Difference of means

difference.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc3 as pm\n",
    "import arviz as az"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = [10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12]\n",
    "b = [9, 11, 9, 11, 9, 11, 9, 11, 9, 11, 9, 11, 9, 11, 9, 11]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [sigma_b, sigma_a, mu_b, mu_a]\n"
     ]
    },
    {
     "data": {
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       "      100.00% [24000/24000 00:08<00:00 Sampling 4 chains, 53 divergences]\n",
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       "    "
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 2_000 tune and 4_000 draw iterations (8_000 + 16_000 draws total) took 10 seconds.\n",
      "There were 17 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 15 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 12 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 9 divergences after tuning. Increase `target_accept` or reparameterize.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    mu_a = pm.Uniform(\"mu_a\", 0, 100)\n",
    "    mu_b = pm.Uniform(\"mu_b\", 0, 100)\n",
    "    \n",
    "    sigma_a = pm.Uniform(\"sigma_a\", 0.001, 1)\n",
    "    sigma_b = pm.Uniform(\"sigma_b\", 0.001, 1)\n",
    "    \n",
    "    obs_a = pm.Normal(\"obs_a\", mu=mu_a, sigma=sigma_a, observed=a)\n",
    "    obs_b = pm.Normal(\"obs_b\", mu=mu_b, sigma=sigma_b, observed=b)\n",
    "    diff = pm.Deterministic(\"diff\", (mu_a - mu_b)/mu_a)\n",
    "    \n",
    "    idata = pm.sample(4000, tune=2000, return_inferencedata=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(idata, var_names=['diff'], hdi_prob=0.95);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "?az.plot_posterior"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}