From b2696a94ab1570c56aa316ec58e2db92b8482f5f Mon Sep 17 00:00:00 2001 From: Ravin Kumar Date: Thu, 4 Jul 2019 07:56:10 -0700 Subject: [PATCH 1/2] Add Chapter 5 Part 2 --- exercises/Chapter5_part2.ipynb | 295 +++++++++++++++++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 exercises/Chapter5_part2.ipynb diff --git a/exercises/Chapter5_part2.ipynb b/exercises/Chapter5_part2.ipynb new file mode 100644 index 0000000..2c53d82 --- /dev/null +++ b/exercises/Chapter5_part2.ipynb @@ -0,0 +1,295 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2 Exercises" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (theano.configdefaults): install mkl with `conda install mkl-service`: No module named 'mkl'\n" + ] + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "from scipy import stats\n", + "import arviz as az\n", + "import pymc3 as pm\n", + "np.random.seed(123)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercise 6\n", + "***" + ] + }, + { + "cell_type": "code", + "execution_count": 140, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'y')" + ] + }, + "execution_count": 140, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(1,7)\n", + "y = np.random.randint(0, 10, size = 6)\n", + "\n", + "plt.figure(figsize=(10, 5))\n", + "order = [0, 1, 2, 5]\n", + "plt.plot(x, y, 'o')\n", + "for i in order:\n", + " x_n = np.linspace(x.min(), x.max(), 100)\n", + " coeffs = np.polyfit(x, y, deg=i)\n", + " ffit = np.polyval(coeffs, x_n)\n", + "\n", + " p = np.poly1d(coeffs)\n", + " yhat = p(x)\n", + " ybar = np.mean(y)\n", + " ssreg = np.sum((yhat-ybar)**2)\n", + " sstot = np.sum((y - ybar)**2)\n", + " r2 = ssreg / sstot\n", + "\n", + " plt.plot(x_n, ffit, label=f'order {i}, $R^2$= {r2:.2f}')\n", + "\n", + "plt.legend(loc=2)\n", + "plt.xlabel('x')\n", + "plt.ylabel('y', rotation=0)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected when we have a low order polynomial our model doesn't fit hte data well, with zero order polynomial we just predict the same value no matter what. With a high order polynomial the fit looks great, but this is only for data we have seen. Typically when a new data point is introduced the model will not do a good job. Additionally if there is noise in the data, the model will think the noise is meaningful, when in reality it's a mistake and means nothing." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercise 8" + ] + }, + { + "cell_type": "code", + "execution_count": 141, + "metadata": {}, + "outputs": [], + "source": [ + "# Generate coin flips\n", + "coins = 30 \n", + "heads = 15\n", + "y_d = np.repeat([0, 1], [coins-heads, heads])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Per the advice in the chapter we will compute Bayes Factor using the SMC method" + ] + }, + { + "cell_type": "code", + "execution_count": 143, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sample initial stage: ...\n", + "Stage: 0 Beta: 0.323242 Steps: 25\n", + "100%|██████████| 2500/2500 [00:03<00:00, 788.54it/s]\n", + "Stage: 1 Beta: 1.000000 Steps: 4\n", + "100%|██████████| 2500/2500 [00:00<00:00, 4013.58it/s]\n", + "Sample initial stage: ...\n", + "Stage: 0 Beta: 0.137451 Steps: 25\n", + "100%|██████████| 2500/2500 [00:03<00:00, 742.91it/s]\n", + "Stage: 1 Beta: 1.000000 Steps: 4\n", + "100%|██████████| 2500/2500 [00:00<00:00, 3219.35it/s]\n" + ] + } + ], + "source": [ + "with pm.Model() as model_BF_0:\n", + " θ = pm.Beta('θ', 1, 1)\n", + " y = pm.Bernoulli('y', θ, observed=y_d)\n", + " trace_BF_0 = pm.sample(2500, step=pm.SMC())\n", + "\n", + "with pm.Model() as model_BF_1:\n", + " θ = pm.Beta('θ', .5, .5)\n", + " y = pm.Bernoulli('y', θ, observed=y_d)\n", + " trace_BF_1 = pm.sample(2500, step=pm.SMC())" + ] + }, + { + "cell_type": "code", + "execution_count": 144, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.4810295815127534" + ] + }, + "execution_count": 144, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model_BF_0.marginal_likelihood / model_BF_1.marginal_likelihood" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Referencing back to Figure 1.4, we can see that a $Beta(1,1)$ prior is flat, meaning all values are equally likely, but a prior $Beta(.5,.5)$ has larger values near 0 and 1. Intuitively it doesn't make much sense that our coin will be very biased heads, or very biased tails. Looking at the data, without inference, it seems like our coin is fair.\n", + "\n", + "The Bayes factor reflects this as the $Beta(1,1)$ model in the numerator yields a Bayes Factor of 1.4, indicating an \"anecotal\" preference. But in this case we're confirming that the Bayes Factor is sensitive to prior as the likelihood function of both models is the same." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercise 9\n", + "What does reduce sample size mean?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "traces = []\n", + "waics = []\n", + "for coins, heads in [(30, 9), (300, 90)]:\n", + "coins, heads = \n", + "y_d = np.repeat([0, 1], [coins-heads, heads])\n", + "for priors in [(4, 8), (8, 4)]:\n", + " with pm.Model() as model:\n", + " θ = pm.Beta('θ', *priors)\n", + " y = pm.Bernoulli('y', θ, observed=y_d)\n", + " trace = pm.sample(2000)\n", + " traces.append(trace)\n", + " waics.append(az.waic(trace))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercise 10" + ] + }, + { + "cell_type": "code", + "execution_count": 160, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.8700347100756574" + ] + }, + "execution_count": 160, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = range(0, 10)\n", + "q = stats.binom(10, 0.5)\n", + "q_pmf = q.pmf(x)\n", + "stats.entropy(q_pmf)" + ] + }, + { + "cell_type": "code", + "execution_count": 159, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.7144085256537243" + ] + }, + "execution_count": 159, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = range(0, 10)\n", + "q = stats.binom(10, 0.25)\n", + "q_pmf = q.pmf(x)\n", + "\n", + "stats.entropy(q_pmf)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 1c2856879be3c974e7eea7272b2bc8b4109094cb Mon Sep 17 00:00:00 2001 From: Ravin Kumar Date: Sat, 6 Jul 2019 18:03:45 -0500 Subject: [PATCH 2/2] Add exercise 10 solution --- exercises/Chapter5_part2.ipynb | 138 +++++++++++++++++++++++---------- 1 file changed, 95 insertions(+), 43 deletions(-) diff --git a/exercises/Chapter5_part2.ipynb b/exercises/Chapter5_part2.ipynb index 2c53d82..3499ea4 100644 --- a/exercises/Chapter5_part2.ipynb +++ b/exercises/Chapter5_part2.ipynb @@ -11,15 +11,7 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "WARNING (theano.configdefaults): install mkl with `conda install mkl-service`: No module named 'mkl'\n" - ] - } - ], + "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", @@ -40,7 +32,7 @@ }, { "cell_type": "code", - "execution_count": 140, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -49,13 +41,13 @@ "Text(0, 0.5, 'y')" ] }, - "execution_count": 140, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -108,7 +100,7 @@ }, { "cell_type": "code", - "execution_count": 141, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -127,7 +119,7 @@ }, { "cell_type": "code", - "execution_count": 143, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -135,15 +127,15 @@ "output_type": "stream", "text": [ "Sample initial stage: ...\n", - "Stage: 0 Beta: 0.323242 Steps: 25\n", - "100%|██████████| 2500/2500 [00:03<00:00, 788.54it/s]\n", + "Stage: 0 Beta: 0.334961 Steps: 25\n", + "100%|██████████| 2500/2500 [00:03<00:00, 788.98it/s]\n", "Stage: 1 Beta: 1.000000 Steps: 4\n", - "100%|██████████| 2500/2500 [00:00<00:00, 4013.58it/s]\n", + "100%|██████████| 2500/2500 [00:01<00:00, 1936.67it/s]\n", "Sample initial stage: ...\n", - "Stage: 0 Beta: 0.137451 Steps: 25\n", - "100%|██████████| 2500/2500 [00:03<00:00, 742.91it/s]\n", + "Stage: 0 Beta: 0.146484 Steps: 25\n", + "100%|██████████| 2500/2500 [00:03<00:00, 700.04it/s]\n", "Stage: 1 Beta: 1.000000 Steps: 4\n", - "100%|██████████| 2500/2500 [00:00<00:00, 3219.35it/s]\n" + "100%|██████████| 2500/2500 [00:00<00:00, 3462.81it/s]\n" ] } ], @@ -161,16 +153,16 @@ }, { "cell_type": "code", - "execution_count": 144, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "1.4810295815127534" + "1.5466473984070264" ] }, - "execution_count": 144, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -193,7 +185,7 @@ "metadata": {}, "source": [ "# Exercise 9\n", - "What does reduce sample size mean?" + "What does reduce sample size mean? Less samples from posterior? or less samples of data/coin flips?" ] }, { @@ -201,20 +193,7 @@ "execution_count": null, "metadata": {}, "outputs": [], - "source": [ - "traces = []\n", - "waics = []\n", - "for coins, heads in [(30, 9), (300, 90)]:\n", - "coins, heads = \n", - "y_d = np.repeat([0, 1], [coins-heads, heads])\n", - "for priors in [(4, 8), (8, 4)]:\n", - " with pm.Model() as model:\n", - " θ = pm.Beta('θ', *priors)\n", - " y = pm.Bernoulli('y', θ, observed=y_d)\n", - " trace = pm.sample(2000)\n", - " traces.append(trace)\n", - " waics.append(az.waic(trace))" - ] + "source": [] }, { "cell_type": "markdown", @@ -225,7 +204,7 @@ }, { "cell_type": "code", - "execution_count": 160, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -234,7 +213,7 @@ "1.8700347100756574" ] }, - "execution_count": 160, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -248,7 +227,40 @@ }, { "cell_type": "code", - "execution_count": 159, + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "_, ax = plt.subplots(figsize=(12, 4))\n", + "ax.vlines(x, 0, q_pmf)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -257,7 +269,7 @@ "1.7144085256537243" ] }, - "execution_count": 159, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -269,6 +281,46 @@ "\n", "stats.entropy(q_pmf)" ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "_, ax = plt.subplots(figsize=(12, 4))\n", + "ax.vlines(x, 0, q_pmf)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This answer intuitively makes sense, because of the lower bound of 0 on the overall distribution is less \"spread out\" with a binomial model where $p=.25$" + ] } ], "metadata": { @@ -287,7 +339,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.8" + "version": "3.7.3" } }, "nbformat": 4,