aflaxman/pymc3_convergence_diags.ipynb

## pymc3_convergence_diags.ipynb
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!date"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Thu Nov 21 16:13:25 PST 2013\r\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One of the challenges in doing MCMC is deciding how long you need to run your chain(s).  There is a line of theoretical research that I am quite fond of which provides asymptotic worst-case upper bounds on the time necessary for a random walk to be close to the stationary distribution for specific Markov chains.\n",
      "\n",
      "Unfortunately, these theoretical guarantees are not often applicable in Bayesian computation, when the question is \"how long does *this* chain need to run?\"\n",
      "\n",
      "MCMC is useful, though, and the statistics community has developed a number of heuristics to provide some evidence that MCMC has gone for long enough.  PyMC3 includes two of them in the `diagnostics` module (so far):\n",
      "\n",
      "    pymc.diagnostics.geweke\n",
      "    pymc.diagnostics.gelman_rubin\n",
      "    \n",
      "Often graphical methods can show that a chain has not converged as well, and PyMC3 includes some plotting routines that are also useful:\n",
      "\n",
      "    pymc.plots.forestplot\n",
      "    pylab.acorr\n",
      "    pymc.plots.traceplot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as mc, pandas as pd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To see all of these methods in action, I am going run 3 chains to sample from a standard normal distribution.  One that has definitely converged, one that has definitely not converged, and one that is borderline."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# set the random seed upfront to make this reproducible\n",
      "\n",
      "np.random.seed(123456)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# model for a simple distribtion: standard normal centered at 1\n",
      "#   p(theta | X) ~ N(1, 1)\n",
      "\n",
      "with mc.Model() as model: theta = mc.Normal('theta', 1., 1.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# To make Markov chains that do and do not converge, vary scaling\n",
      "# parameter in the Metropolis step method (and turn off tuning)\n",
      "\n",
      "with model:\n",
      "    t1 = mc.sample(10000, step=mc.Metropolis(scaling=1., tune=False))\n",
      "    t2 = mc.sample(10000, step=mc.Metropolis(scaling=.01, tune=False))\n",
      "    t3 = mc.sample(10000, step=mc.Metropolis(scaling=.1, tune=False))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         21%                  ] 2162 of 10000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------46%                  ] 4628 of 10000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------70%------            ] 7004 of 10000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------93%---------------   ] 9384 of 10000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 10000 of 10000 complete in 2.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 2500 of 10000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------49%                  ] 4965 of 10000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------73%--------          ] 7382 of 10000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------97%----------------- ] 9767 of 10000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 10000 of 10000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        24%                  ] 2442 of 10000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 4884 of 10000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------73%-------           ] 7347 of 10000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------97%----------------- ] 9762 of 10000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 10000 of 10000 complete in 2.1 sec"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The true posterior distribution as mean 1 and standard deviation 1.  How does this compare to the draws from the three chains?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Definitely Converged'\n",
      "mc.summary(t1)\n",
      "\n",
      "print 'Definitely Not Converged'\n",
      "mc.summary(t2)\n",
      "\n",
      "print 'Borderline'\n",
      "mc.summary(t3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Definitely Converged\n",
        "\n",
        "theta:\n",
        " \n",
        "\tMean             SD               MC Error        95% HPD interval\n",
        "\t------------------------------------------------------------------\n",
        "\t0.999            1.009            0.029            [-0.983  2.996]\n",
        "\t\n",
        "\t\n",
        "\tPosterior quantiles:\n",
        "\t\n",
        "\t2.5             25              50              75             97.5\n",
        "\t |---------------|===============|===============|---------------|\n",
        "\t-0.994           0.325           1.013          1.675         2.996\n",
        "\t\n",
        "Definitely Not Converged\n",
        "\n",
        "theta:\n",
        " \n",
        "\tMean             SD               MC Error        95% HPD interval\n",
        "\t------------------------------------------------------------------\n",
        "\t0.769            0.363            0.036            [ 0.081  1.292]\n",
        "\t\n",
        "\t\n",
        "\tPosterior quantiles:\n",
        "\t\n",
        "\t2.5             25              50              75             97.5\n",
        "\t |---------------|===============|===============|---------------|\n",
        "\t0.109            0.438           0.886          1.032         1.357\n",
        "\t\n",
        "Borderline\n",
        "\n",
        "theta:\n",
        " \n",
        "\tMean             SD               MC Error        95% HPD interval\n",
        "\t------------------------------------------------------------------\n",
        "\t0.647            0.827            0.074            [-0.913  2.276]\n",
        "\t\n",
        "\t\n",
        "\tPosterior quantiles:\n",
        "\t\n",
        "\t2.5             25              50              75             97.5\n",
        "\t |---------------|===============|===============|---------------|\n",
        "\t-0.89            0.077           0.621          1.205         2.311\n",
        "\t\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The `traceplot` method is enough to see the difference between definitely converged and definitely not converged chains, but I would not trust my eye to distinguish borderline from definitely converged."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mc.traceplot(t1)\n",
      "title('Definitely Converged')\n",
      "mc.traceplot(t2)\n",
      "title('Definitely Not Converged')\n",
      "mc.traceplot(t3)\n",
      "title('Borderline')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "<matplotlib.text.Text at 0xc8a2850>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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VK+T9MmYMafPwYWD0aOPaA7SvY6Z9oUmIsjJihfPzI8cQFET6ik9Gof5KSuLf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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb2c0e90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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f0MYGyMykuo/WrZWKg5WBd6Q8PZWDQl6S+sgRYPjwyu+bwRAL/ASDoZR0GzQo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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb5e7950>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nMjvUtjyNn3+mC7iaaNPaNnZn0GLsDRtSNceFC4FPPvH46j0C73NGLampqZg1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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbc92990>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The autocorrelation plot is more discriminating.  It shows that the autocorrelation is gone after 20ish steps in the Definitely-Converged chain. It crosses zero in 400ish steps in the Borderline chain, but it is not clear that it will stay there.  The autocorrelation does not decay to zero within 500 steps in the Definitely-Not-Converged chain."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(15,4))\n",
      "subplot(1,3,1)\n",
      "acorr(t1['theta'], detrend=mlab.detrend_mean, maxlags=500)\n",
      "title('Definitely Converged')\n",
      "\n",
      "subplot(1,3,2)\n",
      "acorr(t2['theta'], detrend=mlab.detrend_mean, maxlags=500)\n",
      "axis(ymin=-.2)\n",
      "title('Definitely Not Converged')\n",
      "\n",
      "subplot(1,3,3)\n",
      "acorr(t3['theta'], detrend=mlab.detrend_mean, maxlags=500)\n",
      "title('Borderline')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "<matplotlib.text.Text at 0xc8be290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lzH3T4cOHERgYiHbt2uHSpUtyxyGyOiEEVqxYATc3Nzz66KMoLCyUO5JdOXP/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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc8d47d0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Geweke diagnostic compares the mean from different blocks of the chain, and should find numbers between -1 and 1 if the chain has converged."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Definitely Converged'\n",
      "g = mc.diagnostics.geweke(t1['theta'])\n",
      "print pd.Series(g[:,1]).describe()\n",
      "\n",
      "print\n",
      "print 'Definitely Not Converged'\n",
      "g = mc.diagnostics.geweke(t2['theta'])\n",
      "print pd.Series(g[:,1]).describe()\n",
      "\n",
      "\n",
      "print\n",
      "print 'Borderline'\n",
      "g = mc.diagnostics.geweke(t3['theta'])\n",
      "print pd.Series(g[:,1]).describe()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Definitely Converged\n",
        "count    20.000000\n",
        "mean     -0.029462\n",
        "std       0.063644\n",
        "min      -0.208553\n",
        "25%      -0.046869\n",
        "50%      -0.019642\n",
        "75%       0.007764\n",
        "max       0.069332\n",
        "dtype: float64\n",
        "\n",
        "Definitely Not Converged\n",
        "count    20.000000\n",
        "mean     -1.747766\n",
        "std       2.297092\n",
        "min      -5.078366\n",
        "25%      -4.287837\n",
        "50%      -0.848601\n",
        "75%       0.377337\n",
        "max       0.659358\n",
        "dtype: float64\n",
        "\n",
        "Borderline\n",
        "count    20.000000\n",
        "mean      0.024733\n",
        "std       0.584330\n",
        "min      -1.393137\n",
        "25%      -0.130932\n",
        "50%       0.072582\n",
        "75%       0.320554\n",
        "max       1.178282\n",
        "dtype: float64\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Gelman-Rubin diagnostic requires multiple runs of each chain, which are supposed to be started from different initial values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with model:\n",
      "    pt1 = mc.psample(2000, step=mc.Metropolis(scaling=1., tune=False),\n",
      "                     start=[{'theta':1+.25*randn()} for j in range(5)],\n",
      "                     threads=5)\n",
      "    pt2 = mc.psample(2000, step=mc.Metropolis(scaling=.001, tune=False),\n",
      "                     start=[{'theta':1+.25*randn()} for j in range(5)],\n",
      "                     threads=5)\n",
      "    pt3 = mc.psample(2000, step=mc.Metropolis(scaling=.1, tune=False),\n",
      "                     start=[{'theta':1+.25*randn()} for j in range(5)],\n",
      "                     threads=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Definitely Converged'\n",
      "print mc.diagnostics.gelman_rubin(pt1)\n",
      "print\n",
      "\n",
      "print 'Definitely Not Converged'\n",
      "print mc.diagnostics.gelman_rubin(pt2)\n",
      "print\n",
      "\n",
      "print 'Borderline'\n",
      "print mc.diagnostics.gelman_rubin(pt3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Definitely Converged\n",
        "{'theta': 1.0009649523705075}\n",
        "\n",
        "Definitely Not Converged\n",
        "{'theta': 19.888103348785531}\n",
        "\n",
        "Borderline\n",
        "{'theta': 1.1738835435268635}\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The forest plot is another way to see summary results, and includes the Gelman-Rubin convergence diagnostic automatically if parallel chains have been run."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure()\n",
      "mc.forestplot(pt1)\n",
      "title('Definitely Converged')\n",
      "\n",
      "figure()\n",
      "mc.forestplot(pt2)\n",
      "title('Definitely Not Converged')\n",
      "\n",
      "figure()\n",
      "mc.forestplot(pt3)\n",
      "title('Borderline')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "<matplotlib.text.Text at 0xd293990>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1lq1atSrYzapVy5cvt1WrVlnXrl2D3ZQ6sW3bNvv666/NzKyoqMgSExNt9erV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\nQg4A4Kz/A1TtDxhbKwIFAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xccb7ad0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gXOv//ve/V0hIiKKioood54EHHlBkZKRiYmKUmpparvXL0sOOHTvUqVMn1ahR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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb21a8d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xcd2fc90>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    }
   ],
   "metadata": {}
  }
 ]
}