update bayes training

This commit is contained in:
ritchie46 committed 2019-04-19 14:37:14 +02:00
1 parent 8805a9b83a
commit 17b2045f12
1 file changed
+390 -90
+390 -90
View File
@@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": 2,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -43,7 +43,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 43, "execution_count": 3,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -73,7 +73,7 @@
"<IPython.core.display.HTML object>" "<IPython.core.display.HTML object>"
] ]
}, },
"execution_count": 43, "execution_count": 3,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@@ -132,7 +132,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 14, "execution_count": 4,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -141,7 +141,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
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truncated "image/png": 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truncated
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
@@ -162,10 +162,10 @@
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"0.4954" "0.496"
] ]
}, },
"execution_count": 14, "execution_count": 4,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@@ -413,7 +413,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 43, "execution_count": 5,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -430,13 +430,13 @@
" <a list of 10 Patch objects>)" " <a list of 10 Patch objects>)"
] ]
}, },
"execution_count": 43, "execution_count": 5,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
}, },
{ {
"data": { "data": {
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truncated "image/png": 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truncated
"text/plain": [ "text/plain": [
"<Figure size 1008x288 with 1 Axes>" "<Figure size 1008x288 with 1 Axes>"
] ]
@@ -478,26 +478,34 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 45, "execution_count": 6,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
} }
}, },
"outputs": [ "outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/miniconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
" return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
]
},
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f056adab550>" "<matplotlib.axes._subplots.AxesSubplot at 0x7f04a8ee9be0>"
] ]
}, },
"execution_count": 45, "execution_count": 6,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
}, },
{ {
"data": { "data": {
"image/png": 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truncated
"text/plain": [ "text/plain": [
"<Figure size 1008x288 with 1 Axes>" "<Figure size 1008x288 with 1 Axes>"
] ]
@@ -528,7 +536,7 @@
} }
}, },
"source": [ "source": [
"## What dis we just do?\n", "## What did we just do?\n",
"\n", "\n",
"The gaussian we fitted is actually a model that explains the data we've seen.\n", "The gaussian we fitted is actually a model that explains the data we've seen.\n",
"\n", "\n",
@@ -816,7 +824,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 147, "execution_count": 7,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -831,14 +839,14 @@
"Initializing NUTS using jitter+adapt_diag...\n", "Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n", "Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [p]\n", "NUTS: [p]\n",
"Sampling 4 chains: 100%|██████████| 22000/22000 [00:03<00:00, 6271.39draws/s]\n" "Sampling 4 chains: 100%|██████████| 14000/14000 [00:02<00:00, 5751.58draws/s]\n"
] ]
} }
], ],
"source": [ "source": [
"coin_flips = [1, 1]\n", "coin_flips = [1, 1]\n",
"with pm.Model():\n", "with pm.Model():\n",
" p = pm.Uniform('p', 0.001, 0.999)\n", " p = pm.Uniform('p', 0, 1)\n",
" \n", " \n",
" likelihood = pm.Bernoulli('observed', p=p, observed=coin_flips)\n", " likelihood = pm.Bernoulli('observed', p=p, observed=coin_flips)\n",
" \n", " \n",
@@ -849,37 +857,28 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 148, "execution_count": 8,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
} }
}, },
"outputs": [ "outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n",
"The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n",
" alternative='`bottom`', obj_type='argument')\n"
]
},
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f054b83a400>,\n", "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f049d161630>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7f054b813c88>]],\n", " <matplotlib.axes._subplots.AxesSubplot object at 0x7f049d18f5f8>]],\n",
" dtype=object)" " dtype=object)"
] ]
}, },
"execution_count": 148, "execution_count": 8,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
}, },
{ {
"data": { "data": {
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truncated "image/png": 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truncated
"text/plain": [ "text/plain": [
"<Figure size 864x144 with 2 Axes>" "<Figure size 864x144 with 2 Axes>"
] ]
@@ -896,7 +895,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 156, "execution_count": 9,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -907,15 +906,15 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"p: 0.3: 0.08795\n", "P(p < 0.3): 0.09008333333333333\n",
"p: 0.5: 0.25275\n", "P(p < 0.5): 0.24941666666666668\n",
"p: 0.8: 0.63875\n" "P(p < 0.8): 0.6446666666666667\n"
] ]
} }
], ],
"source": [ "source": [
"for p in [.3, .5, .8]:\n", "for p in [.3, .5, .8]:\n",
" print(f'p: {p}:', (trace['p'] < p).sum() / trace['p'].shape[0])" " print(f'P(p < {p}):', (trace['p'] < p).sum() / trace['p'].shape[0])"
] ]
}, },
{ {
@@ -934,7 +933,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 161, "execution_count": 10,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -944,16 +943,16 @@
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"[<matplotlib.lines.Line2D at 0x7f054d5a2198>]" "[<matplotlib.lines.Line2D at 0x7f049d0b2080>]"
] ]
}, },
"execution_count": 161, "execution_count": 10,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
}, },
{ {
"data": { "data": {
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truncated
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
@@ -971,7 +970,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 162, "execution_count": 11,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -986,8 +985,7 @@
"Initializing NUTS using jitter+adapt_diag...\n", "Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n", "Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [p]\n", "NUTS: [p]\n",
"Sampling 4 chains: 100%|██████████| 14000/14000 [00:02<00:00, 6167.84draws/s]\n", "Sampling 4 chains: 100%|██████████| 14000/14000 [00:03<00:00, 4603.02draws/s]\n"
"The acceptance probability does not match the target. It is 0.8795086571448326, but should be close to 0.8. Try to increase the number of tuning steps.\n"
] ]
} }
], ],
@@ -1003,37 +1001,28 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 163, "execution_count": 12,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
} }
}, },
"outputs": [ "outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n",
"The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n",
" alternative='`bottom`', obj_type='argument')\n"
]
},
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f0539ff65f8>,\n", "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f048d4c3630>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7f0539fac400>]],\n", " <matplotlib.axes._subplots.AxesSubplot object at 0x7f048d4e2048>]],\n",
" dtype=object)" " dtype=object)"
] ]
}, },
"execution_count": 163, "execution_count": 12,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
}, },
{ {
"data": { "data": {
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truncated
"text/plain": [ "text/plain": [
"<Figure size 864x144 with 2 Axes>" "<Figure size 864x144 with 2 Axes>"
] ]
@@ -1058,7 +1047,7 @@
"source": [ "source": [
"## Who will be elected?\n", "## Who will be elected?\n",
"\n", "\n",
"There will be a new referendum about a possible 'Dexit'.\n", "There will be a new referendum about a possible 'Nexit'.\n",
"\n", "\n",
"People have to vote $1$ for staying and $0$ for leaving.\n", "People have to vote $1$ for staying and $0$ for leaving.\n",
"\n", "\n",
@@ -1067,17 +1056,17 @@
"\\begin{align}\n", "\\begin{align}\n",
"f(x)= \n", "f(x)= \n",
"\\begin{cases}\n", "\\begin{cases}\n",
" 0.2,& \\text{staying } \\\\\n", " 0.8,& \\text{staying } \\\\\n",
" 0.8, & \\text{leaving}\n", " 0.2, & \\text{leaving}\n",
"\\end{cases}\n", "\\end{cases}\n",
"\\end{align}\n", "\\end{align}\n",
"\n", "\n",
"Meanwhile the first votes are coming in. What is the probability of a 'Dexit' occurring?" "Meanwhile the first votes are coming in. What is the probability of a 'Nexit' occurring?"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 13,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -1090,7 +1079,7 @@
"array([1, 1, 1, 1, 1, 1, 1, 0, 0, 1])" "array([1, 1, 1, 1, 1, 1, 1, 0, 0, 1])"
] ]
}, },
"execution_count": 3, "execution_count": 13,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@@ -1102,7 +1091,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 14,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -1112,16 +1101,16 @@
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"[<matplotlib.lines.Line2D at 0x7f9297e93978>]" "[<matplotlib.lines.Line2D at 0x7f048b80eba8>]"
] ]
}, },
"execution_count": 3, "execution_count": 14,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
}, },
{ {
"data": { "data": {
"image/png": 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truncated "image/png": 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truncated
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
@@ -1133,13 +1122,15 @@
} }
], ],
"source": [ "source": [
"# translate Maurice's probabilities to a prior believe\n",
"\n",
"x = np.linspace(0, 1)\n", "x = np.linspace(0, 1)\n",
"plt.plot(x, stats.beta(1.3, 3).pdf(x))" "plt.plot(x, stats.beta(1.3, 3).pdf(x))"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 15,
"metadata": { "metadata": {
"slideshow": { "slideshow": {
"slide_type": "slide" "slide_type": "slide"
@@ -1154,10 +1145,8 @@
"Initializing NUTS using jitter+adapt_diag...\n", "Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n", "Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [p]\n", "NUTS: [p]\n",
"Sampling 4 chains: 100%|██████████| 42000/42000 [00:06<00:00, 6487.09draws/s]\n", "Sampling 4 chains: 100%|██████████| 42000/42000 [00:07<00:00, 5357.62draws/s]\n",
"/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", "The number of effective samples is smaller than 25% for some parameters.\n"
"The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n",
" alternative='`bottom`', obj_type='argument')\n"
] ]
}, },
{ {
@@ -1169,7 +1158,7 @@
}, },
{ {
"data": { "data": {
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truncated
"text/plain": [ "text/plain": [
"<Figure size 864x144 with 2 Axes>" "<Figure size 864x144 with 2 Axes>"
] ]
@@ -1187,10 +1176,7 @@
"Initializing NUTS using jitter+adapt_diag...\n", "Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n", "Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [p]\n", "NUTS: [p]\n",
"Sampling 4 chains: 100%|██████████| 42000/42000 [00:06<00:00, 6164.67draws/s]\n", "Sampling 4 chains: 100%|██████████| 42000/42000 [00:07<00:00, 5601.20draws/s]\n"
"/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n",
"The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n",
" alternative='`bottom`', obj_type='argument')\n"
] ]
}, },
{ {
@@ -1202,7 +1188,7 @@
}, },
{ {
"data": { "data": {
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truncated
"text/plain": [ "text/plain": [
"<Figure size 864x144 with 2 Axes>" "<Figure size 864x144 with 2 Axes>"
] ]
@@ -1220,10 +1206,7 @@
"Initializing NUTS using jitter+adapt_diag...\n", "Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n", "Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [p]\n", "NUTS: [p]\n",
"Sampling 4 chains: 100%|██████████| 42000/42000 [00:06<00:00, 6377.00draws/s]\n", "Sampling 4 chains: 100%|██████████| 42000/42000 [00:07<00:00, 5444.02draws/s]\n"
"/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n",
"The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n",
" alternative='`bottom`', obj_type='argument')\n"
] ]
}, },
{ {
@@ -1235,7 +1218,7 @@
}, },
{ {
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truncated
"text/plain": [ "text/plain": [
"<Figure size 864x144 with 2 Axes>" "<Figure size 864x144 with 2 Axes>"
] ]
@@ -1253,10 +1236,9 @@
"Initializing NUTS using jitter+adapt_diag...\n", "Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (4 chains in 4 jobs)\n", "Multiprocess sampling (4 chains in 4 jobs)\n",
"NUTS: [p]\n", "NUTS: [p]\n",
"Sampling 4 chains: 100%|██████████| 42000/42000 [00:07<00:00, 5921.57draws/s]\n", "Sampling 4 chains: 100%|██████████| 42000/42000 [00:07<00:00, 5619.20draws/s]\n",
"/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", "The acceptance probability does not match the target. It is 0.8897717351599277, but should be close to 0.8. Try to increase the number of tuning steps.\n",
"The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", "The acceptance probability does not match the target. It is 0.8937936259844127, but should be close to 0.8. Try to increase the number of tuning steps.\n"
" alternative='`bottom`', obj_type='argument')\n"
] ]
}, },
{ {
@@ -1268,7 +1250,7 @@
}, },
{ {
"data": { "data": {
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truncated "image/png": 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truncated
"text/plain": [ "text/plain": [
"<Figure size 864x144 with 2 Axes>" "<Figure size 864x144 with 2 Axes>"
] ]
@@ -1294,12 +1276,330 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 16,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"np.save('data/votes.npy', stats.bernoulli(0.68).rvs(1000))" "np.save('data/votes.npy', stats.bernoulli(0.68).rvs(1000))"
] ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A/B/C testing\n",
"\n",
"* Three different colors are tested for the Xomnia website, and randomly assigned to visitors (not uniformly)\n",
"* Should we switch colors?\n",
"* Assume Xomnia goes bankrupt if we don't get at least 35 calls. We expect 1000 visitors next month, what is the probability that we don't make it? Which color should we use?\n",
"\n",
"color | number of visitors | number of calls\n",
"--- | --- | ---\n",
"blue | 2000 | 35\n",
"red | 500 | 8\n",
"green | 1000 | 18"
]
},
{
"cell_type": "code",
"execution_count": 17,
"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: [p]\n",
"Sampling 4 chains: 100%|██████████| 42000/42000 [00:07<00:00, 5808.91draws/s]\n"
]
},
{
"data": {
"image/png": "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 truncated
"text/plain": [
"<Figure size 864x144 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Simple model for one color\n",
"\n",
"with pm.Model():\n",
" \n",
" # prior\n",
" p = pm.Uniform('p', lower=0, upper=1)\n",
" conversions = pm.Binomial('conversions', 2000, p, observed = [35])\n",
" \n",
" samples = pm.sample(10000)\n",
" \n",
"pm.traceplot(samples);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Combining parameters\n",
"\n",
"* You can easily combine multiple parameters and observations in the same model"
]
},
{
"cell_type": "code",
"execution_count": 18,
"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: [p]\n",
"Sampling 4 chains: 100%|██████████| 42000/42000 [00:07<00:00, 5600.55draws/s]\n"
]
},
{
"data": {
"image/png": "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 truncated
"text/plain": [
"<Figure size 864x144 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"with pm.Model():\n",
" \n",
" p = pm.Uniform('p', lower=0, upper=1, shape=3)\n",
" conversions = pm.Binomial('conv', [2000, 500, 1000], p, observed = [35, 8, 18])\n",
" \n",
" trace = pm.sample(10000)\n",
" \n",
"pm.traceplot(trace)\n",
"\n",
"blue = trace['p'][:, 0]\n",
"red = trace['p'][:, 1]\n",
"green = trace['p'][:, 2]"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/miniconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
" return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f048b8700f0>"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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 truncated
"text/plain": [
"<Figure size 864x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12, 4))\n",
"sns.distplot(blue, color='blue', hist=False)\n",
"sns.distplot(red, color='red', hist=False)\n",
"sns.distplot(green, color='green', hist=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Posterior samples\n",
"\n",
"* `pymc3` does not generate a real distribution, but samples from the posterior distribution.\n",
"* With those samples you can \n",
" * Understand the data, draw conclusions\n",
" * Generate predictions\n",
"\n",
"## Exercise\n",
"1. What is the probability that the conversion rate of blue is higher than 2%?\n",
"2. Which color should we choose?\n"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.2357"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(blue > 0.02).sum() / blue.shape[0]"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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 truncated
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"calls = stats.binom(n=1000, p=blue).rvs()\n",
"fig = plt.hist(calls, bins=calls.max() - calls.min())"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[16, 23, 17, ..., 19, 24, 19],\n",
" [13, 19, 23, ..., 8, 28, 17],\n",
" [17, 20, 20, ..., 21, 10, 29]])"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"calls = stats.binom(n=1000, p=np.stack([blue, red, green])).rvs()\n",
"calls"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, 40)"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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 truncated
"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(16, 8))\n",
"plt.title('Calls histogram per color')\n",
"plt.hist(calls.T, (calls.max(1) - calls.min(1)).min(), color='brg', ec='black')\n",
"plt.xlabel('Calls')\n",
"plt.xlim(0, 40)"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.00165 0.019875 0.009775]\n"
]
},
{
"data": {
"text/plain": [
"<BarContainer object of 3 artists>"
]
},
"execution_count": 72,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA7gAAAHiCAYAAADCs2DjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzt3X+0pXddH/r3pzMmoPwOQwJJYFIz5RqUop6muqqrtqmQaGEQYp1crwZvvPG2ptR1azXcXmrM0tZ4tbGUiCs0KTEoCUSQQdAIBLVwNeQEUyQJKUMMZkgYBhLCDwtx8HP/2M/IzsmZOXsmCWfyPa/XWnvN83yfz/Pd32fvs86c9/l+93OquwMAAACPdn9rvQcAAAAADwcBFwAAgCEIuAAAAAxBwAUAAGAIAi4AAABDEHABAAAYgoALwLqpqguq6vWHee7Lquq9Bzn+u1V19mq1VfX5qvrbh/O8hzjGx1bV26rqvqp60yP9fAcZx3dV1e65/Zur6rsegec56HvyEPt+XVX93CPRNwDj2LzeAwDg0aWq7khybJIvJ/lCknck+Zfd/fn1HNdK3X3GQY49bv92Vb0uye7u/n8egWGcmdlrdUx373sE+j8s3f2c9R7DkayqXpbkR7v7O9Z7LAAcGjO4AByOF04h8VuS/L0kDwqHNbPR/595VpL/cSSF242gqjat9xgAWB8b/QcPAB6C7v54kt9N8o1JUlV/UFU/X1XvS/KXSf52VT2jqnZW1T1Vtauq/o8V3Tymqq6uqs9V1Qeq6u/uP1BV51fVR6djt1TV9604t6rqP09LgD9cVafNHfiDqvrR1cZdVV1VJ1fVuUl+MMlPTcuW31ZV/6aqfmtF/X+uql85QF/fMD3XZ6alvy+a2n82yb9L8gNT3+escu7fmrvGT1fVG6vqKdOx36uq81bU//eqesm0/Z+q6s6q+mxV3VhV3zlX99hpSe+9VXVLZr+EmO/njqr6J9P2BdPz/vr0Ot9cVUtztd9SVX86HXvT9F4dbKnwwd6TH6mqW6e+bq+qH5s79l1Vtbuq/nVVfbKq7q6qHznAEzy+qt5TVa+afpHyuqp6TVW9o6q+kOQfrXz/Vy6fnr4GXj6N41NV9f9O78c3JPm1JN8+vW+fqaq/V1V7qmrz3PkvraqbDvI6ALAOBFwADltVnZjke5L86VzzDyU5N8njk3wsyRuS7E7yjMyW7P77+dCTZHuSNyV5SpLfTPLbVfU107GPJvnOJE9M8rNJXl9VT5879+8nuT3JU5P8TJI37w+Ii+juS5P8RpJf7O7HdfcLk7w+yelV9aTpGjcn+YEkV65y/V+T5G1Jfj/J05L8yyS/UVXP7u6fSfLvk1w99X3ZKkN4eZIXJ/mH0+tzb5JLpmO/meSsuec6JbMZ4bdPTTckeV6+8rq9qaoeMx37mSRfPz1ekOTsNV6KFyW5KsmTkuxM8urpOY9K8pYkr5ue5w1JVv6SYaWDvSefTPJPkzwhyY8kubiqvmXu3OMye6+PT3JOkkuq6snznVfVMUneneR93f3y7u7p0P+a5Ocz+7pb9HPA35dkKbOVCNuT/O/dfWuS/zPJH0/v25O6+4Ykn07y3XPn/m9Z5WsCgPUl4AJwOH67qj6TWZD4w8yC3H6v6+6bp2W5xyX5jiQ/3d1f7O6bkvyXzELwfjd29zXd/VdJ/mOSxyT5tiTp7jd1913d/dfdfXWSjyQ5de7cTyb5le7+q+n4bUm+96FcWHffneSPknz/1HR6kk91942rlH9bkscl+YXuvr+7r0vyO5kLpmv4sST/trt3d/eXklyQ5MwpVL8lyfOq6llT7Q8mefNUl+5+fXd/urv3dfcvJzk6ybOn2n+W5Oe7+57uvjPJq9YYx3u7+x3d/eXMQtv+WfRvy+x+Ha+aXuM3J3n/Gn0d8D3p7rd390d75g8z+8XAd86d+1dJLpzOfUeSz89dUzL7JcAfJnnTKp+Zfmt3v2/6WvniGmPc76LpNfqLJL+Sg79vV2QWajMF9hdk9osFAI4gAi4Ah+PF08zWs7r7X3T3/5w7dufc9jOS3NPdn5tr+1hmM3QPqu/uv85XZntTVT9cVTdNy0Q/k9lS6KfOnfvxuRm8/X0/4yFd2czfhJkcfKbuGUnunMY9P4bjD1C/0rOSvGXu+m7N7OZdx06v2duT7Jhqd2Q225wkmZby3jotBf5MZjOf+1+bZ+SB78PH1hjHJ+a2/zKzZeObp35WvsZ35uAO+J5U1RlV9Sc1W67+mcxm/+ffz0+v+LzyX2b2C4T9vjfJYzNbQrzSWuNazcrX6GBfO69P8sKqelxmv0D4b9MvQwA4ggi4ADzc5sPNXUmeUlWPn2t7ZpKPz+2fuH+jZjelOiHJXdPM5WuTnJfZXYiflORDSWru3OOran7/mdNzHu549/vtJM+tqm/MbEntb6xSk+m5TqwH3kxr5fUdzJ1Jzph+WbD/8Zjps83JbEnwWVX17ZkFu/ckyfR525/OLGg9eXpt7stXXpu7M/e6TmM6HHfnwa/xiQcqnqz6nlTV0Ul+K8kvZRbgn5TZHbhrlT4O5LVJfi/JO6rq61YcW/k+fiHJ187tH7dKfytfo/1fOw/6mpjekz/ObFnzD8XyZIAjkoALwCNmWh77/yX5D1X1mKp6bmafrZwPjN9aVS+ZZgx/IsmXkvxJkq/LLGjsTWY3KMp0M6s5T0vy8qr6mqr6/iTfkFloOhR7kjzgb+JOS1yvyWwJ6vunJayruT6zIPVT0xi+K8kLM/s86yJ+LcnP71+GXFVbqmr73PF3ZDbLe2Fmn+XdP1P8+CT7MnttNlfVv8vsc637vTHJK6rqyVV1QmafDT4cf5zZjPJ5VbV5Gtupa5xzoPfkqMyWUe9Nsq+qzkjy/MMY03mZLXv+nap67EHqbkrykqr62qo6ObOvu5X+zfQanZjkXyW5emrfk+SE6TPI8349yU8l+abMlpADcIQRcAF4pJ2VZGtms2NvSfIz3f3OueNvzewmTvdmNjP2kukzmLck+eXMQtaezELF+1b0fX2SbUk+ldkNhs7s7k8f4vguS3LKtEz4t+far5ie84Azdd19f2Y3aDpjGsOvJvnh7v7wgs/9nzK7qdPvV9XnMgv2f3+u/y8leXOSf5IHft7z2szuXv0/Mlta+8U8cLntz07tf57Z51wPa7Zxur6XZBYOP5PZcu3fyeyXEAey6nsyLbl+eWbh+97Mbgq18zDG1JndxOzOJG+du7HWShcnuT+zr50rsvos/FuT3JhZGH57Zl8LSXJdkpuTfKKqPjVX/5ZMy8q7+wuHOnYAHnn1wI/JAABJUlXPTPLhJMd192fXezxHiqq6Psmvdfd/Xe+xPBRV1Um2dfeuQzzvo0l+rLvf9ciMDICHwgwuAKwwfab2/0py1UYPt1X1D6vquGmJ8tlJnpvZ52A3nKp6aWbL5q9b77EAsLrNa5cAwMYx3bxoT2ZLfE9f5+EcCZ6d2bLix2X2d4nP3Ih3D66qP0hySpIfWnHXbACOIJYoAwAAMARLlAEAABiCgAsAAMAQhvgM7lOf+tTeunXreg8DAACAR8CNN974qe7eslbdEAF369atWV5eXu9hAAAA8Aioqo8tUmeJMgAAAEMQcAEAABiCgAsAAMAQBFwAAACGIOACAAAwBAEXAACAIQi4AAAADEHABQAAYAgCLgAAAEMQcAEAABiCgAsAAMAQBFwAAACGsFDArarTq+q2qtpVVeevcvzoqrp6On59VW2d2r+7qm6sqj+b/v3Hc+d869S+q6peVVU1tT+lqt5ZVR+Z/n3yw3OpAAAAjGzNgFtVm5JckuSMJKckOauqTllRdk6Se7v75CQXJ7loav9Ukhd29zclOTvJlXPnvCbJuUm2TY/Tp/bzk7y7u7clefe0DwAAAAe1yAzuqUl2dfft3X1/kquSbF9Rsz3JFdP2NUlOq6rq7j/t7rum9puTPGaa7X16kid09x93dyf59SQvXqWvK+baAQAA4IAWCbjHJ7lzbn/31LZqTXfvS3JfkmNW1Lw0yZ9295em+t0H6PPY7r576uvuJE9bYIwAAABscJsXqKlV2vpQaqrqOZktW37+IfR58EFVnZvZEuc885nPPJRTAQAAGNAiM7i7k5w4t39CkrsOVFNVm5M8Mck90/4JSd6S5Ie7+6Nz9SccoM890xLmTP9+crVBdfel3b3U3UtbtmxZ4DIAAAAY2SIB94Yk26rqpKo6KsmOJDtX1OzM7CZSSXJmkuu6u6vqSUnenuQV3f2+/cXT0uPPVdW3TXdP/uEkb12lr7Pn2gEAAOCA1lyi3N37quq8JNcm2ZTk8u6+uaouTLLc3TuTXJbkyqraldnM7Y7p9POSnJzklVX1yqnt+d39yST/PMnrkjw2ye9OjyT5hSRvrKpzkvxFku9/6JcJwNbjjsvH9uxZ72EAKzzr2GNzxyc+sd7DABhCzW5i/Oi2tLTUy8vL6z0MgCNaVR3azQ6Ar4pKMsLPYwCPpKq6sbuX1qpbZIkyAAAAHPEEXAAAAIYg4AIAADAEARcAAIAhCLgAAAAMQcAFAABgCAIuAAAAQxBwAQAAGIKACwAAwBAEXAAAAIYg4AIAADAEARcAAIAhCLgAAAAMQcAFAABgCAIuAAAAQxBwAQAAGIKACwAAwBAEXAAAAIYg4AIAADAEARcAAIAhCLgAAAAMQcAFAABgCAIuAAAAQxBwAQAAGIKACwAAwBAEXAAAAIYg4AIAADAEARcAAIAhCLgAAAAMQcAFAABgCAIuAAAAQxBwAQAAGIKACwAAwBAEXAAAAIYg4AIAADAEARcAAIAhCLgAAAAMQcAFAABgCAIuAAAAQxBwAQAAGIKACwAAwBAEXAAAAIYg4AIAADCEhQJuVZ1eVbdV1a6qOn+V40dX1dXT8eurauvUfkxVvaeqPl9Vr56rf3xV3TT3+FRV/cp07GVVtXfu2I8+PJcKAADLine truncated
"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mean = (calls > 35).mean(1)\n",
"print(mean)\n",
"\n",
"plt.figure(figsize=(16, 8))\n",
"plt.title('Probability of evading bankrupty')\n",
"plt.bar(np.array(list('brg')), mean, color='brg', ec='black')\n"
]
} }
], ],
"metadata": { "metadata": {