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@ahartikainen
Last active February 22, 2019 01:22
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Simple example on PyStan
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pystan\n",
"import numpy as np\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import arviz as az\n",
"plt.style.use('arviz-darkgrid')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"prior_code = \"\"\"\n",
"data {\n",
" int<lower=0> N;\n",
" vector[N] x;\n",
"}\n",
"parameters {\n",
" real m;\n",
" real b;\n",
" real<lower=0> e;\n",
"}\n",
"model {\n",
" m ~ student_t(3,0,3);\n",
" b ~ student_t(3,0,3);\n",
" e ~ student_t(3,0,1); \n",
"}\n",
"generated quantities {\n",
" vector[N] y;\n",
" vector[N] y_hat;\n",
" for (n in 1:N) {\n",
" y[n] = m * x[n] + b;\n",
" y_hat[n] = normal_rng(m * x[n] + b, e);\n",
" }\n",
"}\n",
"\"\"\""
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_6c53dd550b9b14d90a204933b4726f91 NOW.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wall time: 42 s\n"
]
}
],
"source": [
"%time stan_prior = pystan.StanModel(model_code=prior_code)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"N_prior = 30\n",
"x_prior = np.linspace(0, 100, N_prior)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"stan_prior_data = dict(\n",
" N = N_prior,\n",
" x = x_prior,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"stan_prior_fit = stan_prior.sampling(data=stan_prior_data, check_hmc_diagnostics=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Prior"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x000001EA5802CEB8>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x000001EA5800C710>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x000001EA57FD8320>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x000001EA57FC1128>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x000001EA57F9C208>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x000001EA57F636A0>]],\n",
" dtype=object)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x432 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.traceplot(stan_prior_fit, var_names=['m', 'b', 'e'])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"y_prior = stan_prior_fit.extract(pars=['y'])['y']\n",
"y_prior_hat = stan_prior_fit.extract(pars=['y_hat'])['y_hat']"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(4000, 30)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_prior.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Prior predictive"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for i, yph in enumerate(y_prior_hat):\n",
" plt.plot(x_prior, yph, color='C0', marker='.', lw=0, alpha=0.1)\n",
" if i > 200:\n",
" break"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for i, yp in enumerate(y_prior):\n",
" plt.plot(x_prior, yp, color='C0', lw=1, alpha=0.1)\n",
" if i > 200:\n",
" break"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"N = 20\n",
"\n",
"# linear model parameters\n",
"m = 0.4\n",
"b = 34\n",
"e = 5 # noise term\n",
"\n",
"# x, y_true and observed y\n",
"x = np.sort(np.random.rand(N)*100)\n",
"y_true = x * m + b\n",
"e_arr = np.random.randn(N) * e\n",
"y = y_true + e_arr"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x1ea59d75c18>"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x, y_true, c='k')\n",
"plt.scatter(x, y)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"model_code = \"\"\"\n",
"data {\n",
" int<lower=0> N;\n",
" vector[N] y;\n",
" vector[N] x;\n",
"}\n",
"parameters {\n",
" real m;\n",
" real b;\n",
" real<lower=0> e;\n",
"}\n",
"model {\n",
" m ~ student_t(3,0,3);\n",
" b ~ student_t(3,0,3);\n",
" e ~ student_t(3,0,1);\n",
" y ~ normal(m * x + b, e);\n",
"}\n",
"generated quantities {\n",
" // posterior predictive distribution\n",
" vector[N] log_prob;\n",
" vector[N] y_hat;\n",
" for (n in 1:N) {\n",
" log_prob[n] = normal_lpdf(y[n] | m*x[n],e);\n",
" y_hat[n] = normal_rng(m*x[n]+b,e);\n",
" }\n",
"}\n",
"\"\"\""
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_7d1e497b4f1ae3375a40127da684dc80 NOW.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wall time: 50.7 s\n"
]
}
],
"source": [
"%time stan_model = pystan.StanModel(model_code=model_code)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"stan_data = dict(\n",
" N = N,\n",
" y = y,\n",
" x = x,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"OrderedDict([('m', array(0.35899218)),\n",
" ('b', array(34.83321192)),\n",
" ('e', array(4.39126598)),\n",
" ('log_prob',\n",
" array([-44.81372212, -34.69847686, -42.42557936, -39.75194983,\n",
" -24.4519068 , -19.36426266, -33.67878207, -32.14586911,\n",
" -38.33697397, -26.85609447, -61.20050896, -27.07409723,\n",
" -37.57858784, -31.11124821, -25.45105999, -36.87245722,\n",
" -32.34213404, -27.78958436, -33.83513586, -43.06393297])),\n",
" ('y_hat',\n",
" array([35.95639504, 43.68995848, 37.57363798, 39.83149799, 36.7789591 ,\n",
" 35.81695981, 38.86657944, 38.80969797, 45.20568127, 58.06103361,\n",
" 50.34087965, 60.02304789, 55.22581063, 52.80981958, 59.68379973,\n",
" 56.71086242, 53.98721138, 67.39437044, 50.16140893, 67.13483817]))])"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"stan_map = stan_model.optimizing(data=stan_data)\n",
"stan_map"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"stan_fit = stan_model.sampling(data=stan_data)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Inference for Stan model: anon_model_7d1e497b4f1ae3375a40127da684dc80.\n",
"4 chains, each with iter=2000; warmup=1000; thin=1; \n",
"post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
"\n",
" mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat\n",
"m 0.36 1.1e-3 0.04 0.28 0.33 0.36 0.39 0.44 1379 1.0\n",
"b 34.74 0.06 2.22 30.27 33.32 34.72 36.2 39.16 1365 1.0\n",
"e 4.9 0.02 0.81 3.66 4.31 4.79 5.34 6.83 1841 1.0\n",
"\n",
"Samples were drawn using NUTS at Sun Sep 9 10:11:38 2018.\n",
"For each parameter, n_eff is a crude measure of effective sample size,\n",
"and Rhat is the potential scale reduction factor on split chains (at \n",
"convergence, Rhat=1).\n"
]
}
],
"source": [
"print(stan_fit.stansummary(pars=['m', 'b', 'e']))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Posterior"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"axes = az.densityplot(stan_fit, var_names=['m', 'b', 'e'])\n",
"for i, ax in enumerate(axes.ravel()):\n",
" if ax.get_title() == 'm':\n",
" ax.axvline(m, c='C1')\n",
" elif ax.get_title() == 'b':\n",
" ax.axvline(b, c='C1')\n",
" else:\n",
" ax.axvline(e, c='C1')"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"yhat = stan_fit.extract(pars='y_hat')['y_hat']"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(4000, 20)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"yhat.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Posterior predictive"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1ea5a220828>]"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for i, yh in enumerate(yhat):\n",
" plt.plot(x, yh, color='C0', marker='.', lw=0, alpha=0.1)\n",
" if i > 200:\n",
" break\n",
"plt.plot(x, y, color='k', lw=0, marker='o')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Posterior"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"m_b = stan_fit.extract(pars=['m', 'b'])\n",
"m_hat = m_b['m']\n",
"b_hat = m_b['b']"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1ea5765c8d0>]"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for i, (mh, bh) in enumerate(zip(m_hat, b_hat)):\n",
" plt.plot(x, x*mh+bh, color='C1', lw=1, alpha=0.07)\n",
" if i > 200:\n",
" break\n",
"plt.plot(x, y, color='C0', marker='o', lw=0)\n",
"plt.plot(x, y_true, color='C4', lw=4)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@tommylees112
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You are such a legend! What a great snippet

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