08 Chapter 8/01 H1,2,3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "import numpy as np\n",
    "\n",
    "plt.style.use('seaborn-whitegrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**H1** Run the model below and then inspect the posterior distribution and explain what it is accomplishing.\n",
    "\n",
    "```\n",
    "mp <- map2stan(\n",
    "    alist(\n",
    "        a ~ dnorm(0,1),\n",
    "        b ~ dcauchy(0,1)\n",
    "    ),\n",
    "    data=list(y=1),\n",
    "    start=list(a=0,b=0),\n",
    "    iter=1e4, warmup=100 , WAIC=FALSE )\n",
    "```\n",
    "\n",
    "Compare the samples for the parameters `a` and `b`. Can you explain the different trace plots, using what you know about the Cauchy distribution?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [b, a]\n",
      "Sampling 2 chains: 100%|██████████| 12000/12000 [00:21<00:00, 569.36draws/s]\n",
      "The acceptance probability does not match the target. It is 0.9678954445076582, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.37406415846732366, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The number of effective samples is smaller than 10% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_8h1:\n",
    "    a = pm.Normal('a', mu=0, sd=1)\n",
    "    b = pm.Cauchy('b', alpha=0, beta=1)\n",
    "\n",
    "    model_8h1.trace = pm.sample(5000, tune=1000, chains=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(model_8h1.trace)\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**H2** Recall the divorce rate example from Chapter 5. Repeat that analysis, using map2stan this time, fitting models `m5.1`, `m5.2`, and `m5.3`. Use compare to compare the models on the basis of WAIC. Explain the results.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "waffle = pd.read_csv('../data/WaffleDivorce.csv', sep=';')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, ba, a]\n",
      "Sampling 2 chains: 100%|██████████| 12000/12000 [00:09<00:00, 1316.60draws/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_5_1:\n",
    "    a = pm.Normal('a', mu=10, sd=10)\n",
    "    ba = pm.Normal('ba', mu=0, sd=1)\n",
    "\n",
    "    mu = pm.Deterministic(\n",
    "        'mu',\n",
    "        a\n",
    "        + ba * (waffle['MedianAgeMarriage'] - waffle['MedianAgeMarriage'].mean()) \n",
    "               / waffle['MedianAgeMarriage'].std()\n",
    "    )\n",
    "\n",
    "    sigma = pm.Uniform('sigma', lower=0, upper=10)\n",
    "    divorce = pm.Normal('divorce', mu=mu, sd=sigma, observed=waffle['Divorce'])\n",
    "\n",
    "    model_5_1.name = 'm5.1'\n",
    "    model_5_1.trace = pm.sample(5000, tune=1000, chains=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, br, a]\n",
      "Sampling 2 chains: 100%|██████████| 12000/12000 [00:09<00:00, 1324.85draws/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_5_2:\n",
    "    a = pm.Normal('a', mu=10, sd=10)\n",
    "    br = pm.Normal('br', mu=0, sd=1)\n",
    "\n",
    "    mu = pm.Deterministic(\n",
    "        'mu',\n",
    "        a\n",
    "        + br * (waffle['Marriage'] - waffle['Marriage'].mean())\n",
    "               / waffle['Marriage'].std()\n",
    "    )\n",
    "    \n",
    "    sigma = pm.Uniform('sigma', lower=0, upper=10)\n",
    "    divorce = pm.Normal('divorce', mu=mu, sd=sigma, observed=waffle['Divorce'])\n",
    "\n",
    "    model_5_2.name = 'm5.2'\n",
    "    model_5_2.trace = pm.sample(5000, tune=1000, chains=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, br, ba, a]\n",
      "Sampling 2 chains: 100%|██████████| 12000/12000 [00:12<00:00, 924.38draws/s] \n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_5_3:\n",
    "    a = pm.Normal('a', mu=10, sd=10)\n",
    "    ba = pm.Normal('ba', mu=0, sd=1)\n",
    "    br = pm.Normal('br', mu=0, sd=1)\n",
    "\n",
    "    mu = pm.Deterministic(\n",
    "        'mu',\n",
    "        a\n",
    "        + ba * (waffle['MedianAgeMarriage'] - waffle['MedianAgeMarriage'].mean()) \n",
    "                 / waffle['MedianAgeMarriage'].std()\n",
    "        + br * (waffle['Marriage'] - waffle['Marriage'].mean())\n",
    "                 / waffle['Marriage'].std()\n",
    "    )\n",
    "\n",
    "    sigma = pm.Uniform('sigma', lower=0, upper=10)\n",
    "    divorce = pm.Normal('divorce', mu=mu, sd=sigma, observed=waffle['Divorce'])\n",
    "\n",
    "    model_5_3.name = 'm5.3'\n",
    "    model_5_3.trace = pm.sample(5000, tune=1000, chains=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/petrushev/etc/jup_env/lib/python3.7/site-packages/pymc3/stats.py:218: UserWarning: For one or more samples the posterior variance of the\n",
      "        log predictive densities exceeds 0.4. This could be indication of\n",
      "        WAIC starting to fail see http://arxiv.org/abs/1507.04544 for details\n",
      "        \n",
      "  \"\"\")\n",
      "/home/petrushev/etc/jup_env/lib/python3.7/site-packages/pymc3/stats.py:218: UserWarning: For one or more samples the posterior variance of the\n",
      "        log predictive densities exceeds 0.4. This could be indication of\n",
      "        WAIC starting to fail see http://arxiv.org/abs/1507.04544 for details\n",
      "        \n",
      "  \"\"\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>WAIC</th>\n",
       "      <th>pWAIC</th>\n",
       "      <th>dWAIC</th>\n",
       "      <th>weight</th>\n",
       "      <th>SE</th>\n",
       "      <th>dSE</th>\n",
       "      <th>var_warn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>m5.1</th>\n",
       "      <td>186.26</td>\n",
       "      <td>3.85</td>\n",
       "      <td>0</td>\n",
       "      <td>0.63</td>\n",
       "      <td>12.73</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m5.3</th>\n",
       "      <td>187.82</td>\n",
       "      <td>4.8</td>\n",
       "      <td>1.56</td>\n",
       "      <td>0.3</td>\n",
       "      <td>12.75</td>\n",
       "      <td>0.78</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m5.2</th>\n",
       "      <td>199.77</td>\n",
       "      <td>3.13</td>\n",
       "      <td>13.51</td>\n",
       "      <td>0.08</td>\n",
       "      <td>9.72</td>\n",
       "      <td>9.04</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        WAIC pWAIC  dWAIC weight     SE   dSE var_warn\n",
       "m5.1  186.26  3.85      0   0.63  12.73     0        1\n",
       "m5.3  187.82   4.8   1.56    0.3  12.75  0.78        1\n",
       "m5.2  199.77  3.13  13.51   0.08   9.72  9.04        1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.compare({\n",
    "        model_5_1: model_5_1.trace,\n",
    "        model_5_2: model_5_2.trace,\n",
    "        model_5_3: model_5_3.trace,\n",
    "    },\n",
    "    method='BB-pseudo-BMA'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**H3** Sometimes changing a prior for one parameter has unanticipated effects on other parameters. This is because when a parameter is highly correlated with another parameter in the posterior, the prior influences both parameters. Here’s an example to work and think through. Go back to the leg length example in Chapter 5. Here is the code again, which simulates height and leg lengths for 100 imagined individuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>height</th>\n",
       "      <th>leg_prop</th>\n",
       "      <th>leg_left</th>\n",
       "      <th>leg_right</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10.263800</td>\n",
       "      <td>0.418417</td>\n",
       "      <td>4.273411</td>\n",
       "      <td>4.289282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.754516</td>\n",
       "      <td>0.507177</td>\n",
       "      <td>4.446840</td>\n",
       "      <td>4.488204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9.856607</td>\n",
       "      <td>0.857290</td>\n",
       "      <td>8.436472</td>\n",
       "      <td>8.460830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.221932</td>\n",
       "      <td>0.737102</td>\n",
       "      <td>6.009342</td>\n",
       "      <td>6.024594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11.321814</td>\n",
       "      <td>0.884265</td>\n",
       "      <td>10.026224</td>\n",
       "      <td>10.028492</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      height  leg_prop   leg_left  leg_right\n",
       "0  10.263800  0.418417   4.273411   4.289282\n",
       "1   8.754516  0.507177   4.446840   4.488204\n",
       "2   9.856607  0.857290   8.436472   8.460830\n",
       "3   8.221932  0.737102   6.009342   6.024594\n",
       "4  11.321814  0.884265  10.026224  10.028492"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 100\n",
    "\n",
    "height = stats.norm(loc=10, scale=2).rvs(N)\n",
    "leg_prop = stats.uniform(0.4, 0.5).rvs(N)\n",
    "leg_left = leg_prop * height + stats.norm(loc=0, scale=0.02).rvs(N)\n",
    "leg_right = leg_prop * height + stats.norm(loc=0, scale=0.02).rvs(N)\n",
    "\n",
    "data = pd.DataFrame(dict(\n",
    "    height=height,\n",
    "    leg_prop=leg_prop,\n",
    "    leg_left=leg_left,\n",
    "    leg_right=leg_right\n",
    "))\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And below is the model you fit before, resulting in a highly correlated posterior for the two beta\n",
    "parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/petrushev/etc/jup_env/lib/python3.7/site-packages/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n",
      "  warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n",
      "logp = -190.33, ||grad|| = 2.0003e-05: 100%|██████████| 52/52 [00:00<00:00, 921.22it/s]  \n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, br, bl, a]\n",
      "Sampling 2 chains: 100%|██████████| 7000/7000 [08:12<00:00,  6.53draws/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as m5_8:\n",
    "    a = pm.Normal('a', mu=10, sd=100)\n",
    "    bl = pm.Normal('bl', mu=2, sd=10)\n",
    "    br = pm.Normal('br', mu=2, sd=10)\n",
    "\n",
    "    mu = pm.Deterministic(\n",
    "        'mu',\n",
    "        a\n",
    "        + bl * data.leg_left.values\n",
    "        + br * data.leg_right.values\n",
    "    )\n",
    "\n",
    "    sigma = pm.HalfCauchy('sigma', beta=10)\n",
    "    height = pm.Normal('height', mu=mu, sd=sigma,\n",
    "                       observed=data.height.values)\n",
    "\n",
    "    m5_8.name = 'm5_8'\n",
    "    start = pm.find_MAP()\n",
    "    m5_8.trace = pm.sample(3000, tune=500, chains=2, start=start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(m5_8.trace, varnames=['a', 'bl', 'br'])\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(5, 5), dpi=80)\n",
    "\n",
    "ax.scatter(m5_8.trace['bl'], m5_8.trace['br'], marker='.', alpha=.1)\n",
    "ax.set(aspect='equal', xlabel='bl', ylabel='br')\n",
    "\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the posterior distribution produced by the code above to the posterior distribution produced when you change the prior for br so that it is strictly positive:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/petrushev/etc/jup_env/lib/python3.7/site-packages/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n",
      "  warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n",
      "logp = -190.33, ||grad|| = 0.024316: 100%|██████████| 232/232 [00:00<00:00, 1129.10it/s] \n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, br, bl, a]\n",
      "Sampling 2 chains: 100%|██████████| 16000/16000 [11:03<00:00, 24.10draws/s] \n",
      "There were 573 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The acceptance probability does not match the target. It is 0.6916798890727931, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "There were 143 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The gelman-rubin statistic is larger than 1.2 for some parameters.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as m5_8_s2:\n",
    "    a = pm.Normal('a', mu=10, sd=100)\n",
    "    bl = pm.Normal('bl', mu=2, sd=10)\n",
    "    br = pm.Bound(pm.Normal, lower=0)('br', mu=2, sd=10)\n",
    "\n",
    "    mu = pm.Deterministic(\n",
    "        'mu',\n",
    "        a\n",
    "        + bl * data.leg_left.values\n",
    "        + br * data.leg_right.values\n",
    "    )\n",
    "\n",
    "    sigma = pm.HalfCauchy('sigma', beta=10)\n",
    "    height = pm.Normal('height', mu=mu, sd=sigma,\n",
    "                       observed=data.height.values)\n",
    "\n",
    "    m5_8_s2.name = 'm5_8_s2'\n",
    "    start = pm.find_MAP()\n",
    "    m5_8_s2.trace = pm.sample(5000, tune=3000, chains=2, start=start)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(m5_8_s2.trace, varnames=['a', 'bl', 'br'])\n",
    "None"
   ]
  }
 ],
 "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": "3.7.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}