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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sat Jan 1 16:01:52 PST 2022\r\n"
]
}
],
"source": [
"import numpy as np, matplotlib.pyplot as plt, pandas as pd\n",
"pd.set_option('display.max_rows', 8)\n",
"!date\n",
"\n",
"%load_ext autoreload\n",
"%autoreload 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PyMC3 Model in NumPyro\n",
"\n",
"From https://forum.pyro.ai/t/how-to-convert-a-b-testing-model-in-pymc3-to-pyro/312"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"from collections import namedtuple\n",
"from jax import random\n",
"import jax.numpy as jnp\n",
"import numpyro\n",
"import numpyro.distributions as dist\n",
"from numpyro.infer import MCMC, NUTS, Predictive\n",
"import arviz as az"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"PyMC3 Model:\n",
"\n",
" with pm.Model() as model:\n",
" p_A = pm.Beta('p_A', totalA, 1 - totalA)\n",
" p_B = pm.Beta('p_B', totalB, 1 - totalB)\n",
" delta = pm.Deterministic(\"delta\", p_A - p_B)\n",
" ADist = pm.Bernoulli(\"obsA\", p_A, observed=As)\n",
" BDist = pm.Bernoulli(\"obsB\", p_B, observed=Bs)\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"# NumPyro version of the model\n",
"def model(As, Bs, totalA, totalB):\n",
" p_A = numpyro.sample('p_A', dist.Beta(totalA, 1-totalA))\n",
" p_B = numpyro.sample('p_B', dist.Beta(totalB, 1-totalB))\n",
" delta = numpyro.deterministic('delta', p_A - p_B)\n",
" ADist = numpyro.sample('obsA', dist.BernoulliProbs(p_A), obs=As)\n",
" BDist = numpyro.sample('obsB', dist.BernoulliProbs(p_B), obs=Bs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"PyMC3 Inference:\n",
"\n",
" step = pm.Metropolis()\n",
" trace = pm.sample(20000, step=step, cores=1)\n",
" burned_trace = trace[1000:]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"sample: 100%|██████████| 3000/3000 [00:07<00:00, 423.52it/s, 3 steps of size 9.32e-01. acc. prob=0.91] \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" mean std median 5.0% 95.0% n_eff r_hat\n",
" p_A 0.59 0.19 0.59 0.30 0.91 2116.16 1.00\n",
" p_B 0.29 0.19 0.25 0.01 0.56 1293.08 1.00\n",
"\n",
"Number of divergences: 0\n"
]
}
],
"source": [
"# NumPyro version of the inference\n",
"rng_key = random.PRNGKey(12345)\n",
"\n",
"kernel = NUTS(model)\n",
"mcmc = MCMC(kernel, num_warmup=1_000, num_samples=2_000, thinning=1)\n",
"mcmc.run(\n",
" rng_key,\n",
" As=jnp.array([1,0,0,1,1]),\n",
" Bs=jnp.array([0,0,0,1]),\n",
" totalA=0.55,\n",
" totalB=0.45\n",
")\n",
"posterior_samples = mcmc.get_samples()\n",
"mcmc.print_summary() \n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"posterior_predictive = Predictive(model, posterior_samples)\n",
"posterior_predictions = posterior_predictive(\n",
" rng_key,\n",
" As=jnp.array([1,0,0,1,1]),\n",
" Bs=jnp.array([0,0,0,1]),\n",
" totalA=0.55,\n",
" totalB=0.45\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x432 with 6 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"inference_data = az.from_numpyro(\n",
" posterior=mcmc,\n",
" posterior_predictive=posterior_predictions,\n",
")\n",
"az.plot_trace(inference_data, )\n",
"plt.subplots_adjust(hspace=.5);"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "pymc_latest",
"language": "python",
"name": "pymc_latest"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.12"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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