{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 2. Small Worlds and Large Worlds" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import seaborn as sns\n", "import torch\n", "\n", "import pyro\n", "import pyro.distributions as dist\n", "\n", "from rethinking import MAP, precis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 2.1" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "tensor([0.0000, 0.1500, 0.4000, 0.4500, 0.0000])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ways = torch.tensor([0., 3, 8, 9, 0])\n", "ways / ways.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 2.2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "tensor(0.1641)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dist.Binomial(total_count=9, probs=0.5).log_prob(torch.tensor(6.)).exp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 2.3" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# define grid\n", "p_grid = torch.linspace(start=0, end=1, steps=20)\n", "\n", "# define prior\n", "prior = torch.tensor(1.).repeat(20)\n", "\n", "# compute likelihood at each value in grid\n", "likelihood = dist.Binomial(total_count=9,\n", " probs=p_grid).log_prob(torch.tensor(6.)).exp()\n", "\n", "# compute product of likelihood and prior\n", "unstd_posterior = likelihood * prior\n", "\n", "# standardize the posterior, so it sums to 1\n", "posterior = unstd_posterior / unstd_posterior.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 2.4" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = sns.lineplot(p_grid, posterior, marker=\"o\")\n", "ax.set(xlabel=\"probability of water\", ylabel=\"posterior probability\",\n", " title=\"20 points\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 2.5" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "prior = torch.where(p_grid < 0.5, torch.tensor(0.), torch.tensor(1.))\n", "prior = (-5 * (p_grid - 0.5).abs()).exp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 2.6" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MeanStdDev|0.890.89|
p0.630.140.410.84
\n", "
" ], "text/plain": [ " Mean StdDev |0.89 0.89|\n", "p 0.63 0.14 0.41 0.84" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def model(w):\n", " p = pyro.sample(\"p\", dist.Uniform(0, 1)) # uniform prior\n", " pyro.sample(\"w\", dist.Binomial(9, p), obs=w) # binomial likelihood\n", "\n", "globe_qa = MAP(model).run(torch.tensor(6.))\n", "\n", "# display summary of quadratic approximation\n", "precis(globe_qa)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 2.7" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# analytical calculation\n", "w = 6\n", "n = 9\n", "x = torch.linspace(0, 1, 101)\n", "ax = sns.lineplot(x, dist.Beta(w + 1, n - w + 1).log_prob(x).exp())\n", "ax.set(xlabel=\"proportion water\", ylabel=\"Density\", title=\"n = 9\")\n", "# quadratic approximation\n", "precis_df = precis(globe_qa)\n", "sns.lineplot(x, dist.Normal(precis_df[\"Mean\"][0],\n", " precis_df[\"StdDev\"][0]).log_prob(x).exp())\n", "ax.lines[1].set_linestyle(\"--\")" ] } ], "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": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 }