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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": 7,
"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": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<Container object of 5 artists>"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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wKrA8ySXA+VW1s1330ECfwbEeB65t7euBbVV1qKoOAduZCCNJ0pCdihXH3yT5aZI/abWL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\n6vL/AHQ84m6DhafzAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e925650>"
]
},
"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": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 35000 of 35000 complete in 6.3 secProbability B > A: 0.0\n",
"Confidence interval of B:s lift over A:\n",
"-0.371879871974\n",
"-0.294568058189\n",
"MCMC error: 0.00203363124491\n",
"Plotting p_A_0\n",
"Plotting p_A_1\n",
"Plotting p_A_2\n",
"Plotting p_A_3\n",
"Plotting p_B_0\n",
"Plotting p_B_1\n",
"Plotting p_B_2\n",
"Plotting p_B_3\n",
"Plotting percent_better\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/max/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
" if self._edgecolors == str('face'):\n"
]
},
{
"data": {
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OmF+UtEyb8s0pHxe/7mrH9cqCIAhgvvP3zpKukHShpAsHLVMQBKNNK+OpvJJuNVIcpyKb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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10eca8cd0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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Xe98b+Hvbe+djq9l+XNJmwMFZp2uB3WzfnXunNgE+ansfSesCX7bdrBcsCGYk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\nCG2IylMIIYQQQhui8hRCCCGE0Ib/D4fyspHUOLSnAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f96e390>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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8DSCxAXAdlcOINFKpZ+uK+ZxLVElTegzax+YS0sDFIYQQekAU1jrPDcDOef6W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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10eca8ed0>"
]
},
"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": 375,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-0.367216638707\n",
"-0.298360764744\n",
"Not converging according to formal method\n",
"(2.9026146801069475, 5.6708199502289833, 7.7850070972276058, 8.081753796917603, 7.6527901882342446, 1.9292490938338818, 0.47171158317553213, 0.13324045052897904, -0.22668565839328658, -3.7859306270738071)\n",
"B:s mean is -0.493510107127 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": 365,
"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": 366,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MannwhitneyuResult(statistic=273515399.5, pvalue=0.027581277207720606)\n",
"RanksumsResult(statistic=1.9175665210109343, pvalue=0.055165998636884803)\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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