pymc3_sir_model_debug

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  "name": ""
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!date"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mon Jan 27 10:19:59 PST 2014\r\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import pymc, pymc as pm, numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    From: pymc@googlegroups.com [mailto:pymc@googlegroups.com] On Behalf Of Quentin CAUDRON\n",
      "    Sent: Monday, January 20, 2014 4:16 PM\n",
      "    To: pymc@googlegroups.com\n",
      "    Subject: [pymc] SIR model with PyMC3 - dynamical / compartmental\n",
      "\n",
      "Hi,\n",
      "\n",
      "I'm trying to put together some parameter inference for a compartmental epidemiological model. The simplest form looks like this :\n",
      "\n",
      "\\begin{align}\n",
      "dS/dt &= - r * g * S * I\\\\\n",
      "dI/dt &= g * I ( r * S - 1 )\n",
      "\\end{align}\n",
      "\n",
      "I'd like to use PyMC3 to infer the parameters r and g. \n",
      "\n",
      "odeint won't accept pymc variables, so that won't work. I tried using manual integration ( just a basic forward Euler works here ), but trying to do arithmetic on pymc variables in a loop gives me ValueError: setting an array element with a sequence. :\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = np.linspace(0,1,20)\n",
      "solution = np.zeros_like(t)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with pymc.Model() as model :\n",
      "    r0 = pymc.Normal(\"r0\", 15, sd=10)\n",
      "    gamma = pymc.Uniform(\"gamma\", 0.3, 1.)\n",
      "    \n",
      "    # Use forward Euler to solve\n",
      "    dt = t[1] - t[0]\n",
      "    S = np.zeros_like(solution)\n",
      "    I = np.zeros_like(solution)\n",
      "    S[0] = 0.99\n",
      "    I[0] = 0.01\n",
      "\n",
      "    for i in range(len(t[1:])) :\n",
      "        S[i] = S[i-1] + dt * (-r0 * gamma * S[i-1] * I[i-1])\n",
      "        I[i] = I[i-1] + dt * ( r0 * gamma * S[i-1] * I[i-1] - gamma * I[i-1])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "ValueError",
       "evalue": "setting an array element with a sequence.",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-5-c6feb0e9eed4>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     12\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 13\u001b[1;33m         \u001b[0mS\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mdt\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mr0\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mgamma\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mI\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     14\u001b[0m         \u001b[0mI\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mI\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mdt\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;33m(\u001b[0m \u001b[0mr0\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mgamma\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mI\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mgamma\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mI\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mValueError\u001b[0m: setting an array element with a sequence."
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The problem is `S` is zeros too much like `t`, specifically an array of floats."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S.dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "dtype('float64')"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Forcing `S.dtype` to be `object` sorts that out."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with pm.Model() as model :\n",
      "    r0 = pm.Normal(\"r0\", 15, sd=10)\n",
      "    gamma = pm.Uniform(\"gamma\", 0.3, 1.)\n",
      "    \n",
      "    # Use forward Euler to solve\n",
      "    dt = t[1] - t[0]\n",
      "    S = np.zeros_like(solution, dtype=object)  # FIX #1\n",
      "    I = np.zeros_like(solution, dtype=object)  # FIX #2\n",
      "    S[0] = 0.99\n",
      "    I[0] = 0.01\n",
      "\n",
      "    for i in range(len(t[1:])) :\n",
      "        S[i] = S[i-1] + dt * (-r0 * gamma * S[i-1] * I[i-1])\n",
      "        I[i] = I[i-1] + dt * ( r0 * gamma * S[i-1] * I[i-1] - gamma * I[i-1])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Success!"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}