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Testing hypotheses via a mixture estimation model in PyMC3
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Testing hypotheses via a mixture estimation model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Simple demo of the idea in https://arxiv.org/pdf/1412.2044v2.pdf \n",
"Related discussion: [Christian Robert's Blog post](https://xianblog.wordpress.com/2016/12/05/bayesian-parameter-estimation-versus-model-comparison/), [Discussion on X validated](https://xianblog.wordpress.com/2016/12/05/bayesian-parameter-estimation-versus-model-comparison/) \n",
"The data and code is based on the BEST example of PyMC3"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"import numpy as np\n",
"import pymc3 as pm\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"sns.set(color_codes=True)\n",
"\n",
"%pylab inline\n",
"%config InlineBackend.figure_format = 'retina'\n",
"%qtconsole --colors=linux\n",
"# np.random.seed(20090425)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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AoGMCPQAAdEygBwCAjgn0AADQMYEeAAA6JtADAEDHBHoAAOiYQA8AAB0T6AEA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\nAAB0TKAHAICOCfQAANAxgR4AADr2/wBr1xZwhc2v3gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f224b9afe48>"
]
},
"metadata": {
"image/png": {
"height": 268,
"width": 378
}
},
"output_type": "display_data"
}
],
"source": [
"# drug = (101,100,102,104,102,97,105,105,98,101,100,123,105,103,100,95,102,106,\n",
"# 109,102,82,102,100,102,102,101,102,102,103,103,97,97,103,101,97,104,\n",
"# 96,103,124,101,101,100,101,101,104,100,101)\n",
"# placebo = (99,101,100,101,102,100,97,101,104,101,102,102,100,105,88,101,100,\n",
"# 104,100,100,100,101,102,103,97,101,101,100,101,99,101,100,100,\n",
"# 101,100,99,101,100,102,99,100,99)\n",
"\n",
"Nsbj = 42\n",
"drug = np.random.normal(loc=101.5,scale=1,size=Nsbj)\n",
"placebo = np.random.normal(loc=100.5,scale=1,size=Nsbj)\n",
"\n",
"y1 = np.array(drug)\n",
"y2 = np.array(placebo)\n",
"y = pd.DataFrame(dict(value=np.r_[y1, y2], group=np.r_[['drug']*len(drug), ['placebo']*len(placebo)]))\n",
"\n",
"y.hist('value', by='group');"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using advi...\n",
"Average ELBO = -154.99: 18%|█▊ | 36023/200000 [00:02<00:11, 14756.75it/s]Median ELBO converged.\n",
"Finished [100%]: Average ELBO = -132.25\n",
"\n",
"100%|██████████| 2000/2000 [00:02<00:00, 799.77it/s]\n"
]
},
{
"data": {
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9X0oYfgHdxlxOZFw8pQV57Fv5K9u/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\nuOISli1byuTJ7zN5c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"text/plain": [
"<matplotlib.figure.Figure at 0x7f222a6ce0b8>"
]
},
"metadata": {
"image/png": {
"height": 351,
"width": 854
}
},
"output_type": "display_data"
}
],
"source": [
"# Bayesian Estimation Supersedes the T-Test (BEST) model\n",
"μ_m = y.value.mean()\n",
"μ_s = y.value.std() * 2\n",
"σ_low = 0\n",
"σ_high = 10\n",
"\n",
"with pm.Model() as model:\n",
" group1_mean = pm.Normal('group1_mean', μ_m, sd=μ_s)\n",
" group2_mean = pm.Normal('group2_mean', μ_m, sd=μ_s)\n",
" \n",
" group1_std = pm.Uniform('group1_std', lower=σ_low, upper=σ_high)\n",
" group2_std = pm.Uniform('group2_std', lower=σ_low, upper=σ_high)\n",
" \n",
" group1 = pm.Normal('drug', mu=group1_mean, sd=group1_std, observed=y1)\n",
" group2 = pm.Normal('placebo', mu=group2_mean, sd=group2_std, observed=y2)\n",
" \n",
" diff_of_means = pm.Deterministic('difference of means', group1_mean - group2_mean)\n",
" diff_of_stds = pm.Deterministic('difference of stds', group1_std - group2_std)\n",
" effect_size = pm.Deterministic('effect size', \n",
" diff_of_means / np.sqrt((group1_std**2 + group2_std**2) / 2))\n",
" \n",
" trace = pm.sample(2000, njobs=2)\n",
" \n",
"pm.plot_posterior(trace[100:], \n",
" varnames=['group1_mean', 'group2_mean', 'group1_std', 'group2_std'],\n",
" color='#87ceeb');"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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nExYWxtChd9C1azeio+uTkpLC+vVr+fLLiSQmJvCf/7xFeHg4vXv3K9bP5R+9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\n8tJOxS75aTXHwMUFecpOTtCBlT9p1xL7usO9Js+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mJsUj1TOUmSslfnzl3405/+zgUXnMfs2TO55547ueeeOzdIN2zYcH7/+xtp377pA862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\n/eY0sdwGRVH0fgjhN8DFwM3At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63c+offkZ+b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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f2228741390>"
]
},
"metadata": {
"image/png": {
"height": 351,
"width": 855
}
},
"output_type": "display_data"
}
],
"source": [
"pm.plot_posterior(trace[1000:], \n",
" varnames=['difference of means', 'difference of stds', 'effect size'],\n",
" ref_val=0,\n",
" color='#87ceeb');"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.gridspec.GridSpec at 0x7f22285c0978>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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2aq1vqbVuNOXPkQs45lq7Bm0oBCagq5Ry31LKYaWU3gNiXzxMrzekaSnl/HRG/Sml3Djt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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f2229e815c0>"
]
},
"metadata": {
"image/png": {
"height": 290,
"width": 422
}
},
"output_type": "display_data"
}
],
"source": [
"pm.forestplot(trace[1000:], varnames=[v.name for v in model.vars[:2]])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.gridspec.GridSpec at 0x7f2228481ac8>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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51ZbBUnhhWm3qI0sp12k6VWs9qNa6yZR/qxZwzEX7G1wfCRfAkiml3KOU8s5SykwPq/vr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\nhSRJkqQqTC4kSZIkVfE/20T2rojqOPwAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f2228609828>"
]
},
"metadata": {
"image/png": {
"height": 290,
"width": 395
}
},
"output_type": "display_data"
}
],
"source": [
"pm.forestplot(trace[1000:], varnames=[v.name for v in model.vars[2:]])"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"difference of means:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 0.815 0.232 0.005 [0.380, 1.274]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 0.356 0.668 0.811 0.971 1.254\n",
"\n",
"\n",
"difference of stds:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 0.258 0.173 0.004 [-0.072, 0.607]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" -0.071 0.143 0.259 0.368 0.610\n",
"\n",
"\n",
"effect size:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" \n",
" 0.769 0.225 0.005 [0.341, 1.235]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" \n",
" 0.321 0.628 0.773 0.916 1.219\n",
"\n"
]
}
],
"source": [
"pm.summary(trace[1000:], \n",
" varnames=['difference of means', 'difference of stds', 'effect size'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the Kamary et al (2014) they introduced a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. Their alternative to the traditional construction of Bayes factors or posterior probabilities of a model given the data is to consider the hypotheses or models under\n",
"comparison as components of a mixture model. Therefore, the original testing problem is replaced with an estimation one that focuses on the probability or weight of a given hypothesis within the mixture model.\n",
"\n",
"A reference $\\text{Beta}(a_0,a_0)$ prior on the mixture weights can be used for the common problem of\n",
"testing two contrasting hypotheses or models. In this case the sensitivity of the posterior estimates of the weights to the choice of $a_0$ vanishes as the sample size increases. Kamary et al advocate a default choice of $a_0 = 0.5$, derived from Rousseau and Mengersen (2011)\n",
"\n",
"### Update 2017-03-20\n",
"Sort the mixture weight so to break the multimodality [ref](http://mc-stan.org/documentation/case-studies/identifying_mixture_models.html). However, one must be careful of placing the order of the mixture component, as the less possible component should be place in the front. As a heuristic we can place the component coding for the null hypothesis before the alternative hypothesis, as our strawman null hypothesis is mostly false. "
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using advi...\n",
"Average ELBO = -259.09: 45%|████▍ | 22376/50000 [00:05<00:07, 3862.06it/s]Median ELBO converged.\n",
"Finished [100%]: Average ELBO = -258.85\n",
"\n",
"100%|██████████| 5000/5000 [01:10<00:00, 71.13it/s]\n"
]
}
],
"source": [
"# Hypotheses testing via mixture model estimation\n",
"import theano.tensor as tt\n",
"from pymc3.math import logsumexp\n",
"# from pymc3.dist_math import logpow, gammaln\n",
"\n",
"with pm.Model() as model2:\n",
" #H0\n",
" group0_mean = pm.Normal('group0_mean', μ_m, sd=μ_s)\n",
" group0_std = pm.Uniform('group0_std', lower=σ_low, upper=σ_high)\n",
" \n",
" group1_h0 = pm.Normal('drug_h0', mu=group0_mean, sd=group0_std)\n",
" group2_h0 = pm.Normal('placebo_h0', mu=group0_mean, sd=group0_std)\n",
" \n",
" #H1\n",
" group1_mean = pm.Normal('group1_mean', μ_m, sd=μ_s)\n",
" group2_mean = pm.Normal('group2_mean', μ_m, sd=μ_s)\n",
" \n",
" group1_std = pm.Uniform('group1_std', lower=σ_low, upper=σ_high)\n",
" group2_std = pm.Uniform('group2_std', lower=σ_low, upper=σ_high)\n",
" \n",
" group1_h1 = pm.Normal('drug_h1', mu=group1_mean, sd=group1_std)\n",
" group2_h1 = pm.Normal('placebo_h1', mu=group2_mean, sd=group2_std)\n",
" \n",
" a0 = pm.Dirichlet('a0',a=np.ones((2))*.5)\n",
" # use sort to break multimodality\n",
" a = pm.Deterministic('mixing',tt.sort(a0))\n",
" \n",
" group1 = pm.Mixture('drug', w=a, comp_dists=[group1_h0.distribution,group1_h1.distribution], observed=y1)\n",
" group2 = pm.Mixture('placebo', w=a, comp_dists=[group2_h0.distribution,group2_h1.distribution], observed=y2)\n",
" \n",
"# a = pm.Beta('mixing',alpha=.5,beta=.5)\n",
"# def mixturelogp(w,dist1,dist2):\n",
"# logp1 = dist1.distribution.logp\n",
"# logp2 = dist2.distribution.logp\n",
"# def logp_(value):\n",
"# logps = tt.log(w) + logp1(value) + tt.log(1-w) + logp2(value)\n",
"# return tt.sum(logsumexp(logps))\n",
"# return logp_\n",
"# group1 = pm.DensityDist('drug', mixturelogp(a,group1_h0,group1_h1), observed=y1)\n",
"# group2 = pm.DensityDist('placebo', mixturelogp(a,group2_h0,group2_h1), observed=y2)\n",
"\n",
" #start = pm.find_MAP()\n",
" trace = pm.sample(5000, njobs=2, tune=500, n_init=50000)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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