{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pymc as pm\n", "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Couldn't import dot_parser, loading of dot files will not be possible.\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# A Simple Markow Chain\n", "Let's say we want to estimate parameters of a system such that we can predict the state of the system at timestep $t+1$ given the state $t$. PyMC should be able to deal with this easily.\n", "\n", "Let our system be a moving object in a 1D world. The state is the position of the object. We want to estimate the latent variable/the speed of the object. The next state depends on the previous state and the latent variable the speed." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# define the system and the data\n", "true_pos, true_vel = 0, .7\n", "true_positions = [true_vel * step for step in range(100)]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We assume that we have sligh noise in our observation (but that does not matter here).\n", "\n", "The question is: how do I model the dependency of the next state on the current state.\n", "I could supply the transition function a parameter idx to access the position at time $t$ and then predict the position at time $t+1$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import random\n", "\n", "# we're using `some_tau` for the noise throughout the example.\n", "# this should be replaced with something more meaningful.\n", "some_tau = 1 / .5**2\n", "\n", "# PRIORS\n", "# we don't know too much about the velocity, might be pos. or neg. \n", "vel = pm.Normal(\"vel\", mu=0, tau=some_tau)\n", "\n", "# MODEL\n", "# next_state = prev_state + vel (and some gaussian noise)\n", "# That means that each state depends on the prev_state and the vel.\n", "# We save the states in a list.\n", "states = [pm.Normal(\"s0\", mu=true_positions[0], tau=some_tau)]\n", "for i in range(1, len(true_positions)):\n", " states.append(pm.Normal(name=\"s\" + str(i),\n", " mu=states[-1] + vel,\n", " tau=some_tau))\n", "\n", "# observation with gaussian noise\n", "obs = pm.Normal(\"obs\", mu=states, tau=some_tau, value=true_positions, observed=True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "model = pm.Model([vel, obs])\n", "mcmc = pm.MCMC(model)\n", "mcmc.sample(10000, 5000)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 10000 of 10000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "vel_samples = mcmc.trace(\"vel\")[:]\n", "print \"vel -- mean:%f; std:%f\" % (mean(vel_samples), std(vel_samples))\n", "pm.Matplot.plot(mcmc.get_node(\"vel\"))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "vel -- mean:0.694063; std:0.051844\n", "Plotting vel\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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L1JfLwe8XIx3uOb7/HmjZkn3PFwNqp9ek0royfS2GnECREl9a6m4UakNMnDhh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