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@maxberggren
Created March 29, 2016 17:33
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import scipy \n",
"import scikits.bootstrap as bootstrap \n",
"from scipy.stats import mannwhitneyu as MWU\n",
"\n",
"import pymc as pm\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def decimate(data, by=0.1):\n",
" \"\"\" Multiply every element by 'by' and make to integer \"\"\"\n",
" data = np.array(data)*by\n",
" data = [int(d) for d in data]\n",
" return list(data)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def merge(data, n=2):\n",
" \"\"\" This summs every n elements in an array \"\"\"\n",
" data = np.array(data)\n",
" result = np.zeros(int(len(data)/float(n)))\n",
" for i in range(n):\n",
" d = np.lib.pad(data[i::n], (0,0), 'constant', constant_values=(0, 1))\n",
" result += d\n",
" \n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Working data\n",
"bins_A = [207763, 223077, 210613, 181571, 168385, 159171, 146068, 128502,\n",
" 110505, 94379, 79315, 67084, 57527, 48867, 41862]\n",
"bins_B = [219812, 228003, 208490, 182409, 173357, 164470, 151033, 132412,\n",
" 113750, 95835, 81206, 67876, 58057, 49005, 41808]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Not working data\n",
"bins_A = [1750102, 286721, 122232, 53109, 35203, 23628, 16135,\n",
" 18991, 24309, 11363, 9732, 8494, 5911, 4374,\n",
" 3526, 2462, 2186, 1909, 1811, 1684]\n",
"bins_B = [1726921, 279424, 111627, 48393, 29513, 20356, 13086,\n",
" 18364, 23361, 10805, 8752, 10323, 6007, 4252,\n",
" 3039, 2172, 1829, 1670, 1617, 1569]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Not working data multiplyed by 0.1\n",
"bins_A = decimate([1750102, 286721, 122232, 53109, 35203, 23628, 16135,\n",
" 18991, 24309, 11363, 9732, 8494, 5911, 4374,\n",
" 3526, 2462, 2186, 1909, 1811, 1684], by=0.1)\n",
"bins_B = decimate([1726921, 279424, 111627, 48393, 29513, 20356, 13086,\n",
" 18364, 23361, 10805, 8752, 10323, 6007, 4252,\n",
" 3039, 2172, 1829, 1670, 1617, 1569], by=0.1)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Not working data summing every 4 elements\n",
"bins_A = merge([1750102, 286721, 122232, 53109, 35203, 23628, 16135,\n",
" 18991, 24309, 11363, 9732, 8494, 5911, 4374,\n",
" 3526, 2462, 2186, 1909, 1811, 1684], n=4)\n",
"bins_B = merge([1726921, 279424, 111627, 48393, 29513, 20356, 13086,\n",
" 18364, 23361, 10805, 8752, 10323, 6007, 4252,\n",
" 3039, 2172, 1829, 1670, 1617, 1569], n=4)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"############### LATEST ATEMPT ###################\n",
"# Previously not working data, cutoff really hard\n",
"bins_A = [1750102, 286721, 122232, 53109]\n",
"bins_B = [1726921, 279424, 111627, 48393]"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<Container object of 4 artists>"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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rmpmNQlI0cjzxN+DNzKwyJxMzM6vMycTMzCpzMjEzs8qcTMzMrDInEzMzq8zJxMzMKnMy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\nPHS6/1ar1QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10eeea3d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Viz data\n",
"width = 0.35\n",
"fig, ax = plt.subplots()\n",
"ax.bar(np.arange(len(bins_A)), bins_A, width, color='y')\n",
"ax.bar(np.arange(len(bins_B))+width, bins_B, width, color='r')"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 35000 of 35000 complete in 6.4 secProbability B > A: 0.0\n",
"Confidence interval of B:s lift over A:\n",
"-0.763011099889\n",
"-0.608084992811\n",
"MCMC error: 0.0037988626617\n",
"Plotting percent_better\n",
"Plotting p_A_0\n",
"Plotting p_A_1\n",
"Plotting p_A_2\n",
"Plotting p_B_0\n",
"Plotting p_B_1\n",
"Plotting p_B_2\n"
]
},
{
"data": {
"image/png": 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Jv1QSNG+mlhpqNeGNLB/1mATpltQsn0k0rE3jUBd17ST4xj2nRZnUBpo40s+n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\nLPMEMCt/PAt4JiI2JYqnY+5lMxtMki6WtEHSisK8EUnrJd2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"text/plain": [
"<matplotlib.figure.Figure at 0x112e960d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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+JiNWjwatYl+PZy7tNLLfBRER/W48jcVUPkmrARcDh9l+uP49F9MVK19PSW8C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\nGQHh7kwhAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1101fa3d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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ze4GbqNby2xX4VCn2KWD3wUQ4N5I2pkpq+klWzGoYubpIWgS81PZpUOUjKzlz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\nsQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112272750>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"clicks = range(1, len(bins_A))\n",
"\n",
"# Start with uniform probability over the bins\n",
"p_A = pm.Dirichlet(\"p_A\", theta=np.ones(len(bins_A)))\n",
"p_B = pm.Dirichlet(\"p_B\", theta=np.ones(len(bins_B)))\n",
"\n",
"# A multimodal dist. using the probabilitys of bins\n",
"obs_A = pm.Multinomial(\"obs_A\", p=p_A, n=sum(bins_A), value=bins_A, observed=True)\n",
"obs_B = pm.Multinomial(\"obs_B\", p=p_B, n=sum(bins_B), value=bins_B, observed=True)\n",
"\n",
"@pm.deterministic\n",
"def percent_better(p_B=p_B, p_A=p_A, clicks=clicks):\n",
" exp_clicks_B = np.dot(p_B.astype(float)/sum(p_B), clicks)\n",
" exp_clicks_A = np.dot(p_A.astype(float)/sum(p_A), clicks)\n",
"\n",
" return ((exp_clicks_B / exp_clicks_A) - 1)*100.0\n",
"\n",
"model = pm.Model([p_A, p_B, \n",
" obs_A, obs_B, \n",
" percent_better])\n",
"\n",
"map_ = pm.MAP(model)\n",
"map_.fit()\n",
"mcmc = pm.MCMC(model)\n",
"#mcmc.sample(165000, burn=160000, thin=2)\n",
"mcmc.sample(35000, burn=30000, thin=2)\n",
"\n",
"percent_better_samples = mcmc.trace(\"percent_better\")[:]\n",
"\n",
"print \"Probability B > A: {}\".format((percent_better_samples > 0).mean())\n",
"print \"Confidence interval of B:s lift over A:\"\n",
"print np.percentile(percent_better_samples, 2.5)\n",
"print np.percentile(percent_better_samples, 97.5)\n",
"\n",
"print \"MCMC error: {}\".format(mcmc.stats()['percent_better']['mc error'])\n",
"pm.Matplot.plot(mcmc)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-0.763011099889\n",
"-0.608084992811\n",
"Not converging according to formal method\n",
"(3.4733998300159028, 3.8053861367012995, 0.43959472785041925, 0.44734304154408078, 2.5291389426278985, 5.4718243785644987, 3.2597975924775708, 4.0855060535518959, 7.4438977453069217, 1.9557078735730713)\n",
"B:s mean is -0.997654984107 percent better over A:s mean\n",
"Not in inference interval\n"
]
}
],
"source": [
"print np.percentile(percent_better_samples, 2.5)\n",
"print np.percentile(percent_better_samples, 97.5)\n",
"\n",
"step, stderr = zip(*pm.geweke(mcmc.trace(\"percent_better\")[:], \n",
" first=0.1, last=0.5, intervals=10))\n",
"\n",
"if sum([abs(s) > 3 for s in stderr]) > 2:\n",
" print \"Not converging according to formal method\"\n",
" print stderr\n",
"else:\n",
" print \"Converging according to formal method\"\n",
" print stderr\n",
" \n",
"exp_clicks_A = np.dot(bins_A, range(1, len(bins_A)+1)) / float(sum(bins_A))\n",
"exp_clicks_B = np.dot(bins_B, range(1, len(bins_B)+1)) / float(sum(bins_B))\n",
"\n",
"lift = (exp_clicks_B/exp_clicks_A - 1)*100.0\n",
"print \"B:s mean is {} percent better over A:s mean\".format(lift)\n",
"\n",
"if np.percentile(percent_better_samples, 2.5) < lift < np.percentile(percent_better_samples, 97.5):\n",
" print \"In interval\"\n",
"else:\n",
" print \"Not in inference interval\""
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def unfold(hist):\n",
" rewards = range(1, len(hist))\n",
" data = []\n",
" for count, reward in zip(hist, rewards):\n",
" data += [reward]*count\n",
" \n",
" return data"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MannwhitneyuResult(statistic=2274409450324.0, pvalue=2.7476557216956373e-21)\n",
"RanksumsResult(statistic=9.3992504971126802, pvalue=5.4953115687785614e-21)\n"
]
}
],
"source": [
"print MWU(unfold(bins_A), unfold(bins_B))\n",
"print scipy.stats.ranksums(unfold(bins_A), unfold(bins_B))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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