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Last active November 30, 2019 21:32
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Translating the MTH594 RStan examples to PyMC3
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"import pymc3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Examples in PyMC3\n",
"\n",
"For MTH594 - Bayesian Data Analysis, we have worked with RStan throughout.\n",
"However, PyMC3 is for Python in many ways at least as comfortable, if not more, as RStan for working with MCMC type Bayesian inference.\n",
"Here, thus, are some of the examples we have had earlier - adapted for PyMC3 as a platform.\n",
"\n",
"We will be building on the posts\n",
"\n",
"* [A first look at computation](https://medium.com/cuny-csi-mth594-bayesian-data-analysis/a-first-look-at-computation-2bcb4301b5f)\n",
"* [Computation: 2.11.13 in RStan](https://medium.com/cuny-csi-mth594-bayesian-data-analysis/computation-2-11-13-in-rstan-4fba47363281)\n",
"* [Posterior predictive checking](https://medium.com/cuny-csi-mth594-bayesian-data-analysis/posterior-predictive-checking-6-7-2-350ec57c05dc)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A first look at computation\n",
"\n",
"In this post, we introduced a simple Binomial model with a uniform Beta prior, and used it for a hypothetical observation with 2 successes among 20 trials to address the question of whether or not 10% is a plausible success probability."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"binomial_model = pymc3.Model()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"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 2 jobs)\n",
"NUTS: [p]\n",
"Sampling 4 chains: 100%|██████████| 4000/4000 [00:02<00:00, 1694.64draws/s]\n"
]
}
],
"source": [
"with binomial_model:\n",
" p = pymc3.Beta('p',1,1)\n",
" y = pymc3.Binomial('y',20,p,observed=2)\n",
" binomial_trace = pymc3.sample(chains=4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A summary of the sample trace gives us the same information as a printout of the Stan model."
]
},
{
"cell_type": "code",
"execution_count": 4,
"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>mean</th>\n",
" <th>sd</th>\n",
" <th>mc_error</th>\n",
" <th>hpd_2.5</th>\n",
" <th>hpd_97.5</th>\n",
" <th>n_eff</th>\n",
" <th>Rhat</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>p</th>\n",
" <td>0.136</td>\n",
" <td>0.069</td>\n",
" <td>0.002</td>\n",
" <td>0.021</td>\n",
" <td>0.272</td>\n",
" <td>906.407</td>\n",
" <td>1.008</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" mean sd mc_error hpd_2.5 hpd_97.5 n_eff Rhat\n",
"p 0.136 0.069 0.002 0.021 0.272 906.407 1.008"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pymc3.summary(binomial_trace).round(3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By comparing to the blog post, we see that our results are pretty close to the ones achieved there."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is a range of useful plot provided through the package `arviz` and accessed through `pymc3.plots`:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x123301d68>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x1232ac710>]],\n",
" dtype=object)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x144 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pymc3.plots.traceplot(binomial_trace)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x12585d1d0>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x125815198>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x1257f5550>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x12537d9b0>]],\n",
" dtype=object)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1987.2x331.2 with 4 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pymc3.plots.autocorrplot(binomial_trace)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([<matplotlib.axes._subplots.AxesSubplot object at 0x125ca5be0>],\n",
" dtype=object)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pymc3.plots.plot_posterior(binomial_trace)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2.11.13 in PyMC3\n",
"\n",
"Here, the dataset under study is one with fatal airplane passengers in the 1970s and 1980s.\n",
"The task is first to derive a posterior from a joint Poisson sampling model, and then later on to use a rate/exposure Poisson regression model.\n",
"\n",
"We first get the data loaded"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>year</th>\n",
" <th>FatAcc</th>\n",
" <th>Deaths</th>\n",
" <th>DeathRate</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1976</td>\n",
" <td>24</td>\n",
" <td>734</td>\n",
" <td>0.19</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1977</td>\n",
" <td>25</td>\n",
" <td>516</td>\n",
" <td>0.12</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1978</td>\n",
" <td>31</td>\n",
" <td>754</td>\n",
" <td>0.15</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1979</td>\n",
" <td>31</td>\n",
" <td>877</td>\n",
" <td>0.16</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1980</td>\n",
" <td>22</td>\n",
" <td>814</td>\n",
" <td>0.14</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>1981</td>\n",
" <td>21</td>\n",
" <td>362</td>\n",
" <td>0.06</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>1982</td>\n",
" <td>26</td>\n",
" <td>764</td>\n",
" <td>0.13</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>1983</td>\n",
" <td>20</td>\n",
" <td>809</td>\n",
" <td>0.13</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>1984</td>\n",
" <td>16</td>\n",
" <td>223</td>\n",
" <td>0.03</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1985</td>\n",
" <td>22</td>\n",
" <td>1066</td>\n",
" <td>0.15</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" year FatAcc Deaths DeathRate\n",
"0 1976 24 734 0.19\n",
"1 1977 25 516 0.12\n",
"2 1978 31 754 0.15\n",
"3 1979 31 877 0.16\n",
"4 1980 22 814 0.14\n",
"5 1981 21 362 0.06\n",
"6 1982 26 764 0.13\n",
"7 1983 20 809 0.13\n",
"8 1984 16 223 0.03\n",
"9 1985 22 1066 0.15"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas\n",
"\n",
"accidents = pandas.DataFrame({\n",
" \"year\": range(1976, 1986),\n",
" \"FatAcc\": [24,25,31,31,22,21,26,20,16,22],\n",
" \"Deaths\": [734,516,754,877,814,362,764,809,223,1066],\n",
" \"DeathRate\": [.19,.12,.15,.16,.14,.06,.13,.13,.03,.15]\n",
"})\n",
"accidents"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(23.8, 22.177777777777777)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"accidents.FatAcc.mean(), accidents.FatAcc.var()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Solving for alpha and beta that generate a Gamma distribution with this mean and variance, we get:\n",
"* alpha = 25.55\n",
"* beta = 1.07\n",
"\n",
"The proposed model will be\n",
"* FatAcc ~ Poisson(theta)\n",
"* theta ~ Gamma(25.55, 1.07)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"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: [theta]\n",
"Sampling 2 chains: 100%|██████████| 2000/2000 [00:01<00:00, 1839.66draws/s]\n"
]
}
],
"source": [
"poisson_model = pymc3.Model()\n",
"with poisson_model:\n",
" theta = pymc3.Gamma(\"theta\", 25.55, 1.07)\n",
" FatAcc = pymc3.Poisson(\"FatAcc\", theta, observed=accidents.FatAcc)\n",
" poisson_trace = pymc3.sample()"
]
},
{
"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>mean</th>\n",
" <th>sd</th>\n",
" <th>mc_error</th>\n",
" <th>hpd_2.5</th>\n",
" <th>hpd_97.5</th>\n",
" <th>n_eff</th>\n",
" <th>Rhat</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>theta</th>\n",
" <td>23.73</td>\n",
" <td>1.488</td>\n",
" <td>0.067</td>\n",
" <td>20.871</td>\n",
" <td>26.651</td>\n",
" <td>434.992</td>\n",
" <td>0.999</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" mean sd mc_error hpd_2.5 hpd_97.5 n_eff Rhat\n",
"theta 23.73 1.488 0.067 20.871 26.651 434.992 0.999"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pymc3.summary(poisson_trace).round(3)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x125f22dd8>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x125cc4400>]],\n",
" dtype=object)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x144 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 993.6x331.2 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pymc3.plots.plot_trace(poisson_trace)\n",
"pymc3.plots.plot_autocorr(poisson_trace)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Poisson regression\n",
"\n",
"Next up, the idea is to regress on an exposure proportional to the number of passenger miles flown.\n",
"It is here worth remembering that the rate variable counts deaths per 1e8 miles."
]
},
{
"cell_type": "code",
"execution_count": 13,
"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>year</th>\n",
" <th>FatAcc</th>\n",
" <th>Deaths</th>\n",
" <th>DeathRate</th>\n",
" <th>MilesE12</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1976</td>\n",
" <td>24</td>\n",
" <td>734</td>\n",
" <td>0.19</td>\n",
" <td>0.386316</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1977</td>\n",
" <td>25</td>\n",
" <td>516</td>\n",
" <td>0.12</td>\n",
" <td>0.430000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1978</td>\n",
" <td>31</td>\n",
" <td>754</td>\n",
" <td>0.15</td>\n",
" <td>0.502667</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1979</td>\n",
" <td>31</td>\n",
" <td>877</td>\n",
" <td>0.16</td>\n",
" <td>0.548125</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1980</td>\n",
" <td>22</td>\n",
" <td>814</td>\n",
" <td>0.14</td>\n",
" <td>0.581429</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>1981</td>\n",
" <td>21</td>\n",
" <td>362</td>\n",
" <td>0.06</td>\n",
" <td>0.603333</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>1982</td>\n",
" <td>26</td>\n",
" <td>764</td>\n",
" <td>0.13</td>\n",
" <td>0.587692</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>1983</td>\n",
" <td>20</td>\n",
" <td>809</td>\n",
" <td>0.13</td>\n",
" <td>0.622308</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>1984</td>\n",
" <td>16</td>\n",
" <td>223</td>\n",
" <td>0.03</td>\n",
" <td>0.743333</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1985</td>\n",
" <td>22</td>\n",
" <td>1066</td>\n",
" <td>0.15</td>\n",
" <td>0.710667</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" year FatAcc Deaths DeathRate MilesE12\n",
"0 1976 24 734 0.19 0.386316\n",
"1 1977 25 516 0.12 0.430000\n",
"2 1978 31 754 0.15 0.502667\n",
"3 1979 31 877 0.16 0.548125\n",
"4 1980 22 814 0.14 0.581429\n",
"5 1981 21 362 0.06 0.603333\n",
"6 1982 26 764 0.13 0.587692\n",
"7 1983 20 809 0.13 0.622308\n",
"8 1984 16 223 0.03 0.743333\n",
"9 1985 22 1066 0.15 0.710667"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"accidents[\"MilesE12\"] = 1e-4 * accidents.Deaths / accidents.DeathRate\n",
"accidents"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Similar to how we need to build the model specifically to predict while it is running in RStan, we need to create a way to insert new data into the model.\n",
"The way this works in PyMC3 is by creating a *shared Theano variable* for the predictor."
]
},
{
"cell_type": "code",
"execution_count": 14,
"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: [theta]\n",
"Sampling 2 chains: 100%|██████████| 2000/2000 [00:01<00:00, 1634.01draws/s]\n"
]
}
],
"source": [
"import theano\n",
"\n",
"Me12 = theano.shared(accidents.MilesE12.values)\n",
"regression_model = pymc3.Model()\n",
"with regression_model:\n",
" theta = pymc3.Gamma(\"theta\", 25.55,1.07)\n",
" FatAcc = pymc3.Poisson(\"FatAcc\", \n",
" Me12 * theta, \n",
" observed=accidents.FatAcc)\n",
" regression_trace = pymc3.sample()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"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>mean</th>\n",
" <th>sd</th>\n",
" <th>mc_error</th>\n",
" <th>hpd_2.5</th>\n",
" <th>hpd_97.5</th>\n",
" <th>n_eff</th>\n",
" <th>Rhat</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>theta</th>\n",
" <td>39.026</td>\n",
" <td>2.42</td>\n",
" <td>0.1</td>\n",
" <td>34.208</td>\n",
" <td>43.77</td>\n",
" <td>508.181</td>\n",
" <td>1.001</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" mean sd mc_error hpd_2.5 hpd_97.5 n_eff Rhat\n",
"theta 39.026 2.42 0.1 34.208 43.77 508.181 1.001"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pymc3.summary(regression_trace).round(3)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x12658bdd8>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x122ef6c50>]],\n",
" dtype=object)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x144 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 993.6x331.2 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pymc3.plots.plot_trace(regression_trace)\n",
"pymc3.plots.plot_autocorr(regression_trace)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 1000/1000 [00:01<00:00, 520.15it/s]\n"
]
}
],
"source": [
"Me12.set_value(append(accidents.MilesE12, 0.8))\n",
"regression_pp = pymc3.sample_posterior_predictive(regression_trace, model=regression_model)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"regression_prediction = regression_pp[\"FatAcc\"][:,-1]"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([21, 43])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pymc3.stats.hpd(regression_prediction)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Posterior Predictive Checking\n",
"\n",
"We continue the airplane fatalities data with checking two modeling assumptions:\n",
"\n",
"1. independence from year to year\n",
"2. lack of a trend over time\n",
"\n",
"The approach we take in the [corresponding blog post](https://medium.com/cuny-csi-mth594-bayesian-data-analysis/posterior-predictive-checking-6-7-2-350ec57c05dc) is by using autocorrelation of the year-by-year predictions for the first check, and by using correlation against the year for the second. In both, our approach is to generate model predictions that match the entire sequence of years.\n",
"\n",
"Since we did not foresee this when building the models above, we will produce the draws by hand for the Poisson model, and produce predictions just as we did above for the exposure model. For the exposure model, we will use the fact that the prediction input in `Me12` can be taken to be either a single point or an array of predictor values.\n",
"\n",
"## Autocorrelation for independence"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12d35f160>]"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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4D1gIbKf1rJhtIvKYiFzdttlPgXtEZBPwJnCnMUavulDHqWts5rW1e5gypDf9Y8OsjuOT/uuydMKCAvjDJ7lWR1FeLsCdjYwxC2g9UNr+tkfbfZ0DTPRsNGU3/1pfTFVdE/dcpKP2cxUTFsS9lwzgT5/msragknFpvayOpLyUnqqgukVjs4v/W1bAyORoslJ6Wh3Hp31vYn8SokL4n092oH8gq9PRclfd4p31RZRUHeVHl6Uj4t8LcnRWSKCTB6YMYlNRlS7Hp05Ly111ucZmF898ns/I5GgmD9KzpDzh+lFJpMeH8+eFuTS3uKyOo7yQlrvqcvOyi9hXXc8Dlw/SUbuHOB3Cz6dmUHCglnnZOqmYOpmWu+pSDc0tPLM0n9EpPZmUftKlD6oTLh8ST1ZKT55cnMfRRp1UTB1Py111qXnriijVUXuXEBF+MS2D8poGXli52+o4ystouasuU9vQzNOf5zMmtScTB+ope11hTGoMlw+J5/+W7aK6TicVU/+h5a66zNzlBVTUNPDQFUN01N6FfjJlMDX1zfzzS51UTP2HlrvqEmWH65m7vIArhyUwKlnPa+9KmX0jmXZ+H15YWUhVXaPVcZSX0HJXXeIvi3JpcRkenJphdRS/8KPL0znS0MzzK3Tfu2ql5a48bnvpYd5ZX8wdF6TQL6aH1XH8QkafSK4clsCLK3dzsFZH70rLXXmYMYbffbydyJBA7rsk3eo4fuXHl6VT19TCcyt037vSclce9unW/XyZf4AHLk8nqkeg1XH8SnrvCL4zrC8vryrkkI7e/Z6Wu/KYusZmfvNRDhl9InSVJYv88JKB1DW28MpqXUzb32m5K4/52+f57Kuu5zfXnE+AU3+1rDC4TwSXZsTz8upCvWrVz+k7UHlEQcURnltRwHUjExmTGmN1HL9278UDOFjbyLzsoo43Vral5a46zRjDrz7MITjAyYPT9NRHq41JjWF0Sk+eW1GgM0b6MS131WkLtuxneV4FD0wZRHxkiNVxFDBn8gCKDx3l4y2lVkdRFtFyV51SU9/Erz/cRmZCJHdM0IOo3uKyjHjS48P5xxe7dLUmP6XlrjrlL4vyqDjSwP9cN1QPonoRh0O456I0duyvYdWuSqvjKAvou1Gdsy3F1byyupBbx6Uwol+01XHUCa4e3pdeYUG8uLLQ6ijKAlru6py0uAwPv7+FmLBg/vvbg62Oo04hJNDJd8cls2RHGXsr66yOo7qZlrs6J6+v3cPm4moeuWoIUaF6Jaq3unV8Ck4RXl5daHUU1c3cKncRmSoiuSKSLyIPnmabm0QkR0S2icgbno2pvEn54Xr+/GkuFw6M5erhfa2Oo86gd2QIVwxNYN66Imobmq2Oo7pRh+UuIk7gGWAakAnMFJHME7ZJBx4CJhpjzgN+3AVZlZf4zcfbaWhx8ZtrztdFOHzAnRNTqWlo5r0NupC2P3Fn5D4WyDfGFBhjGoG3gOknbHMP8Iwx5hCAMabcszGVt1ixs4IPN+3jBxcPoH9smNVxlBtG9otmeFIUL60qxOXS0yL9hTvlngi0v465uO229gYBg0RkpYisEZGpp3ogEZktItkikl1RUXFuiZVl6ptaeOT9rfSPDWPO5AFWx1FuEhHunJjKropaVu46YHUc1U08dUA1AEgHLgZmAs+JyEnnxhlj5hpjsowxWXFxcR56atVdnlteQGFlHY9NP4+QQKfVcdRZmHZ+Aj17BPLG2r1WR1HdxJ1yLwH6tfs+qe229oqB+caYJmPMbiCP1rJXNlF0sI5nvsjniqF9mJSu/zD7mpBAJzdl9WNRThllh+utjqO6gTvlvg5IF5H+IhIEzADmn7DN+7SO2hGRWFp30+hyMDbym49yEIRfXpnZ8cbKK80cm0yLy/D2Op0t0h90WO7GmGbgPmAhsB2YZ4zZJiKPicjVbZstBCpFJAdYCvzMGKPXPNvEF7nlLMop4/7LBtI3OtTqOOocpcaGMSk9lje/2quzRfoBt/a5G2MWGGMGGWMGGGN+13bbo8aY+W1fG2PMT4wxmcaYocaYt7oytOo+Dc0t/PrDHNJiw7j7wjSr46hOumVcCqXV9SzN1RMa7E6vUFVn9OLKQnYfqOX/XX0eQQH66+LrLh8ST+/IYF5fq8vw2Z2+W9VpVdQ08LfP87ksI57Jg/Qgqh0EOB3MGJPMsrwKig7qfDN2puWuTuvxhbk0NLfw8JVDrI6iPGjG2H4I8NY6PS3SzrTc1SltLalm3voi7piQSlpcuNVxlAclRIVyaUY887KLadIDq7al5a5OYozhsQ9z6NkjiPsv08sV7Gjm2GQqahpYsl1nCrErLXd1koXbyviq8CA/mTJIp/O1qcmD4kiICuHNr3TXjF1puavjNLW4+NOnOxgYH86MMf06/g+UTwpwOrgpqx/Ld+qBVbvSclfHeWtdEQUHanloWoauiWpzN41pPbA6L1uvWLUjffeqbxxpaOapxXmM6x/DpRnxVsdRXSwxOpSLB8czL7tIr1i1IS139Y25y3Zx4EgjD10xRBfh8BMzxyZTdriBz3fogVW70XJXQOvSec+t2M1VwxIY0e+k2ZqVTV0yOI7ekcG8oQdWbUfLXQHwv5/n09Ti4mffHmx1FNWNApwObs7qx7K8CooP6YFVO9FyV+ytrOPNr/YyY2w/Unrp0nn+5uaxyQjoVMA2o+WueHJJHk6HcP+lesGSPzp2YPXtdUV6xaqNaLn7ubyyGv69sYQ7L0ild2SI1XGURWaOTaa8Rg+s2omWu5/7y6JcwoICdMFrP3fJ4Dj6RIboGqs2ouXuxzYVVbFwWxn3TEqjZ1iQ1XGUhQKcDm4a03rFan1zi9VxlAdoufuxJxbnEd0jkO9dmGp1FOUFZrRdsVp+uMHqKMoDtNz91Po9h/git4LZF6UREaKTgynoGx3KpRm9qaipx2WM1XFUJ2m5+6knF+cRExbEHRNSrY6ivMhtE1JochkO1jZaHUV1kpa7H1pXeJAVOw8wZ3IaYcEBVsdRXmTSwFiCAxyUHa63OorqJC13P/TEZ3nEhgdx6/gUq6MoL+NwCL0jQ6hpaGbH/sNWx1Gd4Fa5i8hUEckVkXwRefAM210vIkZEsjwXUXnS2oJKVu2qZM7kAfQI0lG7OllcRDAi8PoaPS3Sl3VY7iLiBJ4BpgGZwEwRyTzFdhHAj4C1ng6pPOfJxTuJiwjWUbs6rUCHg15hwby3oZgjDc1Wx1HnyJ2R+1gg3xhTYIxpBN4Cpp9iu98AfwR0Z52X+mr3QVYXVPL9i9IICXRaHUd5sd6RwdQ2tvDvjSVWR1HnyJ1yTwTazyhU3HbbN0RkFNDPGPOxB7MpD3tqSR6x4cHcMk5H7erMwoMDGJoYxcurCjF6WqRP6vQBVRFxAH8FfurGtrNFJFtEsisqKjr71OosZBceZGV+66g9NEhH7erMBOHOC1LJLz/CyvxKq+Ooc+BOuZcA7VdKTmq77ZgI4HzgCxEpBMYD8091UNUYM9cYk2WMyYqLizv31OqsPbVkJ73CgrhlfLLVUZSPuGp4ArHhQby0arfVUdQ5cKfc1wHpItJfRIKAGcD8Y3caY6qNMbHGmFRjTCqwBrjaGJPdJYnVWVu/5xArdh5g9kVpeoaMcltwgJOZY5NZsqOcvZW6kIev6bDcjTHNwH3AQmA7MM8Ys01EHhORq7s6oOq8p5fsJCZMz2tXZ++WcSk4RXhldaHVUdRZcmsYZ4xZACw44bZHT7PtxZ2PpTzl66IqluVV8IupGXo1qjprfaJCmDY0gbezi3hgyiD9HfIheoWqzT29ZCfRPQK5bYKO2tW5ufOCVGrqm3lvQ7HVUdRZ0HK3sc3FVXy+o5x7JqURriMudY5GJUczPCmKF1YW4nLpaZG+Qsvdxp5espOo0EBu11G76gQRYdakNHYfqGWJLsPnM7TcbWprSTWLt5cz68L+Ol+76rQrzu9DYnQoz60osDqKcpOWu009vWQnESEB3Dkx1eooygYCnA7umpjKV7sPsrm4yuo4yg1a7ja0taSaRTll3H1hGpE6alcectOYfoQHB/D8Cr2oyRdoudvQU0t2EqmjduVhkSGBzBjTj4+3lFJSddTqOKoDWu42s7Wkms9yyph1YRpRoTpqV551bMDw4pc6evd2Wu42c2zUfteFqVZHUTaU1LMHVw5N4M2v9lJd12R1HHUGWu42cmzUfvck3deuus6cyQOobWzh1TWFVkdRZ6DlbiNPLs7Tfe2qy2X2jeTiwXG8uLKQ+qYWq+Oo09Byt4mNew+xeHs53588QEftqsvdO3kAlbWNvJNd1PHGyhJa7jbx18/yiAkL4s4LUq2OovzA2P4xjEyO5tnlBTS3uKyOo05By90G1hRUsmLnAX5w8QCdtU91CxHh3skDKD50lI+3lFodR52ClruPM8bwl0W5xEcE63ztqltdPqQ36fHh/H3pLp1QzAtpufu45TsPsK7wEPdfOpCQQF0bVXUfh0P44SUDyS2rYVFOmdVx1Am03H2Yy2V4fGEuidGh3DxG10ZV3e+qYQn0jw3jfz/fiTE6evcmWu4+7OMtpWwpqean3xpEUID+KFX3C3A6+OElA9m27zCf63TAXkUbwUc1Nrt4fFEuGX0imD4i0eo4yo9NH9GX5JgePL1ER+/eRMvdR721bi97Kuv4xbQMnA6xOo7yY4FOBz+4eACbiqtZlldhdRzVRsvdBx1paOapxTsZnxbDxYPirI6jFNeNSiIxOpQnF+vo3Vtoufug55YXUFnbyIPThiCio3ZlvaAAB/dfOpCvi6pYsl33vXsDLXcfs7+6nrnLC7hiaB9G9Iu2Oo5S37h+dBL9Y8N4fFGunvfuBdwqdxGZKiK5IpIvIg+e4v6fiEiOiGwWkSUiolfTdJE/LdxBi8vw0LQhVkdR6jiBTgcPTBnEjv01fLh5n9Vx/F6H5S4iTuAZYBqQCcwUkcwTNtsIZBljhgHvAn/ydFAFm4qqeG9DCbMm9adfTA+r4yh1kquGJpDRJ4K/fpZHk845Yyl3Ru5jgXxjTIExphF4C5jefgNjzFJjTF3bt2uAJM/GVMYYHvsoh9jwYH5w8QCr4yh1Sg6H8LNvD2ZPZR3vZBdbHcevuVPuiUD7eT2L2247nVnAJ6e6Q0Rmi0i2iGRXVOgpU2fjo82lrN9ziJ99exAROqWv8mKXZsQzKjmaJxfnUdvQbHUcv+XRA6oiciuQBfz5VPcbY+YaY7KMMVlxcXoKn7vqGpv5/YLtZCZEcsPoflbHUeqMRISHr8ykvKaBf3yxy+o4fsudci8B2jdKUtttxxGRy4GHgauNMQ2eiaegdV3UfdX1PDb9PL1gSfmE0Sk9mT6iL3NXFFB0sK7j/0B5nDvlvg5IF5H+IhIEzADmt99AREYCz9Ja7HqSqwfl7q/hnyt2c1NWElmpMVbHUcptv5iagUPgD5/ssDqKX+qw3I0xzcB9wEJgOzDPGLNNRB4TkavbNvszEA68IyJfi8j80zycOgvGGB55fyvhIQE8qKc+Kh/TNzqUOZMH8PGWUtYWVFodx++4tWyPMWYBsOCE2x5t9/XlHs6lgH9tKOGrwoP84bqhxIQFWR1HqbP2/YsGMG9dEb/+MIf5900kwKnXTXYXfaW91IEjDfzPgu2MSo7mpiw9iKp8U2iQk0e/k0lO6WHmriiwOo5f0XL3Uv/vg20cqW/m99cNw6EHUZUPm3p+AtPO78OTi3eyq+KI1XH8hpa7F/p4cykfbynlR5enM7hPhNVxlOq0X08/j9BAJz9/dzMtOu9Mt9By9zKVRxp45IOtDEuK4vsXpVkdRymPiI8I4dGrMlm/5xCvrC60Oo5f0HL3IsYYHm3bHfPnG4brwSdlK9eNSuTiwXH88dMd7Nh/2Oo4tqft4UXeyS7W3THKtkSEP10/jIiQQO59bQM19U1WR7I1LXcvkVdWw6PztzJxYC/mTNaJwZQ9xUeG8Mx3R7H3YB0/e2ezrtrUhbTcvUBdYzM/fH0D4cEBPHHzCJ1iQNna2P4xPDQtg0+37ef5FbutjmNbWu5e4Ffzt5FfcYQnbx5JfESI1XGU6nKzLuzPFUP78PtPtrNgS6nVcWzJrStUVdd5aeVu5mUXc98lA7kwPdbqOEp1CxEDLI7eAAAKE0lEQVTh8RuHU364gf96cyMhgQ4uzehtdSxb0ZG7hZbuKOexj3K4fEhvHpgyyOo4SnWrHkEBvHDXGDL7RjLntQ2szD9gdSRb0XK3yPbSw9z3xgaGJETy1Azdz678U2RIIC/fNZb+vcK4++VsPt2qu2g8RcvdAsWH6pj10joiQgL55x1jCAvWvWPKf/UMC+K1u8cxuE8Ec17bwBOf5eHSq1g7Tcu9mxUdrOPmZ9dwpKGZf96ZRZ8oPYCqVFxEMG/NHs/1o5J4aslO7n19PYdqG62O5dO03LvRnspaZsxtLfbX7x7PeX2jrI6klNcICXTy+I3D+OWVQ1i8vZzL/rqM9zYU67nw50jLvZtsLz3MjLlrqGts5o17xjE0SYtdqROJCHdPSuOj+y8kpVcPfjJvE7c8v5ZNRVVWR/M5Wu7dYP6mfVz391W4jOGNe3TErlRHhiRE8q85F/Dba85n277DTH9mJbf9cy1rCyp1JO8mPZLXhZpaXPx5YS5zlxcwJrUnz9wySi9SUspNDodw6/gUrhmZyGtr9vD8igJunruGjD4R3DymH9eMSKSnrlB2WmLVv4JZWVkmOzvbkufuDuv3HOLhf29hx/4abp+Qwi+vzCQoQP9QUj7gxStbP9/1sbU5TlDf1MK/NhTz9roiNhdXE+R0cNGgOK4c1ofLhvQmMiTQ6ojdQkTWG2OyOtpOR+4eVlHTwBOL83hj7V4SokJ49rbRfPu8PlbHUsrnhQQ6uWVcCreMSyFn32HeXV/Mgi2lLN5eRpDTwYQBvbg8szeXZcTTNzrU6riW05G7hxQdrGPu8gLmZRfR1OLiron9eWDKIML1HHbla7x05H4qLpdhY1EVn7SVfGFlHQAZfSKYPDiOyYPiyEqJsdVfzTpy7wa1Dc18llPG/E37WJZXgUPg+lFJzL4ojbS4cKvjKWV7DocwOqUno1N68vCVQ9hVUcuS7WUsy6vghS938+yyAkIDnYxLi2HigFgmDOjFkIRIv7gi3K1yF5GpwFOAE3jeGPOHE+4PBl4BRgOVwM3GmELPRrWey2XILathZf4BVu+qZNWuSo42tZAYHcrsi9K4Y0KqXpSklEVEhIHx4QyMD+f7kwdwpKGZ1bsq+XJnBV/mH+B3udsBiAgJYGxqDGP6xzCiXzTDkqLoEWS/cW6H/0ci4gSeAaYAxcA6EZlvjMlpt9ks4JAxZqCIzAD+CNzcFYG7gzGGg7WNFByoZXdFLTv217B1XzU5+w5zpKEZgP6xYdyYlcR3hvdldHJPHH4wElDKl4QHBzAlszdTMltnmyytPsragoOs3V3J2oKDLNlRDoDTIaTHh5OZEMmQhEgG94kgLS6MvlGhPv2+duefq7FAvjGmAEBE3gKmA+3LfTrwq7av3wX+JiJivOCE1OYWF40tLuoaWzja2EJdYws19U0crm+i+mgTB2ubOHCkgQM1DZTVNLCv6iilVUepbWz55jFCAh1kJkRy3ahEhiVFc8GAXnrARikfkxAVyjUjE7lmZCIAB2sb+broEBv3VrGlpJqVuw7w3saSb7YPDnCQHNODhOhQEqND6BMZSkx4EDE9gugZFkhkSCARIQGEBQcQGugkJNDpVbt73Cn3RKCo3ffFwLjTbWOMaRaRaqAX4PE5PJfmlvPYhzm4jMEYvvnc4jK0GENzi4tml6G5xdDY4qLFjQmIAhxCr/Ag4iNCGBAXxqT0WPr17EFaXBhpseEk9gz1qh+aUqrzYsKCuDSj93HzyFceaSCv7AiFlbXsPlBL4YFaSqvrydlXzYEjHc91E+AQAp0OAp2tn50OwSHS+tkBguAQ+O64ZGZf1LXLaXbrjiYRmQ3MBkhOTj6nx4gKDWRoYhQi4BBBaD2o4pDWP68CHK0vaKBTCApwEBzgJCjAQY8gJ6GBTnoEBRAREkBkaCCRIQHEhAURFRqIiJa3UgD0GWp1Asv0Cg9mQngwEwb0Oum+phYXh+oaOVjb+nGkvpkjDa0f9U0tHG10Ud/cQnOLi6YWQ1Pb4NJlDC2u1t29LmMwQJ+orv/L351yLwH6tfs+qe22U21TLCIBQBStB1aPY4yZC8yF1lMhzyXwqOSejErueS7/qVLKHdP+0PE2fijQ6SA+IsRnrjJ35+TPdUC6iPQXkSBgBjD/hG3mA3e0fX0D8Lk37G9XSil/1eHIvW0f+n3AQlpPhXzBGLNNRB4Dso0x84F/Aq+KSD5wkNZ/AJRSSlnErX3uxpgFwIITbnu03df1wI2ejaaUUupc2eeaXKWUUt/QcldKKRvScldKKRvScldKKRvScldKKRuybD53EakA9ljy5O6JpQumT/Bh+nocT1+P4+nr8R9d/VqkGGPiOtrIsnL3diKS7c6E+P5CX4/j6etxPH09/sNbXgvdLaOUUjak5a6UUjak5X56c60O4GX09Tievh7H09fjP7zitdB97kopZUM6cldKKRvScm8jIjeKyDYRcYnIaY90i8hUEckVkXwRebA7M3YnEYkRkc9EZGfb51NOoi8iLSLyddvHiVNB+7SOftYiEiwib7fdv1ZEUrs/Zfdx4/W4U0Qq2v0+3G1Fzu4iIi+ISLmIbD3N/SIiT7e9XptFZFR35tNy/4+twHXA8tNt0G6x8GlAJjBTRDK7J163exBYYoxJB5a0fX8qR40xI9o+ru6+eF3LzZ/1NwvDA0/QujC8LZ3F7/7b7X4fnu/WkN3vJWDqGe6fBqS3fcwG/tENmb6h5d7GGLPdGJPbwWbfLBZujGkEji0WbkfTgZfbvn4ZuMbCLFZw52fd/jV6F7hM7Lteoz/97rvFGLOc1vUrTmc68IpptQaIFpGE7kmn5X62TrVYeKJFWbpab2NMadvX+4Hep9kuRESyRWSNiNjpHwB3ftbHLQwPHFsY3o7c/d2/vm0XxLsi0u8U9/sTS/uiWxfItpqILAb6nOKuh40xH3R3Hqud6fVo/40xxojI6U6rSjHGlIhIGvC5iGwxxuzydFblEz4E3jTGNIjI92n9q+ZSizP5Lb8qd2PM5Z18CHcWC/cZZ3o9RKRMRBKMMaVtf0qWn+YxSto+F4jIF8BIwA7l7rGF4W2iw9fDGNP+//154E/dkMubWdoXulvm7LizWLhdtF/0/A7gpL9sRKSniAS3fR0LTARyui1h19KF4Y/X4etxwv7kq4Ht3ZjPG80Hbm87a2Y8UN1uV2fXM8boR+v78Vpa94k1AGXAwrbb+wIL2m13BZBH6+j0Yatzd+Hr0YvWs2R2AouBmLbbs4Dn276+ANgCbGr7PMvq3B5+DU76WQOPAVe3fR0CvAPkA18BaVZntvj1+D2wre33YSmQYXXmLn493gRKgaa27pgFzAHmtN0vtJ5htKvt/ZHVnfn0ClWllLIh3S2jlFI2pOWulFI2pOWulFI2pOWulFI2pOWulFI2pOWulFI2pOWulFI2pOWulFI29P8BFYFavabRn7AAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from scipy import stats\n",
"import seaborn\n",
"simulations = vstack([stats.poisson(pt[\"theta\"]).rvs(size=(10,)) for pt in poisson_trace])\n",
"\n",
"autocorrs = hstack([corrcoef(accidents[\"FatAcc\"][1:],accidents[\"FatAcc\"][:-1])[1,0]] \n",
" + [corrcoef(sim[1:],sim[:-1])[1,0] for sim in simulations])\n",
"seaborn.kdeplot(autocorrs[1:])\n",
"plot([autocorrs[0],autocorrs[0]], [0.0,1.0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the exposure model, we generated the predictions we need while we were busy trying to predict a next value: the first 10 columns of `regression_pp` contain exposure predictions for the dataset itself."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12c8f4f60>]"
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"expsimulations = regression_pp[\"FatAcc\"][:,:10]\n",
"autocorrs = hstack([corrcoef(accidents[\"FatAcc\"][1:],accidents[\"FatAcc\"][:-1])[1,0]] \n",
" + [corrcoef(sim[1:],sim[:-1])[1,0] for sim in expsimulations])\n",
"seaborn.kdeplot(autocorrs[1:])\n",
"plot([autocorrs[0],autocorrs[0]], [0.0,1.0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Correlation for time trend"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12d35f780>]"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"autocorrs = hstack([corrcoef(accidents[\"FatAcc\"],accidents[\"year\"])[1,0]] \n",
" + [corrcoef(sim,accidents[\"year\"])[1,0] for sim in simulations])\n",
"seaborn.kdeplot(autocorrs[1:])\n",
"plot([autocorrs[0],autocorrs[0]], [0.0,1.0])"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x12d4f9470>]"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"autocorrs = hstack([corrcoef(accidents[\"FatAcc\"],accidents[\"year\"])[1,0]] \n",
" + [corrcoef(sim,accidents[\"year\"])[1,0] for sim in expsimulations])\n",
"seaborn.kdeplot(autocorrs[1:])\n",
"plot([autocorrs[0],autocorrs[0]], [0.0,1.0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Model Comparison\n",
"\n",
"The final step in the course generating the blog posts is to compare models using WAIC and/or LOO-IC to determine which of the models is more appropriate for a task.\n",
"\n",
"And lo! We have two models to compare!\n",
"\n",
"The functions `pymc3.waic` and `pymc3.loo` both take the computed trace and the model itself in order to calculate their values - so that is what we will feed in for the two models."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, the pure Poisson model:"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.7/site-packages/pymc3/stats.py:168: FutureWarning: arrays to stack must be passed as a \"sequence\" type such as list or tuple. Support for non-sequence iterables such as generators is deprecated as of NumPy 1.16 and will raise an error in the future.\n",
" return np.stack(logp)\n"
]
},
{
"data": {
"text/plain": [
"WAIC_r(WAIC=60.19682715933937, WAIC_se=3.513384325773337, p_WAIC=0.8298099549951771, var_warn=0)"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pymc3.waic(poisson_trace, poisson_model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And then next the exposure model. We need to remember to reset the predictor variable to its original value."
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.7/site-packages/pymc3/stats.py:219: 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/plain": [
"WAIC_r(WAIC=80.57746169610748, WAIC_se=8.223603611452416, p_WAIC=2.3826393641896826, var_warn=1)"
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Me12.set_value(accidents.MilesE12)\n",
"pymc3.waic(regression_trace, regression_model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also do both in one shot, using `pymc3.compare`:"
]
},
{
"cell_type": "code",
"execution_count": 71,
"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>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>Poisson</th>\n",
" <td>60.2</td>\n",
" <td>0.83</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>3.51</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Exposure</th>\n",
" <td>80.58</td>\n",
" <td>2.38</td>\n",
" <td>20.38</td>\n",
" <td>0</td>\n",
" <td>8.22</td>\n",
" <td>6.05</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" WAIC pWAIC dWAIC weight SE dSE var_warn\n",
"Poisson 60.2 0.83 0 1 3.51 0 0\n",
"Exposure 80.58 2.38 20.38 0 8.22 6.05 1"
]
},
"execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"poisson_model.name = \"Poisson\"\n",
"regression_model.name = \"Exposure\"\n",
"pymc3.compare({poisson_model: poisson_trace, regression_model: regression_trace})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The quite a bit lower value for WAIC for the pure Poisson model is an argument against using the exposure model. All in all, we've seen several signs that the exposure model might not be appropriate here: both the posterior predictive check and the model comparison provide evidence against using it. So what's going on there?\n",
"\n",
"The posterior predictive check specifically told us that the assumption of a lack of a time trend was unreasonable. Not only was it unreasonable, but the trend that can be observed was given by a far more negative correlation than the model would predict. So there is a falling trend in accidents / passenger-mile present. The exposure model we are using is not really able to account for this - maybe if we added an offset to the exposure, making it a linear fit, we could model this falling trend. But unless we accurately model the falling trend (produced one might suspect by progress in airline safety) the flatness assumption in the Poisson model is closer to the truth than the rising trend produced by an exposure model."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
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"file_extension": ".py",
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.2"
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