{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Rethinking Statistics course in pymc3 - Week 10"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lecture 19: Gaussian Processes\n",
"\n",
"- [Video](https://www.youtube.com/watch?v=pwMRbt2CbSU)\n",
"- [Slides](https://speakerdeck.com/rmcelreath/l19-statistical-rethinking-winter-2019)\n",
"\n",
"Lecture 20: Missing Values and Measurement Error\n",
"\n",
"- [Video](https://www.youtube.com/watch?v=UgLF0aLk85s)\n",
"- [Slides](https://speakerdeck.com/rmcelreath/l19-statistical-rethinking-winter-2019)\n",
"\n",
"[Proposed problems](https://github.com/gbosquechacon/statrethinking_winter2019/blob/master/homework/week10.pdf) and [solutions in R](https://github.com/gbosquechacon/statrethinking_winter2019/blob/master/homework/week10_solutions.pdf) for the exercises of the week."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import pymc3 as pm\n",
"import numpy as np\n",
"import pandas as pd\n",
"import theano\n",
"import theano.tensor as tt\n",
"from scipy import stats\n",
"from scipy.special import expit as logistic\n",
"from sklearn import preprocessing\n",
"\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib.patches import Ellipse\n",
"import altair as alt\n",
"alt.data_transformers.enable('default', max_rows=None)\n",
"import arviz as az\n",
"\n",
"import warnings\n",
"warnings.filterwarnings('ignore')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> Consider the relationship between brain volume (`brain`) and body mass (`body`) in the data(`Primates301`). These values are presented as single values for each species. However, there is always a range of sizes in a species, and some of these measurements are taken from very small samples. So these values are measured with some unknown error.\n",
"\n",
"> We don't have the raw measurements to work with—that would be best. But we can imagine what might happen if we had them. Suppose error is proportional to the measurement. This makes sense, because larger animals have larger variation. As a consequence, the uncertainty is not uniform across the values and this could mean trouble.\n",
"\n",
"> Let's make up some standard errors for these measurements, to see what might happen. Load the data and scale the the measurements so the maximum is 1 in both cases:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
" \n",
" \n",
" name \n",
" genus \n",
" species \n",
" subspecies \n",
" spp_id \n",
" genus_id \n",
" social_learning \n",
" research_effort \n",
" brain \n",
" body \n",
" group_size \n",
" gestation \n",
" weaning \n",
" longevity \n",
" sex_maturity \n",
" maternal_investment \n",
" B \n",
" M \n",
" Bse \n",
" Mse \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" Allenopithecus_nigroviridis \n",
" Allenopithecus \n",
" nigroviridis \n",
" NaN \n",
" 1 \n",
" 1 \n",
" 0.0 \n",
" 6.0 \n",
" 58.02 \n",
" 4655.0 \n",
" 40.0 \n",
" NaN \n",
" 106.15 \n",
" 276.0 \n",
" NaN \n",
" NaN \n",
" 0.118102 \n",
" 0.035808 \n",
" 0.011810 \n",
" 0.003581 \n",
" \n",
" \n",
" 2 \n",
" Alouatta_belzebul \n",
" Alouatta \n",
" belzebul \n",
" NaN \n",
" 3 \n",
" 3 \n",
" 0.0 \n",
" 15.0 \n",
" 52.84 \n",
" 6395.0 \n",
" 7.4 \n",
" NaN \n",
" NaN \n",
" NaN \n",
" NaN \n",
" NaN \n",
" 0.107558 \n",
" 0.049192 \n",
" 0.010756 \n",
" 0.004919 \n",
" \n",
" \n",
" 3 \n",
" Alouatta_caraya \n",
" Alouatta \n",
" caraya \n",
" NaN \n",
" 4 \n",
" 3 \n",
" 0.0 \n",
" 45.0 \n",
" 52.63 \n",
" 5383.0 \n",
" 8.9 \n",
" 185.92 \n",
" 323.16 \n",
" 243.6 \n",
" 1276.72 \n",
" 509.08 \n",
" 0.107130 \n",
" 0.041408 \n",
" 0.010713 \n",
" 0.004141 \n",
" \n",
" \n",
" 4 \n",
" Alouatta_guariba \n",
" Alouatta \n",
" guariba \n",
" NaN \n",
" 5 \n",
" 3 \n",
" 0.0 \n",
" 37.0 \n",
" 51.70 \n",
" 5175.0 \n",
" 7.4 \n",
" NaN \n",
" NaN \n",
" NaN \n",
" NaN \n",
" NaN \n",
" 0.105237 \n",
" 0.039808 \n",
" 0.010524 \n",
" 0.003981 \n",
" \n",
" \n",
" 5 \n",
" Alouatta_palliata \n",
" Alouatta \n",
" palliata \n",
" NaN \n",
" 6 \n",
" 3 \n",
" 3.0 \n",
" 79.0 \n",
" 49.88 \n",
" 6250.0 \n",
" 13.1 \n",
" 185.42 \n",
" 495.60 \n",
" 300.0 \n",
" 1578.42 \n",
" 681.02 \n",
" 0.101533 \n",
" 0.048077 \n",
" 0.010153 \n",
" 0.004808 \n",
" \n",
" \n",
"
\n",
"
"
],
"text/plain": [
" name genus species subspecies \\\n",
"0 Allenopithecus_nigroviridis Allenopithecus nigroviridis NaN \n",
"2 Alouatta_belzebul Alouatta belzebul NaN \n",
"3 Alouatta_caraya Alouatta caraya NaN \n",
"4 Alouatta_guariba Alouatta guariba NaN \n",
"5 Alouatta_palliata Alouatta palliata NaN \n",
"\n",
" spp_id genus_id social_learning research_effort brain body \\\n",
"0 1 1 0.0 6.0 58.02 4655.0 \n",
"2 3 3 0.0 15.0 52.84 6395.0 \n",
"3 4 3 0.0 45.0 52.63 5383.0 \n",
"4 5 3 0.0 37.0 51.70 5175.0 \n",
"5 6 3 3.0 79.0 49.88 6250.0 \n",
"\n",
" group_size gestation weaning longevity sex_maturity \\\n",
"0 40.0 NaN 106.15 276.0 NaN \n",
"2 7.4 NaN NaN NaN NaN \n",
"3 8.9 185.92 323.16 243.6 1276.72 \n",
"4 7.4 NaN NaN NaN NaN \n",
"5 13.1 185.42 495.60 300.0 1578.42 \n",
"\n",
" maternal_investment B M Bse Mse \n",
"0 NaN 0.118102 0.035808 0.011810 0.003581 \n",
"2 NaN 0.107558 0.049192 0.010756 0.004919 \n",
"3 509.08 0.107130 0.041408 0.010713 0.004141 \n",
"4 NaN 0.105237 0.039808 0.010524 0.003981 \n",
"5 681.02 0.101533 0.048077 0.010153 0.004808 "
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d = pd.read_csv('../../data/Primates301.csv', header=0, sep=';')\n",
"d.dropna(subset=['brain','body'], inplace=True)\n",
"d['B'] = d['brain']/np.max(d['brain'])\n",
"d['M'] = d['body']/np.max(d['body'])\n",
"d['Bse'] = d['B']*0.1\n",
"d['Mse'] = d['M']*0.1\n",
"d.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now I'll make up some standard errors for B and M, assuming error is 10% of the measurement (_I just did_).\n",
"\n",
"Ignoring measurement error, the corresponding `ulam` (_pymc3_) model is:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"Bse = theano.shared(np.array(d['Bse']))\n",
"M = theano.shared(np.array(d['M']))\n",
"Mse = theano.shared(np.array(d['Mse']))\n",
"B = theano.shared(np.array(d['B']))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"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, a]\n",
"Sampling 4 chains, 0 divergences: 100%|██████████| 14000/14000 [00:09<00:00, 1439.68draws/s]\n"
]
}
],
"source": [
"with pm.Model() as model_11: \n",
" # Priors\n",
" a = pm.Normal('a', mu=0, sd=1)\n",
" b = pm.Normal('b', mu=0, sd=0.5)\n",
" sigma = pm.Exponential('sigma', lam=1)\n",
" \n",
" # Regression\n",
" mu = a + b*np.log(M)\n",
" brain_hat = pm.Lognormal('brain_hat', mu, sigma, observed=B)\n",
"\n",
" # Prior sampling, trace definition and posterior sampling\n",
" #prior = pm.sample_prior_predictive()\n",
" posterior_11 = pm.sample(tune=3000)\n",
" #posterior_pred_11 = pm.sample_posterior_predictive(posterior_11)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Your job is to add the measurement errors to this model. Use the divorce/marriage example in the chapter as a guide. It might help to initialize the unobserved true values of `B` and `M` using the observed values, by adding a list like this to `ulam` (_in pymc3 this is done by defining a `start` parameter in the `pm.sample` function_)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Running the model without measurement error (the code was given in the assignment), we get:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" \n",
" mean \n",
" sd \n",
" mcse_mean \n",
" mcse_sd \n",
" hpd_5.5% \n",
" hpd_94.5% \n",
" ess_mean \n",
" ess_sd \n",
" ess_bulk \n",
" ess_tail \n",
" r_hat \n",
" \n",
" \n",
" \n",
" \n",
" a \n",
" 0.42 \n",
" 0.06 \n",
" 0.0 \n",
" 0.0 \n",
" 0.34 \n",
" 0.52 \n",
" 770.0 \n",
" 770.0 \n",
" 765.0 \n",
" 936.0 \n",
" 1.00 \n",
" \n",
" \n",
" b \n",
" 0.78 \n",
" 0.01 \n",
" 0.0 \n",
" 0.0 \n",
" 0.76 \n",
" 0.80 \n",
" 819.0 \n",
" 819.0 \n",
" 818.0 \n",
" 1011.0 \n",
" 1.01 \n",
" \n",
" \n",
" sigma \n",
" 0.29 \n",
" 0.02 \n",
" 0.0 \n",
" 0.0 \n",
" 0.26 \n",
" 0.32 \n",
" 1021.0 \n",
" 1005.0 \n",
" 1033.0 \n",
" 859.0 \n",
" 1.01 \n",
" \n",
" \n",
"
\n",
"
"
],
"text/plain": [
" mean sd mcse_mean mcse_sd hpd_5.5% hpd_94.5% ess_mean ess_sd \\\n",
"a 0.42 0.06 0.0 0.0 0.34 0.52 770.0 770.0 \n",
"b 0.78 0.01 0.0 0.0 0.76 0.80 819.0 819.0 \n",
"sigma 0.29 0.02 0.0 0.0 0.26 0.32 1021.0 1005.0 \n",
"\n",
" ess_bulk ess_tail r_hat \n",
"a 765.0 936.0 1.00 \n",
"b 818.0 1011.0 1.01 \n",
"sigma 1033.0 859.0 1.01 "
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.summary(posterior_11, var_names=['a','b', 'sigma'], credible_interval=.89).round(2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll plot this implied relationship in a moment, after fitting the measurement error model too. To build the measurement error model, all we really need to do is add the observation process. This means that the observed values arise from their own distribution, each having a true value as the mean. We use these unknown true values in the regression. It looks like this:"
]
},
{
"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 (4 chains in 4 jobs)\n",
"NUTS: [B_true, M_true, b, a, sigma]\n",
"Sampling 4 chains, 0 divergences: 100%|██████████| 8000/8000 [00:31<00:00, 251.14draws/s]\n"
]
}
],
"source": [
"N = len(d)\n",
"\n",
"with pm.Model() as model_12: \n",
" # Priors\n",
" sigma = pm.Exponential('sigma', lam=1)\n",
" a = pm.Normal('a', 0., 1.)\n",
" b = pm.Normal('b', 0., 1.)\n",
" \n",
" # Regression for the true values\n",
" M_true = pm.Normal('M_true', mu=0.5, sd=1, shape=N)\n",
" mu = a + b*np.log(M_true)\n",
" B_true = pm.Lognormal('B_true', mu, sigma, shape=N)\n",
" \n",
" # Observed variables\n",
" B_obs = pm.Normal('B_obs', B_true, Bse, observed=B)\n",
" M_obs = pm.Normal('M_obs', M_true, Mse, observed=M)\n",
" \n",
" # Start value and additional kwarg for NUTS and trace definition\n",
" start = dict(B_true=d.B.values, M_true=d.M.values)\n",
" posterior_12 = pm.sample(1000,\n",
" tune=1000,\n",
" start=start,\n",
" nuts_kwargs=dict(target_accept=.95))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" \n",
" mean \n",
" sd \n",
" mcse_mean \n",
" mcse_sd \n",
" hpd_5.5% \n",
" hpd_94.5% \n",
" ess_mean \n",
" ess_sd \n",
" ess_bulk \n",
" ess_tail \n",
" r_hat \n",
" \n",
" \n",
" \n",
" \n",
" a \n",
" 0.42 \n",
" 0.06 \n",
" 0.0 \n",
" 0.0 \n",
" 0.32 \n",
" 0.51 \n",
" 4743.0 \n",
" 4679.0 \n",
" 4774.0 \n",
" 2964.0 \n",
" 1.0 \n",
" \n",
" \n",
" b \n",
" 0.78 \n",
" 0.01 \n",
" 0.0 \n",
" 0.0 \n",
" 0.76 \n",
" 0.81 \n",
" 4753.0 \n",
" 4752.0 \n",
" 4754.0 \n",
" 3002.0 \n",
" 1.0 \n",
" \n",
" \n",
" sigma \n",
" 0.26 \n",
" 0.02 \n",
" 0.0 \n",
" 0.0 \n",
" 0.23 \n",
" 0.29 \n",
" 4990.0 \n",
" 4918.0 \n",
" 5002.0 \n",
" 3137.0 \n",
" 1.0 \n",
" \n",
" \n",
"
\n",
"
"
],
"text/plain": [
" mean sd mcse_mean mcse_sd hpd_5.5% hpd_94.5% ess_mean ess_sd \\\n",
"a 0.42 0.06 0.0 0.0 0.32 0.51 4743.0 4679.0 \n",
"b 0.78 0.01 0.0 0.0 0.76 0.81 4753.0 4752.0 \n",
"sigma 0.26 0.02 0.0 0.0 0.23 0.29 4990.0 4918.0 \n",
"\n",
" ess_bulk ess_tail r_hat \n",
"a 4774.0 2964.0 1.0 \n",
"b 4754.0 3002.0 1.0 \n",
"sigma 5002.0 3137.0 1.0 "
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.summary(posterior_12, var_names=['a','b', 'sigma'], credible_interval=.89).round(2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For now, notice that the posterior distributions of a and b are nearly identical to `model_11`. Adding measurement error hasn't changed a thing! Plotting the regression against the observed values:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"d['B_true'] = np.mean(posterior_12['B_true'], axis=0)\n",
"d['M_true'] = np.mean(posterior_12['M_true'], axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"aux = pd.DataFrame()\n",
"aux['x'] = np.arange(len(d))/len(d)\n",
"aux['avg_curve'] = np.exp(posterior_12['a'].mean())*aux['x']**(posterior_12['b'].mean())\n",
"\n",
"for i in range(50):\n",
" aux[f'curve_{i}'] = np.exp(posterior_12['a'][i])*aux['x']**(posterior_12['b'][i])"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"aux_plot = aux.melt(id_vars=['x'],\n",
" value_vars=aux.columns[2:].tolist(),\n",
" var_name='posteriors',\n",
" value_name='y')"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.vegalite.v3+json": {
"$schema": "https://vega.github.io/schema/vega-lite/v3.3.0.json",
"config": {
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"tooltip": null
},
"view": {
"height": 300,
"width": 400
}
},
"datasets": {
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{
"B": 0.11810206200256479,
"B_true": 0.116462449688558,
"Bse": 0.01181020620025648,
"M": 0.035807692307692304,
"M_true": 0.03602399656484449,
"Mse": 0.0035807692307692307,
"body": 4655,
"brain": 58.02,
"genus": "Allenopithecus",
"genus_id": 1,
"gestation": null,
"group_size": 40,
"longevity": 276,
"maternal_investment": null,
"name": "Allenopithecus_nigroviridis",
"research_effort": 6,
"sex_maturity": null,
"social_learning": 0,
"species": "nigroviridis",
"spp_id": 1,
"subspecies": null,
"weaning": 106.15
},
{
"B": 0.10755796201681357,
"B_true": 0.110342019538364,
"Bse": 0.010755796201681357,
"M": 0.049192307692307695,
"M_true": 0.047790078307424474,
"Mse": 0.0049192307692307695,
"body": 6395,
"brain": 52.84,
"genus": "Alouatta",
"genus_id": 3,
"gestation": null,
"group_size": 7.4,
"longevity": null,
"maternal_investment": null,
"name": "Alouatta_belzebul",
"research_effort": 15,
"sex_maturity": null,
"social_learning": 0,
"species": "belzebul",
"spp_id": 3,
"subspecies": null,
"weaning": null
},
{
"B": 0.10713049850387771,
"B_true": 0.1082720941983897,
"Bse": 0.010713049850387771,
"M": 0.041407692307692305,
"M_true": 0.04082682792618366,
"Mse": 0.004140769230769231,
"body": 5383,
"brain": 52.63,
"genus": "Alouatta",
"genus_id": 3,
"gestation": 185.92,
"group_size": 8.9,
"longevity": 243.6,
"maternal_investment": 509.08,
"name": "Alouatta_caraya",
"research_effort": 45,
"sex_maturity": 1276.72,
"social_learning": 0,
"species": "caraya",
"spp_id": 4,
"subspecies": null,
"weaning": 323.16
},
{
"B": 0.10523744580373319,
"B_true": 0.10632568533948064,
"Bse": 0.01052374458037332,
"M": 0.03980769230769231,
"M_true": 0.03927622203931924,
"Mse": 0.003980769230769231,
"body": 5175,
"brain": 51.7,
"genus": "Alouatta",
"genus_id": 3,
"gestation": null,
"group_size": 7.4,
"longevity": null,
"maternal_investment": null,
"name": "Alouatta_guariba",
"research_effort": 37,
"sex_maturity": null,
"social_learning": 0,
"species": "guariba",
"spp_id": 5,
"subspecies": null,
"weaning": null
},
{
"B": 0.10153276202495573,
"B_true": 0.10474510886323234,
"Bse": 0.010153276202495573,
"M": 0.04807692307692308,
"M_true": 0.0465858569277565,
"Mse": 0.004807692307692308,
"body": 6250,
"brain": 49.88,
"genus": "Alouatta",
"genus_id": 3,
"gestation": 185.42,
"group_size": 13.1,
"longevity": 300,
"maternal_investment": 681.02,
"name": "Alouatta_palliata",
"research_effort": 79,
"sex_maturity": 1578.42,
"social_learning": 3,
"species": "palliata",
"spp_id": 6,
"subspecies": null,
"weaning": 495.6
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",
"text/plain": [
"\n",
"\n",
"If you see this message, it means the renderer has not been properly enabled\n",
"for the frontend that you are using. For more information, see\n",
"https://altair-viz.github.io/user_guide/troubleshooting.html\n"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot = alt.Chart(d)\\\n",
" .mark_circle()\\\n",
" .encode(\n",
" x=alt.X('M',title='body mass',scale=alt.Scale(domain=(0, 1))),\n",
" y=alt.Y('B',title='brain volume',scale=alt.Scale(domain=(0, 1)))\n",
" )\n",
"\n",
"plot_2 = alt.Chart(aux_plot)\\\n",
" .mark_line(clip=True)\\\n",
" .encode(\n",
" x=alt.X('x',scale=alt.Scale(domain=(0, 1))),\n",
" y=alt.Y('y',scale=alt.Scale(domain=(0, 1))),\n",
" color = alt.Color('posteriors', legend=None)\n",
" )\n",
"\n",
"plot_3 = alt.Chart(d)\\\n",
" .mark_point()\\\n",
" .encode(\n",
" x=alt.X('M_true',scale=alt.Scale(domain=(0, 1))),\n",
" y=alt.Y('B_true',scale=alt.Scale(domain=(0, 1)))\n",
" )\n",
"\n",
"plot_4 = alt.Chart(aux)\\\n",
" .mark_line(clip=True, color='black')\\\n",
" .encode(\n",
" x=alt.X('x',scale=alt.Scale(domain=(0, 1))),\n",
" y=alt.Y('avg_curve',scale=alt.Scale(domain=(0, 1)))\n",
" )\n",
"\n",
"alt.hconcat(plot + plot_2, plot + plot_3 + plot_4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(_On the left chart_) The two points in the upper right are gorillas. Most primates are small, and obviously gorillas have something special going on.\n",
"\n",
"(_On the right chart_) Now let's plot the estimated values on this. The open points are the posterior mean estimates. Notice that they have moved\n",
"towards the regression line, as you'd expect. But even the outlier gorillas haven't moved much. The assumed error just isn't big enough to get them any closer. If you increase the amount of error, you can get all of the species to fall right on the regression line. Try for example 30% error. The model will mix poorly, but take a look at the inferred true values. The truth of this example is that there are just so many small primates that they\n",
"dominate the relationship. And their measurement errors are also smaller (in absolute terms). So adding plausible amounts of measurement error here doesn't make a big difference. We still don't have a good explanation for gorillas.\n",
"\n",
"Before moving on, I'll also plot the estimated species values with 50% compatibility ellipses."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"aux_ellipse = pd.concat([pd.DataFrame(pm.stats.hpd(posterior_12['B_true'], alpha=0.1)).rename({0:'B_true_lower_hpdi',1:'B_true_upper_hpdi'}, axis=1),\n",
" pd.DataFrame(pm.stats.hpd(posterior_12['M_true'], alpha=0.1)).rename({0:'M_true_lower_hpdi',1:'M_true_upper_hpdi'}, axis=1),\n",
" pd.DataFrame(np.mean(posterior_12['B_true'], axis=0)).rename({0:'B_true_avg'}, axis=1),\n",
" pd.DataFrame(np.mean(posterior_12['M_true'], axis=0)).rename({0:'M_true_avg'}, axis=1)],\n",
" axis=1)\n",
"\n",
"aux_ellipse['B_true_hpdi'] = abs(aux_ellipse.B_true_lower_hpdi - aux_ellipse.B_true_upper_hpdi)\n",
"aux_ellipse['M_true_hpdi'] = abs(aux_ellipse.M_true_lower_hpdi - aux_ellipse.M_true_upper_hpdi)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ells = [Ellipse(xy=aux_ellipse.loc[i,['M_true_avg','B_true_avg']].values,\n",
" width=aux_ellipse.loc[i,'M_true_hpdi'],\n",
" height=aux_ellipse.loc[i,'B_true_hpdi'])\n",
" for i in range(len(aux_ellipse))]\n",
"\n",
"fig = plt.figure(0, figsize=(8, 6))\n",
"ax = fig.add_subplot(111, aspect='equal')\n",
"ax.set_ylabel('brain volume')\n",
"ax.set_xlabel('body mass')\n",
"for e in ells:\n",
" ax.add_artist(e)\n",
" e.set_alpha(0.1)\n",
"\n",
"ax.set_xlim(0, 1.2)\n",
"ax.set_ylim(0, 1.2)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> Now consider missing values, this data set is lousy with them. You can ignore measurement error in this problem. Let's get a quick idea of the missing values by counting them in each variable:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"name 0\n",
"genus 0\n",
"species 0\n",
"subspecies 267\n",
"spp_id 0\n",
"genus_id 0\n",
"social_learning 98\n",
"research_effort 115\n",
"brain 117\n",
"body 63\n",
"group_size 114\n",
"gestation 161\n",
"weaning 185\n",
"longevity 181\n",
"sex_maturity 194\n",
"maternal_investment 197\n",
"dtype: int64"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d = pd.read_csv('../../data/Primates301.csv', header=0, sep=';')\n",
"d.isna().sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We’ll continue to focus on just brain and body, to stave off insanity. Consider only those species with measured body masses:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"name 0\n",
"genus 0\n",
"species 0\n",
"subspecies 223\n",
"spp_id 0\n",
"genus_id 0\n",
"social_learning 39\n",
"research_effort 53\n",
"brain 56\n",
"body 0\n",
"group_size 52\n",
"gestation 98\n",
"weaning 122\n",
"longevity 118\n",
"sex_maturity 131\n",
"maternal_investment 134\n",
"B 56\n",
"M 0\n",
"dtype: int64"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d.dropna(subset=['body'], inplace=True)\n",
"d['B'] = d['brain']/np.max(d['brain'])\n",
"d['M'] = d['body']/np.max(d['body'])\n",
"d.isna().sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, consider whether there is a pattern to the missing values. Does it look like\n",
"missing values are associated with particular values of body mass? Draw a DAG that\n",
"represents how missingness works in this case. Which type (MCAR, MAR, MNAR)\n",
"is this?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compare the inferences to an analysis that drops all the missing values. Has anything changed? Why or why not? Hint: Consider the density of data in the ranges where there are missing values. You might want to plot the imputed brain sizes together with the observed values."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks like the missing brain values are almost all for small bodied species. This implies at least a MAR (dog eats students homework) mechanism. Let's try a DAG to express it:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`M` here is body mass, `B` (unobserved, suggested by the circle) is brain size, R_B is the missingness mechanism, and `B*` is the observed brain sizes (with missing values). The arrow from `M` to `R_B` indicates that body size influences missingness. In this case, it would imply that small body size makes a missing brain value more likely.\n",
"\n",
"Now let's do some imputation. Remember that the model for imputation is really no different than an ordinary model. It just needs a prior for any variable with missing values. In this case, the missing values are in the outcome, so the likelihood is the prior we need. So the model doesn't change at all."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# PyMC3 can handle missing value quite naturally.\n",
"body = d['B'].values.copy()\n",
"mask = np.isnan(body)\n",
"#body[~mask] = -999\n",
"#body = np.ma.masked_values(body, value=-999)\n",
"body = np.ma.masked_array(data=body, mask=mask)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"M = theano.shared(np.array(d['M']))\n",
"B = theano.shared(np.array(d['B']))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"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: [brain_hat_missing, sigma, b, a]\n",
"Sampling 4 chains, 0 divergences: 100%|██████████| 10000/10000 [01:25<00:00, 117.63draws/s]\n"
]
}
],
"source": [
"with pm.Model() as model_21: \n",
" # Priors\n",
" a = pm.Normal('a', mu=0, sd=1)\n",
" b = pm.Normal('b', mu=0, sd=1)\n",
" sigma = pm.Exponential('sigma', lam=1)\n",
" \n",
" # Regression\n",
" mu = a + b*np.log(M)\n",
" brain_hat = pm.Lognormal('brain_hat', mu, sigma, observed=body) # please note that body contains masked values\n",
" \n",
" # Prior sampling, trace definition and posterior sampling\n",
" #prior = pm.sample_prior_predictive()\n",
" posterior_21 = pm.sample(tune=2000)\n",
" #posterior_pred_21 = pm.sample_posterior_predictive(posterior_21)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is the posterior summary for the imputation model:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" \n",
" mean \n",
" sd \n",
" mcse_mean \n",
" mcse_sd \n",
" hpd_5.5% \n",
" hpd_94.5% \n",
" ess_mean \n",
" ess_sd \n",
" ess_bulk \n",
" ess_tail \n",
" r_hat \n",
" \n",
" \n",
" \n",
" \n",
" a \n",
" 0.43 \n",
" 0.06 \n",
" 0.0 \n",
" 0.0 \n",
" 0.33 \n",
" 0.51 \n",
" 1333.0 \n",
" 1328.0 \n",
" 1332.0 \n",
" 1340.0 \n",
" 1.0 \n",
" \n",
" \n",
" b \n",
" 0.78 \n",
" 0.01 \n",
" 0.0 \n",
" 0.0 \n",
" 0.76 \n",
" 0.81 \n",
" 1140.0 \n",
" 1137.0 \n",
" 1140.0 \n",
" 1108.0 \n",
" 1.0 \n",
" \n",
" \n",
" sigma \n",
" 0.29 \n",
" 0.02 \n",
" 0.0 \n",
" 0.0 \n",
" 0.27 \n",
" 0.32 \n",
" 1912.0 \n",
" 1902.0 \n",
" 1899.0 \n",
" 1321.0 \n",
" 1.0 \n",
" \n",
" \n",
"
\n",
"
"
],
"text/plain": [
" mean sd mcse_mean mcse_sd hpd_5.5% hpd_94.5% ess_mean ess_sd \\\n",
"a 0.43 0.06 0.0 0.0 0.33 0.51 1333.0 1328.0 \n",
"b 0.78 0.01 0.0 0.0 0.76 0.81 1140.0 1137.0 \n",
"sigma 0.29 0.02 0.0 0.0 0.27 0.32 1912.0 1902.0 \n",
"\n",
" ess_bulk ess_tail r_hat \n",
"a 1332.0 1340.0 1.0 \n",
"b 1140.0 1108.0 1.0 \n",
"sigma 1899.0 1321.0 1.0 "
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.summary(posterior_21, var_names=['a','b', 'sigma'], credible_interval=.89).round(2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The same analysis on only complete cases:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"d = pd.read_csv('../../data/Primates301.csv', header=0, sep=';')\n",
"d.dropna(subset=['body', 'brain'], inplace=True)\n",
"d['B'] = d['brain']/np.max(d['brain'])\n",
"d['M'] = d['body']/np.max(d['body'])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"M = theano.shared(np.array(d['M']))\n",
"B = theano.shared(np.array(d['B']))"
]
},
{
"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 (4 chains in 4 jobs)\n",
"NUTS: [sigma, b, a]\n",
"Sampling 4 chains, 0 divergences: 100%|██████████| 10000/10000 [00:06<00:00, 1527.08draws/s]\n"
]
}
],
"source": [
"with pm.Model() as model_22: \n",
" # Priors\n",
" a = pm.Normal('a', mu=0, sd=1)\n",
" b = pm.Normal('b', mu=0, sd=1)\n",
" sigma = pm.Exponential('sigma', lam=1)\n",
" \n",
" # Regression\n",
" mu = a + b*np.log(M)\n",
" brain_hat = pm.Lognormal('brain_hat', mu, sigma, observed=B)\n",
" \n",
" # Prior sampling, trace definition and posterior sampling\n",
" #prior = pm.sample_prior_predictive()\n",
" posterior_22 = pm.sample(tune=2000)\n",
" #posterior_pred_22 = pm.sample_posterior_predictive(posterior_22)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" \n",
" mean \n",
" sd \n",
" mcse_mean \n",
" mcse_sd \n",
" hpd_5.5% \n",
" hpd_94.5% \n",
" ess_mean \n",
" ess_sd \n",
" ess_bulk \n",
" ess_tail \n",
" r_hat \n",
" \n",
" \n",
" \n",
" \n",
" a \n",
" 0.43 \n",
" 0.06 \n",
" 0.0 \n",
" 0.0 \n",
" 0.34 \n",
" 0.52 \n",
" 773.0 \n",
" 762.0 \n",
" 774.0 \n",
" 899.0 \n",
" 1.00 \n",
" \n",
" \n",
" b \n",
" 0.78 \n",
" 0.01 \n",
" 0.0 \n",
" 0.0 \n",
" 0.76 \n",
" 0.80 \n",
" 751.0 \n",
" 749.0 \n",
" 751.0 \n",
" 978.0 \n",
" 1.00 \n",
" \n",
" \n",
" sigma \n",
" 0.29 \n",
" 0.02 \n",
" 0.0 \n",
" 0.0 \n",
" 0.27 \n",
" 0.31 \n",
" 1166.0 \n",
" 1166.0 \n",
" 1137.0 \n",
" 870.0 \n",
" 1.01 \n",
" \n",
" \n",
"
\n",
"
"
],
"text/plain": [
" mean sd mcse_mean mcse_sd hpd_5.5% hpd_94.5% ess_mean ess_sd \\\n",
"a 0.43 0.06 0.0 0.0 0.34 0.52 773.0 762.0 \n",
"b 0.78 0.01 0.0 0.0 0.76 0.80 751.0 749.0 \n",
"sigma 0.29 0.02 0.0 0.0 0.27 0.31 1166.0 1166.0 \n",
"\n",
" ess_bulk ess_tail r_hat \n",
"a 774.0 899.0 1.00 \n",
"b 751.0 978.0 1.00 \n",
"sigma 1137.0 870.0 1.01 "
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.summary(posterior_22, var_names=['a','b', 'sigma'], credible_interval=.89).round(2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_Let's add a quick model comparison:_"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"model_21.name = 'model_11'\n",
"model_22.name = 'model_12'"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" \n",
" WAIC \n",
" pWAIC \n",
" dWAIC \n",
" weight \n",
" SE \n",
" dSE \n",
" var_warn \n",
" \n",
" \n",
" \n",
" \n",
" model_12 \n",
" -869.7 \n",
" 2.46 \n",
" 0 \n",
" 1 \n",
" 37.81 \n",
" 0 \n",
" 0 \n",
" \n",
" \n",
" model_11 \n",
" -869.41 \n",
" 2.59 \n",
" 0.29 \n",
" 0 \n",
" 37.81 \n",
" 0.03 \n",
" 0 \n",
" \n",
" \n",
"
\n",
"
"
],
"text/plain": [
" WAIC pWAIC dWAIC weight SE dSE var_warn\n",
"model_12 -869.7 2.46 0 1 37.81 0 0\n",
"model_11 -869.41 2.59 0.29 0 37.81 0.03 0"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.compare({model_21: posterior_21,\n",
" model_22: posterior_22})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Really no difference from before. Let's plot the imputed values:"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"d = pd.read_csv('../../data/Primates301.csv', header=0, sep=';')\n",
"d.dropna(subset=['body'], inplace=True)\n",
"d['B'] = d['brain']/np.max(d['brain'])\n",
"d['M'] = d['body']/np.max(d['body'])"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"aux = pd.concat([pd.DataFrame(d.M[np.isnan(d.loc[:, 'B'])]).reset_index(drop=True),\n",
" pd.DataFrame(np.mean(posterior_21['brain_hat_missing'], axis=0)).reset_index(drop=True).rename({0:'B'}, axis=1),\n",
" pd.DataFrame(pm.stats.hpd(posterior_21['brain_hat_missing'], alpha=0.5)).rename({0:'B_lower_hpdi',1:'B_upper_hpdi'}, axis=1)],\n",
" axis = 1)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.vegalite.v3+json": {
"$schema": "https://vega.github.io/schema/vega-lite/v3.3.0.json",
"config": {
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},
"view": {
"height": 300,
"width": 400
}
},
"data": {
"name": "data-ba9ad9c6de9be31ad925cdb10e11dd2a"
},
"datasets": {
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{
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"name": "Brachyteles_arachnoides",
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{
"B": 0.2252936267225762,
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"brain": 110.68,
"genus": "Bunopithecus",
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"name": "Bunopithecus_hoolock",
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"species": "hoolock",
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{
"B": 0.15470108087202558,
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"body": 3165,
"brain": 76,
"genus": "Cacajao",
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"name": "Cacajao_calvus",
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"species": "calvus",
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{
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"brain": 68.77,
"genus": "Cacajao",
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"name": "Cacajao_melanocephalus",
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"species": "melanocephalus",
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",
"text/plain": [
"\n",
"\n",
"If you see this message, it means the renderer has not been properly enabled\n",
"for the frontend that you are using. For more information, see\n",
"https://altair-viz.github.io/user_guide/troubleshooting.html\n"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# generate the points\n",
"points = alt.Chart(aux).mark_point(\n",
" filled=True,\n",
" size=50,\n",
" color='black'\n",
").encode(\n",
" x=alt.X('M', title='body mass M',scale=alt.Scale(domain=(0, 1))),\n",
" y=alt.Y('B', title='brain size B',scale=alt.Scale(domain=(0, 1)))\n",
")\n",
"\n",
"points2 = alt.Chart(d).mark_point(\n",
" filled=True,\n",
" size=50,\n",
" color='blue',\n",
" opacity=0.3\n",
").encode(\n",
" x=alt.X('M', scale=alt.Scale(domain=(0, 1))),\n",
" y=alt.Y('B', scale=alt.Scale(domain=(0, 1)))\n",
")\n",
"\n",
"# generate the error bars\n",
"errorbars = alt.Chart(aux).mark_errorbar().encode(\n",
" x=alt.X(\"M\"),\n",
" y=alt.Y(\"B_lower_hpdi:Q\", title=None),\n",
" y2=\"B_upper_hpdi:Q\"\n",
")\n",
"\n",
"points + errorbars + points2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Black open points are the imputed values, with 50% compatibility intervals. Imputation hasn't done much, apparently because all but one of the missing values are in a very dense region of the body size range. So almost no information was lost, the missing info is redundant."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "py_36_gabi",
"language": "python",
"name": "py_36_gabi"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.6"
}
},
"nbformat": 4,
"nbformat_minor": 4
}