{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "using Mamba\n", "using Pandas" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " X Y\n", "0 24 472\n", "1 24 403\n", "2 26 454\n", "3 32 575\n", "4 33 546\n", "5 35 781\n", "6 38 750\n", "7 40 601\n", "8 40 814\n", "9 43 792\n", "10 43 745\n", "11 44 837\n", "12 48 868\n", "13 52 988\n", "14 56 1092\n", "15 56 1007\n", "16 57 1233\n", "17 58 1202\n", "18 59 1123\n", "19 59 1314\n" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Data\n", "FP = open(raw\"./data-salary.txt\")\n", "Data = read_csv(FP)\n", "close(FP)\n", "Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```stan\n", "data {\n", " int N;\n", " real X[N];\n", " real Y[N];\n", "}\n", "\n", "paramters {\n", " real a;\n", " real b;\n", " real sigma;\n", "}\n", "\n", "model{\n", " for (n in 1:N) {\n", " Y[n] ~ normal(a + b*X[n], sigma);\n", " }\n", "}\n", "```" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Object of type \"Mamba.Model\"\n", "-------------------------------------------------------------------------------\n", "a:\n", "A monitored node of type \"Mamba.ScalarStochastic\"\n", "NaN\n", "-------------------------------------------------------------------------------\n", "b:\n", "A monitored node of type \"Mamba.ScalarStochastic\"\n", "NaN\n", "-------------------------------------------------------------------------------\n", "y:\n", "An unmonitored node of type \"0-element Mamba.ArrayStochastic{1}\"\n", "Float64[]\n", "-------------------------------------------------------------------------------\n", "sigma:\n", "A monitored node of type \"Mamba.ScalarStochastic\"\n", "NaN\n" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Model Definition\n", "model = Model(\n", " y = Stochastic(1,\n", " (a, b, x, sigma) -> MvNormal(a + b*x, sigma),\n", " false\n", " ),\n", " b = Stochastic(() -> Normal(0, 100)),\n", " a = Stochastic(() -> Normal(0, 100)),\n", " sigma = Stochastic(() -> Rayleigh(100))\n", ")" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Object of type \"Mamba.Model\"\n", "-------------------------------------------------------------------------------\n", "a:\n", "A monitored node of type \"Mamba.ScalarStochastic\"\n", "NaN\n", "-------------------------------------------------------------------------------\n", "b:\n", "A monitored node of type \"Mamba.ScalarStochastic\"\n", "NaN\n", "-------------------------------------------------------------------------------\n", "y:\n", "An unmonitored node of type \"0-element Mamba.ArrayStochastic{1}\"\n", "Float64[]\n", "-------------------------------------------------------------------------------\n", "sigma:\n", "A monitored node of type \"Mamba.ScalarStochastic\"\n", "NaN\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## Sampling Scheme\n", "scheme = [NUTS(:a), NUTS(:b),Slice(:sigma,10)]\n", "setsamplers!(model, scheme)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Dict{Symbol,Any} with 2 entries:\n", " :y => [472, 403, 454, 575, 546, 781, 750, 601, 814, 792, 745, 837, 868, 988, …\n", " :x => [24, 24, 26, 32, 33, 35, 38, 40, 40, 43, 43, 44, 48, 52, 56, 56, 57, 58…" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Data Conversion\n", "Dat = Dict{Symbol, Any}(\n", " :x => Array(Data[:X]),\n", " :y => Array(Data[:Y])\n", ")" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "4-element Array{Dict{Symbol,Any},1}:\n", " Dict{Symbol,Any}(Pair{Symbol,Any}(:a, 0.0321085),Pair{Symbol,Any}(:b, -1.13885),Pair{Symbol,Any}(:y, [472, 403, 454, 575, 546, 781, 750, 601, 814, 792, 745, 837, 868, 988, 1092, 1007, 1233, 1202, 1123, 1314]),Pair{Symbol,Any}(:sigma, 1.38256)) \n", " Dict{Symbol,Any}(Pair{Symbol,Any}(:a, -0.402152),Pair{Symbol,Any}(:b, -0.365622),Pair{Symbol,Any}(:y, [472, 403, 454, 575, 546, 781, 750, 601, 814, 792, 745, 837, 868, 988, 1092, 1007, 1233, 1202, 1123, 1314]),Pair{Symbol,Any}(:sigma, 0.723508))\n", " Dict{Symbol,Any}(Pair{Symbol,Any}(:a, -0.40549),Pair{Symbol,Any}(:b, 1.02008),Pair{Symbol,Any}(:y, [472, 403, 454, 575, 546, 781, 750, 601, 814, 792, 745, 837, 868, 988, 1092, 1007, 1233, 1202, 1123, 1314]),Pair{Symbol,Any}(:sigma, 1.82913)) \n", " Dict{Symbol,Any}(Pair{Symbol,Any}(:a, -0.349698),Pair{Symbol,Any}(:b, 0.66123),Pair{Symbol,Any}(:y, [472, 403, 454, 575, 546, 781, 750, 601, 814, 792, 745, 837, 868, 988, 1092, 1007, 1233, 1202, 1123, 1314]),Pair{Symbol,Any}(:sigma, 1.24675)) " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Initial Values\n", "inits = [\n", " Dict{Symbol, Any}(\n", " :y => Dat[:y],\n", " :a => rand(Normal(0, 1)),\n", " :b => rand(Normal(0, 1)),\n", " :sigma => rand(Rayleigh(1))\n", " ) for i in 1:4\n", "]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MCMC Simulation of 4000 Iterations x 4 Chains...\n", "\n", "Chain 1: 0% [0:14:45 of 0:14:47 remaining]\n", "Chain 1: 10% [0:00:23 of 0:00:25 remaining]\n", "Chain 1: 20% [0:00:11 of 0:00:14 remaining]\n", "Chain 1: 30% [0:00:07 of 0:00:10 remaining]\n", "Chain 1: 40% [0:00:05 of 0:00:08 remaining]\n", "Chain 1: 50% [0:00:03 of 0:00:06 remaining]\n", "Chain 1: 60% [0:00:02 of 0:00:06 remaining]\n", "Chain 1: 70% [0:00:02 of 0:00:05 remaining]\n", "Chain 1: 80% [0:00:01 of 0:00:05 remaining]\n", "Chain 1: 90% [0:00:00 of 0:00:05 remaining]\n", "Chain 1: 100% [0:00:00 of 0:00:04 remaining]\n", "\n", "Chain 2: 0% [0:00:02 of 0:00:02 remaining]\n", "Chain 2: 10% [0:00:03 of 0:00:03 remaining]\n", "Chain 2: 20% [0:00:02 of 0:00:02 remaining]\n", "Chain 2: 30% [0:00:02 of 0:00:02 remaining]\n", "Chain 2: 40% [0:00:01 of 0:00:02 remaining]\n", "Chain 2: 50% [0:00:01 of 0:00:02 remaining]\n", "Chain 2: 60% [0:00:01 of 0:00:02 remaining]\n", "Chain 2: 70% [0:00:01 of 0:00:02 remaining]\n", "Chain 2: 80% [0:00:00 of 0:00:02 remaining]\n", "Chain 2: 90% [0:00:00 of 0:00:02 remaining]\n", "Chain 2: 100% [0:00:00 of 0:00:02 remaining]\n", "\n", "Chain 3: 0% [0:00:03 of 0:00:03 remaining]\n", "Chain 3: 10% [0:00:02 of 0:00:02 remaining]\n", "Chain 3: 20% [0:00:01 of 0:00:02 remaining]\n", "Chain 3: 30% [0:00:01 of 0:00:02 remaining]\n", "Chain 3: 40% [0:00:01 of 0:00:02 remaining]\n", "Chain 3: 50% [0:00:01 of 0:00:02 remaining]\n", "Chain 3: 60% [0:00:01 of 0:00:02 remaining]\n", "Chain 3: 70% [0:00:01 of 0:00:02 remaining]\n", "Chain 3: 80% [0:00:00 of 0:00:02 remaining]\n", "Chain 3: 90% [0:00:00 of 0:00:02 remaining]\n", "Chain 3: 100% [0:00:00 of 0:00:02 remaining]\n", "\n", "Chain 4: 0% [0:00:02 of 0:00:02 remaining]\n", "Chain 4: 10% [0:00:02 of 0:00:02 remaining]\n", "Chain 4: 20% [0:00:01 of 0:00:02 remaining]\n", "Chain 4: 30% [0:00:01 of 0:00:02 remaining]\n", "Chain 4: 40% [0:00:01 of 0:00:02 remaining]\n", "Chain 4: 50% [0:00:01 of 0:00:02 remaining]\n", "Chain 4: 60% [0:00:01 of 0:00:02 remaining]\n", "Chain 4: 70% [0:00:01 of 0:00:02 remaining]\n", "Chain 4: 80% [0:00:00 of 0:00:02 remaining]\n", "Chain 4: 90% [0:00:00 of 0:00:02 remaining]\n", "Chain 4: 100% [0:00:00 of 0:00:02 remaining]\n", "\n", "Iterations = 2001:4000\n", "Thinning interval = 1\n", "Chains = 1,2,3,4\n", "Samples per chain = 2000\n", "\n", "Empirical Posterior Estimates:\n", " Mean SD Naive SE MCSE ESS \n", "sigma 84.830678 14.721287 0.164588995 1.1485763 164.27514\n", " b 21.162207 1.466046 0.016390893 0.0966641 230.01954\n", " a -84.781791 64.746234 0.723884897 4.2566201 231.36583\n", "\n", "Quantiles:\n", " 2.5% 25.0% 50.0% 75.0% 97.5% \n", "sigma 62.778817 74.428245 82.753547 92.489267 122.244135\n", " b 18.257467 20.174237 21.187008 22.167201 24.030171\n", " a -210.843690 -128.179143 -87.292266 -41.565201 42.611077\n", "\n" ] } ], "source": [ "## MCMC Simulations\n", "sim = mcmc(model, Dat, inits, 4000, burnin=2000, thin=1, chains=4)\n", "Mamba.describe(sim)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", " \n", " Value\n", " \n", " \n", " -300\n", " -200\n", " -100\n", " 0\n", " 100\n", " \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", " \n", " 0.000\n", " 0.002\n", " 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"metadata": { "collapsed": false }, "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", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "30\n", "\n", "\n", "40\n", "\n", "\n", "50\n", "\n", "\n", "60\n", "\n", "\n", "400\n", "\n", "\n", "600\n", "\n", "\n", "800\n", "\n", "\n", "1000\n", "\n", "\n", "1200\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "y1\n", "\n", "\n" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots\n", "gr()\n", "Plots.plot(Dat[:x],Dat[:y],st=:scatter)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Julia 0.6.1", "language": "julia", "name": "julia-0.6" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }