOG0a1bNzp06MD+/fufWV6WEb22bNlCq1ateO+994iIiGDBggWsWLFCjlAc2k8//YSL\niwtr1qzh77//Zty4cWzYkHUnD3iTbty4wapVq6hSpYrcoTikiIgIrl27RkhICJcvX2bChAmEhITI\nHZZDSk5O5vPPP6dmzZpyh+LQwsPDuXz5MiEhITx69IjWrVvTqJHtJCA53d69eylXrhy9e/cmKiqK\nnj178s4776RbXpak3KNHD+vPUVFRBAYGyhGGw/vggw9o0aIFAN7e3jbjdgv/8ff3Z9GiRYwfP17u\nUBzS0aNHadiwIQBFixYlLi6OxMREMRe4HTqdjuXLl7Ns2YuPVJUTVatWjbfffhuAXLlykZycLOaq\ntqN58+bWn6OiosidO/czy8s2rdCDBw/o378/SUlJrF69Wq4wHJpKpbIOer969WprghZsibmtn+3B\ngwe89dZb1t+9vLx48OCBSMp2KJXKTJsZLitTKBQ4OTkBsH79eurVqycS8jN07NiRe/fu8c03zx5W\n9Y0n5Q0bNrBx40YUCoX1KGrw4MEEBQWxceNGDh48SHBwcI6/fP2sdlqzZg1nz5597oeZUzyrrQT7\nnh5NV5zRCBllz549hIaG5vh9+POEhIRw/vx5Ro0axZYtW9It98aTcrt27WjXrl2aZREREcTFxeHh\n4UHdunUZM2bMmw7D4dlrJ0hNQPv372fx4sV2p4rLidJrKyF9AQEBPHjwwPr7vXv38PX1lTEiITs4\ndOgQy5YtY8WKFbi52U6DKkBkZCQ+Pj4EBgZSqlQpzGYzDx8+xNvbdu53kKn39e7duwkLCwPgwoUL\n5MmTR44wHN6NGzdYt24dCxcuzPbzjGYkMceKraCgIHbt2gXA2bNnCQgIwMXFReaohKwsISGB2bNn\n88033+Du/vx5gnOqiIgIVq5cCaTeRkpOTk43IYNMs0TFxMQQHBxMYmIiRqORCRMmUL58+cwOw+HN\nmzeP7du3kzt3buvlxpUrV6JWy9YVwGEdOHCA5cuXc/XqVby9vfHz8xOX054yd+5cjh07hkqlYuLE\niZQsWVLukBxSZGQkM2bMICoqCrVaTUBAAAsXLsTDw/4UrDnV+vXrWbhwIYUKFbLun2bNmiU67j5F\nr9czfvx47ty5g16vZ/DgwdSrVy/d8mLqRkEQBEFwEGJEL0EQBEFwECIpC4IgCIKDEElZEARBEByE\nSMqCIAiC4CBEUhYEQRAEByGSsiAIgiA4CJGUhVd24MABunbtykcffUS7du0YMWIECQkJAJw8eZKb\nN29myHbq1atHVFTUa69/6NAhli5d+trxjB49ms2bN792PY91794dSZJISUmxTn+XUbG+iTqftHDh\nQhYsWPBS6zxriMGs7N69e/z+++8AhIWFsWnTJpkjErIikZSFV2I0GhkzZgwLFixg9erVbNiwgbx5\n87Jx40YAQkNDuXHjRoZs63XHaH68fp06dejXr19GhJShvvvuOxQKBZGRkezevRvIuFjfRJ2vw2w2\ns2jRIlljeFPCw8OtSbl169a0adNG5oiErEgMDSW8Er1eT0pKComJifj4+AAwcuRIIHWA+p07d/LX\nX38xbtw41Go1c+bMQafTkZKSwqRJkyhdujTjxo3D39+fCxcucO3aNdq0acP//vc/oqOjGTZsGBaL\nhdKlS1uHzUxOTmbs2LHExsaSmJhIkyZN6NOnD8eOHWPJkiXodDoaN25MvXr17K4fFhbGkSNHGDFi\nBGPGjLFOaHHy5EnWrl1L+fLlmTdvHidOnECv11O1alVGjx4NwLhx47h06RJ58uQhKSnJpj26du3K\nxIkTKVGiBDNmzOD8+fOsWrUKs9lM/fr12b9/P19//bV1px0YGMjs2bNRqVSUKlWKEydO8MknnxAf\nH8+cOXMoWrQoR44cYfbs2dSvX5/u3btz6NAhbt26xeTJk6lRowaRkZF8+umnuLq6UrduXb7++mv+\n/PNPlEql9TN6Vp2dOnXi0KFD3L9/n7FjxxISEsKVK1cYMGAArVq1Ii4ujkmTJhETE0N8fDw9e/a0\nO1PZ9evX6d+/P/fu3aNatWoEBwcD2G3LCRMmcPv2bXr37o1er39um+3YsYM1a9YAqdOXfv755+TK\nlYvw8HAWLlwIgEajYerUqeTNmzfdtnrS7du3mTJlCikpKSQlJTF8+HBq1qzJuHHj0Gq1XL16ldmz\nZ9OpUydWr15N/vz5OXbsGPPnz2ft2rV069aNsmXLcunSJe7fv0+/fv14++23mTdvHgCenp4kJCRg\nNpsZOnSodex6Z2dnnJ2d+eyzz/D390831tWrV/Pzzz9by8+ePZtcuXK96p+qkNVIgvCKli5dKlWo\nUEHq1auXtGTJEunKlSvW17p27SodPXpUkiRJ+uWXX6QLFy5IkiRJW7dulYYMGSJJkiQFBwdLI0aM\nkCRJkm7duiVVrlxZkiRJmjt3rjRnzhxJkiQpMjJSKlWqlHTr1i3pxo0b0k8//SRJkiTp9XqpcuXK\nUkJCghQeHi5VqVJFiouLe+b6oaGh0ujRo9O8hx9++MG6bMeOHVJwcLD1tYEDB0r79u2TDh8+LHXo\n0EGSJElKSkqSgoKCpLCwsDT1LFmyRPrhhx+s771nz56SwWCQTp48KQ0ePFgym83SsmXLrOV79eol\n7d+/X5IkSSpVqpRkNpvTxPfkz++++64UEhIiSZIkhYWFSQMGDJAkSZI6deok7du3T5IkSQoJCbHW\n86Rn1blp0ybr59CzZ09JkiQpPDxcat26tSRJkjRlyhQpNDTU+r4bNWokPXz4ME39X3/9tdSqVSvJ\nbDZLBoNBatiwoXTp0qV02/LmzZtSvXr1JEmSpMWLFz+zzW7fvi21bNlSMhgMkiRJ0urVq6UZM2ZI\nycnJUpMmTaTY2FhJkiRpz5490uDBg5/ZVk/q27evFB4eLkmSJN2/f1969913JbPZLAUHB6f5ftSv\nX1+6fv26tV06d+5sjXXq1KmSJEnStWvXpFq1alnbYv78+Wl+Tk5OloKCgqS7d+9KkpT6fRs3btwz\nY61cubIUHR0tSZIkHT58WLp48aLNexCyL3GmLLyyvn370qFDB3777Td+//13OnTowIgRI+jYsSPw\n38QQfn5+zJw5E4PBQFxcXJqj/mrVqgGQJ08eEhMTkSSJCxcuWOsoU6aMdfYZHx8fjh8/ztq1a9Fo\nNBgMBmJjYwEoXLiwdVD8p9dPb7D8kydPEhYWZj0TCw8P5+TJk9Z7vImJidy8eROj0UjFihUBcHZ2\ntk7s/qRatWrxf//3f7Rs2RInJydKlSrFqVOn+OOPP6hTpw5KpRKlUkmnTp1Qq9VcvXqVmJiYF27r\nJ9vp8Xs+d+6cdXmTJk2YPHnyC9cHWN9TQECAdbziwMBA4uLirO1x5swZQkNDAdBqtdy8eRMvLy+b\n2B6/v3LlynHp0iWOHTtmty2LFy9uXS8oKOiZbXby5Enu379P7969kSQJo9FIvnz5uHjxIvfv32fQ\noEFIkmQzDaW9tnpSeHh4mqsdWq2W6OjoNG0Cz57YpE6dOgAUKFAAhUJhXf9p//zzD35+fvj7+1tj\nCwkJeWas7dq1o3fv3jRp0oSmTZtSqFChdOMQsh+RlIVXlpKSQq5cuWjevDnNmzenadOmzJw505oQ\nHxszZgxTp06lWrVq7N+/3zpjCmAzHeXjHeGTO1mz2QzA6tWrMRqN1p3ak5cln55F68n1TSaTTewP\nHjxg4sSJLF68GJ1OB6TunDt06EDPnj3TlF25cqX1kvCT8Tzprbfe4uLFixw7doyqVatSsmRJIiIi\nOH78OFOnTuXEiROEhoYSGhqKTqdjyJAhNnU8y5OTkDxuoyeT0ZPxvUqdT34Oj+vXarVMmjSJsmXL\nPrOeJ7dtsVhQKBTptuWtW7esPz+vzc6dO0f58uVt5hE/f/48efLk4bvvvnvu+7KXWHU6HQsXLrR7\nSfjJ79GT3yGj0ZimnMViSbONZ/V7eDKGp8vai3Xs2LHcvn2b/fv3M3DgQIKDg60HAUL2Jzp6Ca/k\n8OHDdOjQgcTEROuya9euUbBgQSB1R/04GUZHR1OsWDEsFgs7d+7EYDDYrfPxTqlo0aKcPHkSgFOn\nTpGcnAykJtKiRYsC8Ouvv6LX6+3Wld76j5nNZoYPH86oUaPInz+/dXnlypX55ZdfrEl30aJFXL9+\nnaJFi3Lq1Ckgdbq606dP22xTqVRStGhRNmzYQLVq1ahUqRIRERHExMSQJ08eoqOjyZs3Lzqdjlu3\nbnHq1Clr7E8eiNg7gEhPkSJFrO/zcWeup71snU+qXLky27dvB1IPwKZMmZImGT127NgxLBYLBoOB\nM2fOUKJEiXTbUqlUWhPc89qsXLly/PXXX9Z5oHfu3MnevXspXLgwMTExXLp0CUidGm/Dhg0v/L4q\nVarEtm3bAHj48CHTp0+3W87d3Z3bt28DWPsCPPb496tXr6JSqfD29rbb1oULF+bhw4fcuXMHgCNH\njlChQoV0Y4uPj2fhwoUEBgbSqVMnOnfubPf7JmRf4kxZeCW1a9fm2rVr9OjRA2dnZyRJwtfXl4kT\nJwKplyYnTZrE+PHj6dOnD927dydv3rz07t2bMWPG2D3LeXwG0b17d4YNG0aPHj0oVqyYNXG2bduW\nESNGcPjwYRo0aMD777/PqFGjGDt2bJp60lv/sV27dnH27FlWrFjB8uXLUSgUdOrUiWbNmnHq1Ck6\nduyISqWibNmy5M+fn3z58rF161bat29Pnjx50lzifFJQUBAzZ85k0aJFqFQqYmNjqVy5svW1lStX\n0qVLF4oVK8bgwYNZvHgx1apVs77v8uXL8+WXXzJhwgSqVq1q0y5Pe3wFIiAggLp166JQKGzOmF+2\nzicNGjSITz75hM6dO2M0Gmnfvr3dM/LixYszdOhQbt68SfPmzSlSpAhFihSx25YWiwVfX1/atGnD\nmjVrntlm/v7+TJgwgX79+uHi4oKTkxMzZ85Ep9Mxe/ZsJkyYYL3KMXXq1Bd+XxMmTGDixIls27YN\no9HIgAED7Jbr0aMH48ePp3DhwlSqVCnNayaTiQEDBnDz5k3rd75KlSqMGDECjUZjbSedTscXX3zB\nsGHD0Gq1uLi4MG3atHRjdXd3JzExkTZt2pArVy40Gg1ffPHFc9+TkH2IqRsFIYsKDw/H09OTkiVL\nEhkZyahRo9ixY4fcYWV73bp1Y8CAAdSsWVPuUIRsSJwpC0IWpVarrWeLJpOJzz77TO6QcoTXfW5e\nEJ5FnCkLgiAIgoMQHb0EQRAEwUGIpCwIgiAIDkIkZUEQBEFwECIpC4IgCIKDEElZEARBEByESMqC\nIAiC4CD+HyWCVcWb+42FAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f41028e6c90>"
]
},
"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."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sunspot_df = get_rdataset('sunspot.year', cache=True).data"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\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</td>\n",
" <td>5.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1701</td>\n",
" <td>11.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1702</td>\n",
" <td>16.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1703</td>\n",
" <td>23.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1704</td>\n",
" <td>36.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" time sunspot.year\n",
"0 1700 5.0\n",
"1 1701 11.0\n",
"2 1702 16.0\n",
"3 1703 23.0\n",
"4 1704 36.0"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sunspot_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For this problem, the model is\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" x_i\\ |\\ \\lambda_i\n",
" & \\sim \\textrm{Poisson}(\\lambda_i) \\\\\n",
" \\lambda_1, \\lambda_2, \\ldots\n",
" & \\sim P \\\\\n",
" P\n",
" & \\sim \\textrm{DP}(\\alpha, U(0, 300)) \\\\\n",
" \\alpha\n",
" & \\sim \\textrm{Gamma}(1, 1).\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"N = sunspot_df.shape[0]\n",
"\n",
"K = 30"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to alpha and added transformed alpha_log_ to model.\n",
"Applied logodds-transform to beta and added transformed beta_logodds_ to model.\n",
"Applied interval-transform to mu and added transformed mu_interval_ to model.\n"
]
}
],
"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('beta', beta * T.concatenate([[1], T.extra_ops.cumprod(1 - beta[:-1])]))\n",
" component = pm.Categorical('component', w, shape=N)\n",
" \n",
" mu = pm.Uniform('mu', 0., 300., shape=K)\n",
" obs = pm.Poisson('obs', mu[component], observed=sunspot_df['sunspot.year'])"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 20000 of 20000 complete in 180.8 sec"
]
}
],
"source": [
"with model:\n",
" step1 = pm.Metropolis(vars=[alpha, beta, w, mu, obs])\n",
" step2 = pm.ElemwiseCategorical([component], np.arange(K))\n",
" \n",
" trace_ = pm.sample(20000, [step1, step2])"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"trace = trace_[10000::10]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the sunspot model, the posterior distribution of $\\alpha$ is concentrated between one and three, 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": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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eO5cghjRBAuL8VR1sDhdmjMvjve7c4XTjzGVNzPOCZUSsqHYWu4vXed0WR8Rj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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f410a903a10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace, varnames=['alpha']);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Indeed, we see that there are (on average) about ten to fifteen components used by this model."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_components_used = np.apply_along_axis(lambda x: np.unique(x).size, 1, trace['component'])"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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yBgDgFBB0Bn7xxRdr+vTpSk5OVkREhP/xYy+vCgAAGlfQAt+wYYMk6auvvvI/ZlkWBQ4A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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f4102756e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"bins = np.arange(n_components_used.min(), n_components_used.max() + 1)\n",
"ax.hist(n_components_used + 1, bins=bins, normed=True, lw=0, alpha=0.75);\n",
"\n",
"ax.set_xticks(bins + 0.5);\n",
"ax.set_xticklabels(bins);\n",
"ax.set_xlim(bins.min(), bins.max() + 1);\n",
"ax.set_xlabel('Number of mixture components used');\n",
"\n",
"ax.set_ylabel('Posterior probability');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now calculate and plot the fitted density estimate."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x_plot = np.arange(250)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"post_pmf_contribs = sp.stats.poisson.pmf(np.atleast_3d(x_plot),\n",
" trace['mu'][:, np.newaxis, :])\n",
"post_pmfs = (trace['beta'][:, 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": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Adg4/d+W79dMO6tmFb0Np2CJNXYQQQowmrtqkbS+UsxfJeb1WULcz9Vgs2yPd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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f41004227d0>"
]
},
"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.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": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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A1zJ1lar294vO2xrUqyskUxdCCNFxeFSmXl1tfabu6+uPt7ces9k6Qa6kxPHe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\nDYJNnYiIqEGwqRMRETWIPw9Yr150TyLuAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f41050d0510>"
]
},
"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['beta'][:, 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['beta'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0),\n",
" '--', c='k');\n",
"\n",
"ax.legend(loc=1);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have only scratched the surface in terms of applications of the Dirichlet process and Bayesian nonparametric statistics in general. This post is the first in a series I have planned on Bayesian nonparametrics, so stay tuned.\n",
"\n",
"This post is available as an [IPython](http://ipython.org/) notebook [here](https://nbviewer.jupyter.org/gist/AustinRochford/62c283a3f0fae90b5e39)."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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