Lighthouse_problem.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:316f1dafb7c84a48a7d00ae2b4f8bb356ac223eca3123d067cfab9fda8aa06f6"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from IPython.display import Image\n",
      "from IPython.html.widgets import interact"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Image('Lighthouse_schematic.jpg',width=500)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "jpeg": 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       "metadata": {
        "jpeg": {
         "width": 500
        }
       },
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<IPython.core.display.Image at 0x7554ef0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following is a classic estimation problem called the \"lighthouse problem\". The figure shows a set of receivers distributed at coordinates $x_k$ along the shore and a lighthouse located at some position $(\\alpha,\\beta)$ offshore. The idea is that the coastline is equipped with a continuous strip of photodetectors. The lighthouse flashes the shore $N$ times at some random angle $\\theta_k$. The strip of  photodetectors registers the $k^{th}$ flash position $x_k$, but the the angle $\\theta_k$ of the flash is unknown. Furthermore, the lighthouse beam is laser-like so there is no smearing along the strip of photodetectors. In other words, the lighthouse is actually more of a disco-ball in a dark nightclub.\n",
      "\n",
      "The problem is how to estimate $ \\alpha  $ given we already have $\\beta$.\n",
      "\n",
      "From basic trigonometry, we have the following:\n",
      "\n",
      "$$ \\beta \\tan(\\theta_k) = x_k - \\alpha $$\n",
      "\n",
      "The density function for the angle is assumed to be the following:\n",
      "\n",
      "$$ f_{\\alpha}(\\theta_k) = \\frac{1}{\\pi} $$\n",
      "\n",
      "This means that the density of the angle is uniformly distributed between $ \\pm \\pi/2 $. Now, what we really want is the density function for $x_k$ which will tell us the probability that the $k^{th}$ flash will be recorded at position $ x_k $. After a transformation of variables, we obtain the following:\n",
      "\n",
      "$$ f_{\\alpha}(x_k) = \\frac{\\beta}{\\pi(\\beta ^2 +(x_k-\\alpha)^2)} $$\n",
      "\n",
      "which we plot below for some reasonable factors\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xi = linspace(-10,10,150)\n",
      "alpha = 1\n",
      "f = lambda x: 1/(pi*(1+(x-alpha)**2))\n",
      "plot(xi,f(xi))\n",
      "xlabel('$x$',fontsize=24)\n",
      "ylabel(r'$f_{\\alpha}(x)$',fontsize=24);\n",
      "vlines(alpha,0,.35,linestyles='--',lw=4.)\n",
      "grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x756fc50>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As shown in figure, the peak for this distribution is when $ x_k=\\alpha $. Because there is no coherent processing, the recording of a signal at one position does not influence what we can infer about the position of another measurement. Thus, we can justify assuming independence between the individual $x_k$ measurements. The encouraging thing about this distribution is that it is centered at the variable we are trying to estimate, namely $\\alpha$.\n",
      "\n",
      "The temptation here is to just average out the $x_k$ measurements because of this tendency of the distribution around $\\alpha$. Later, we will see why this is a bad idea."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using Maximum  Likelihood Estimation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given $N$ measurements, we form the likelihood as the following:\n",
      "\n",
      "$$ L(\\alpha) = \\prod_{k=1}^N f_{\\alpha}(x_k)$$\n",
      "\n",
      "And this is the function we want to maximize for our maximum likelihood estimator. Let's process the logarithm of this to  make the product easy to work with as this does not influence the position of the maximum $ \\alpha $. Then,\n",
      "\n",
      "$$\\mathcal{L}(\\alpha)=\\sum_{k=1}^N \\ln f_{\\alpha}(x_k) = \\texttt{constant}- \\sum_{k=1}^N \\ln (\\beta ^2 +(x_k-\\alpha)^2) $$\n",
      "\n",
      "Taking the first derivative gives us the equation would have to solve in order to compute the estimator for $ \\alpha $,\n",
      "\n",
      "$$ \\frac{d \\mathcal{L}}{d \\alpha} = 2 \\sum_{k=1}^N \\frac{x_k-\\alpha}{\\beta^2+(x_k-\\alpha)^2}=0$$\n",
      "\n",
      "Unfortunately, there is no easy way to solve for the optimal $ \\alpha $ for this equation. However, we are not defenseless at this point because Python has all the tools we need to overcome this. Let's start by getting a quick look at the histogram of the $x_k$ measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "beta  =alpha = 1\n",
      "theta_samples=((2*np.random.rand(250)-1)*pi/2)\n",
      "x_samples = alpha+beta*np.tan(theta_samples)\n",
      "hist(x_samples);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x756f610>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The  histogram  above shows that although many of the measurements are in one bin, even for relatively few samples, we still observe measurements that are very for displaced from the main group. This is because we initially assumed that the $\\theta_k$ angle could be anywhere between $[-\\pi/2,\\pi/2]$, which is basically expressing our ignorance of the length of the coastline.\n",
      "\n",
      "With that in mind, let's turn to the maximum likelihood estimation. We will need some tools from `sympy`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy as S\n",
      "a=S.symbols('alpha',real=True)\n",
      "x = S.symbols('x',real=True)\n",
      "# form derivative of the log-likelihood\n",
      "dL=sum((xk-a)/(1+(xk-a)**2)  for xk in x_samples)\n",
      "S.plot(dL,(a,-15,15),xlabel=r'$\\alpha$',ylabel=r'$dL(\\alpha)/d\\alpha$')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZH9u3wxdfwJ/+BBXWQIUVBbZIgJUFtm+WQNRO339v51InJtp51dnZduFLixZu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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x94bd970>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<sympy.plotting.plot.Plot at 0x94adb90>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above figure shows that the zero-crossing of the derivative of the log-likelihood crosses where the $\\alpha$ is to be estimated. Thus, our next task is to solve for the zero-crossing, which will then reveal the maximum likelihood estimate of $\\alpha$ given the set of measurements $\\lbrace x_k \\rbrace$.\n",
      "\n",
      "\n",
      "There are tools in `scipy.optimize` that can help us compute the zero-crossing as demonstrated in the cell below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import optimize\n",
      "from scipy.optimize import fmin_l_bfgs_b\n",
      "\n",
      "# convert sympy function to numpy version with lambdify\n",
      "alpha_x  = fmin_l_bfgs_b(S.lambdify(a,(dL)**2),0,bounds=[(-3,3)],approx_grad=True)\n",
      "\n",
      "print alpha_x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(array([ 0.99435905]), array([  3.76209349e-14]), {'warnflag': 2, 'task': 'ABNORMAL_TERMINATION_IN_LNSRCH', 'grad': array([  1.64970679e-05]), 'nit': 5, 'funcalls': 150})\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Comparing The Maximum likelihood Estimator to Just Plain Averaging"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Whew. That was a lot of work to compute the maximum likelihood estimation. Earlier we observed that the density function is peaked around the $\\alpha$ we are trying to estimate. Why not just take the average of the $\\lbrace x_k \\rbrace$ and use that to estimate $\\alpha$?\n",
      "\n",
      "Let's try computing the average in the cell below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'alpha using average =',x_samples.mean()\n",
      "print 'maximum likelihood estimate = ', alpha_x[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "alpha using average = -14.7935661293\n",
        "maximum likelihood estimate =  [ 0.99435905]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you run this notebook a few times, you will see that estimate using the average has enormous variance. This is a consequence of the fact that we can have very large absolute values for $\\lbrace x_k \\rbrace$ corresponding to values of $\\theta_k$ near the edges of the $[-\\pi/2,\\pi/2]$ interval."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def run_trials(n=100):\n",
      "    o=[]\n",
      "    for i in range(100):\n",
      "        theta_samples=((2*np.random.rand(250)-1)*pi/2)\n",
      "        x_samples = alpha+beta*np.tan(theta_samples)\n",
      "        o.append(x_samples)\n",
      "    return np.array(o)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "o= run_trials()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following figure shows the histogram of the measurements. As shown, there are many measurements away from the central part. This is the cause of our widely varying average. What if we just trimmed away the excess outliers? Would that leave us with an easier to implement procedure for estimating $\\alpha$?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(o[np.where(abs(o)<200)]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x778e7b0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following graph shows what happens when we include only a relative neighborhood around zero in our calculation of the average value. Note that the figure shows a wide spread of average values depending upon how big a neighborhood around zero we decide to keep. This is an indication that the average is not a good estimator for our problem because it is very sensitive to outliers."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(range(100,10000,100),[o[np.where(abs(o)<i)].mean() for i in range(100,10000,100)],'-o')\n",
      "xlabel('width of neighborhood around zero')\n",
      "ylabel('value of average estimate')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.text.Text at 0x9a27430>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4BfgmcLSZPZ10YJ3R0NDMpEmXU1e3d3+V56vuShkxAhYvLs8qrzlzGmlpmd1u\nW0vLbObOnVeiiFxXeUJxlahgCUXSVwkPKab6NJ0oCTP770Qjiyn1V3n6F2lX/yrvTEL5ylfaby+H\nhLJjR/Zf5/btVd0cidtb/iyKq0Rx2lA+FL1OBj4K1ANnJhhTpxTzr/J8XYZThg8Piacc21BqarL3\nlait3ZV1uytf3ijvKlHBEoqZXZy+LukA4NbEIuqkYv5VHreEAuXZhjJ9+kSef34Gq1a1JdgxYy5j\n2rTJJYzKdYVXeblK1JVe7luBw4odSFcV86/yQgmloaGZu+9uBKqZNq2Vf/qniXuq1bpS5dXQ0Myc\nOY3s2FFNTU0r48ePYOHC1ezYUc2mTSuBvgwYMJSamlamT59YsApvypQJfOMbcPXVV/CBD1RRW7uL\nadMme4N8BfKE4ipRnDaUu9JW9yE83X5bYhF10vTpE2lpmdGu2qurf5WvX99WAsmU2VbT1AQrVrS1\n1Rx0UJiHZPfuePOQdGz7aWb+/Jtobf0V0EwYYKDz7UKjR0/gjDMmcMMNhWNw5csTiqtEcUoo/5a2\n3Aq8amYrch3c3VJfsOeeewWDB1cxalTX/ypftw6OOy77vtxtNVcwZcoE+vSB/feHjRvjzZTY8XqN\nUTIJy+nJJPO98onTDuTKnycUV4nitKE0dUMce2XKlAl89rMTOO44uPDC3MdlVjFlViPlq/KK01aT\nakeJk1A6Xq86x3L298ol34OZrnJ4QnGVKGdCkbSF3HOamJkNSCakrhk6NCSEXOJ0L86XUOK01aTa\nUd73vsLxdrxea47l7O+Vy/r1cGSH0dFcpfGE4ipRztp+M9vfzPrneJVVMoHCsybG6V6cr7po+vSJ\njBkzo9220FZzOhASVkvL5Xzzm/Eerux4vYlUV39rz3LbWJwd3ysfr/LqGfw5FFeJYvfykjQUqE2t\nx5wGuNsMHQoLOky/1SZflVWqKmzVqmrOPbeVv//7jj2qUutz517B9u3te1ClSj/r189m/Xp4/vnC\njeip7dOmXYFZFUceuYtx447lkUfC9TdtWovZRTz11BAmTYrfLuQJpWfw51BcJYrTy+tMQsP8CGAd\nYd73F4Fjkg2tcwrP6569GmnTppXtqsL+/GdYtix7MpgyZULWL/VCDfa5TJkygRtvnMAZZ8A552Q/\n5oAD4KabYNCgnJdpxxNKz+BVXq4SxXlS/sfAeOCvZnYY8EnCpFdlpVAbSm3tRAYO7FiNBH33+kn7\nvXm48tXKOoNaAAAWRElEQVRX4T3vyb1/2LAwZH5cnlB6Bk8orhLFSSg7zewNYB9JVWb2IGEYloIk\nTZa0RNLLkr6XZf+Bku6Q9LSkRyUdE/fcTNlKKKlBIz/0oXrmz2/kggtGctRRVzBsWD2TJl3BVVdN\nZsCA7K3wnXnSfm8ernzttfwJZfhweP31eHFs2wbvvgsDyq6Fy3WWJxRXieK0obwVze++ALhR0jpg\nS6GTJFUBVwOnAauAxyTdaWYvph12GfCkmX1W0pHAfwKnxTy3nYMOgrfegl27oKoqe6+uP/5xBl/+\n8iQefngC990Xts2Zk31m4c48ad/Vhyt37gxzq+R6mBJCQolbQklNrJU+NbGrTJ5QXCWKU0I5izDc\nyj8A9wFLgf8T47yxwFIzWx7N8nhLdK10RwEPApjZS8DoqPE/zrntVFfDwIGwYUNYz9Wu8cAD81i2\nrG1bod5bcUyZMoGrrprEaaddgdRW+inUiL5qVajS6tMn9zHDhsUvoXh1V8/hCcVVojgllG8Bt5jZ\nKsL88nGNBNKfqF8JfDjjmKeBvwH+V9JYQoP/ITHP7WDo0LYH+3K1a0AVr73WVpJJfel//etXMGRI\n15+0TzXYjxgB114Lo0YVPufVV+HQQ/Mf09kSiieUnsETiqtEcRJKf6BR0luEksIfzGxtjPNyPRSZ\n7ifAVZIWA88Ciwlz18c5F4D6+vo9y3361LFuXR3HHJO7XWO//XYxaFD4kj7kkLBtypQJDBo0gdtu\ng2P2su/amDHQ0hIvoRRqP4GQUBYvjvfenlB6Dn8OxRVTU1MTTU1Nib9PnKFX6oF6SccBXwCaJa00\ns08WOHUVkP61OopQ0ki/9mbg3NS6pGVAC7BvoXNT0hPK88+3Nczna9eYPRuWLWtLKK2tsHx5SAZ7\n6/DDQ0Kpqyt8bJwSSmervHzYlZ7BSyiumOrq6qhL+1KaNWtWIu/TmeHr1wGvAxsI88oX8jhwhKTR\nwGrgbGBq+gGSBgLbzOxdSecDfzGzLZIKnptNetfhVJXVV75yBSNHVjFiRFtV1o03hgTysY+FY5cv\nDyWB2tqsl+2UMWPCnPNxvPYanHhi/mO8yqt38gcbXSWK82Djtwklk6HAH4BvmNkLhc4zs1ZJFxPG\nYa8CrjOzFyVdEO2/hjAU/m8lGfAccF6+cwu9Z2bX4fSqrPe/v237YYfRrmH+r3+NN/5WHIcfDrff\nHu/YV1+Fz3wm/zGdTSiHlc1MNa6rGhqaqa9v5OWXq5k0Kfc8OZlz5nTXcd35Xj3luHKJKTUobmLM\nLO8L+Bfg+ELHleIVwm/zn/9p9q1vta3v2mVWU2O2dWu7w+zaa82+/vW29f/4D7OLL7aiWLTI7IQT\n4h37/vebPfdc/mN27zbr27fjZ8jmzDPNbr893nu78nT33X+xMWMuM7Do9Rerrr5gzzJclmW5O48r\nx5jK/bhyiSm8wr8vzJL4Tk7iot31ykwot91m9rnPta2vWmU2dGjH/7Tz5pnV1bWtX3ih2Zw5HY/r\nig0bzAYMCIkgn927zfr1M9u0qfA1Dz3U7JVXCh83frzZggXx4nTlaeLEGe3+88OMGMvdeVw5xlTu\nx5VLTOkvzIr4XZx6xXkOpWJkDr+Sa1iTJKu8Bg0K3ZELTQe8YUPoydO/f+Frxq328jaUyhd/npxS\nHVeOMZX7ceUSU/J6VELJbENZvhxGj+543KhR4Qu6NepZ/Ne/FncOkVTX4Xzi9PBKidvTa906TyiV\nLv48OaU6rhxjKvfjyiWm5PWohBK3hNK3Lxx8MKxYAe+8E5JQnOdG4jr88MI9vQoNCpkuTgllxw7Y\nujWMTuwqV/x5cjLnzOmu48oxpnI/rlxiCsKguMmQmSV28aRJsvT4d+8O1UjbtoWhWC68ED7wAbjo\noo7nnnoq1NeHKqovfQmee654cV1+eRhOZebM3Mf8/OehFDN3buHr/ehHYdDHH/849zGrVsFJJ8V/\nZsWVr4aGZubOnbdn3p1x44bzyCNronlyViLV0L//kHbL3XlcOcZU7seVS0xhHqfT+fSnT8XMij7q\nX/dWsCVsn31CgnjjjVBNtHw5TJmS/dhUO0rcKXs7Y8wYmD8//zGdKaEMGwaLFuU/xttPeo5c8+44\nV+56VJUXhC/VVLVXvi/t0aNDwilmg3xK6mn5fOIMu5ISp8rLn5J3zpVaj0soqQEizfInlFQJJYmE\nUuxG+bgJxUsozrlS6pEJZd26UJVVU5N7sqnRo5NLKMOHw+bN4ZVLZ0oocXp5eUJxzpVaj0soqa7D\nr76avctwymGHJVflJeUvpWzdCps2xa+iOvjg8Jl25ZnzyxOKc67UelSjPLSVUJYvz18CGDkyHNev\nXzJfxKlBIo8/PvTamTOncc+YOzt29EUayhlnhHF1CjXA9ukTugOvXx9KK9msXx/eyznnSqXHJZQh\nQ8L8IYVKKPfd10x1dSO7dlUzeXK8L/a4GhqaeeqpRp55pporr1zJmjUDeP31fweaCeNdhiH1Gxuh\npSX0GS/03qm55fMlFC+hOOdKqccllFQJpaYG3vve7Mek5pvftq3zX+yFpK796qupeVguB1IPkDSS\nSiYpLS2zmTv3ilgJZc2a3KUQTyjOuVLrsW0o+aq8cs03P3fuvL1+/47XzjfOTrB9e1XB6w4blr+n\nlw+74pwrtR5bQtm8OXeVV6755uN8sRfS8dr5xtkJamvztLZHUlVeuXgJxTlXaj22hJLvGZRc883H\n+WIvpOO1842zk5qW+PSC1833LMrOnaHX2KBBnY3WOeeKJ9ESiqTJwM8Jsy7+2sx+mrF/MPB7YFgU\ny8/M7LfRvuXAJmAXsNPMxsZ5zwMOgC1bYN994cADsx+Tb775vdXx2hMYNuy3jBhxUTTOzlqki/aM\ns5OalriQYcNgwYLs+zZsaBs23znnSiWxwSElVQEvAacBq4DHgKmWNpWvpHqgxsx+ECWXl4CDLUwB\nvAw4yczezPMeli3+4cNh8GB49tnc8WUOwDdt2ulF7eVVzGs3NDQza1YjL71UzbhxHaf+3LatL6++\nOpSPfay4vdWccz2TpEQGh0wyoYwHZprZ5Gj9+wBm9pO0Yy4AjjWziyS9F7jPzN4X7VsGnGxmG/K8\nR4eE0tDQzBe/2EjfvtWcfHLlf8Gmeo21lXiaqa6+idbWX5HZDRlgzJgZXHXVpIr+zM65ZCWVUJKs\n8hoJrEhbXwl8OOOYa4H5klYD/YEvpO0z4M+SdgHXmNm1hd4w9eW7ZUvxuwOXSsdeY41RMgnLXe2G\n7JxzxZZkQolT9LkMeMrM6iSNAeZJOs7MNgOnmNkaSUOi7UvMrEMrQn19/Z7lhoYWWlpuaLe/0r9g\n408J26YYvdWccz1HU1MTTU1Nib9PkgllFZA+D+IoQikl3UeI/sQ2s5aomutI4HEzWxNtXy/pDmAs\nkDehNDXVZ+4GKvsLNv6UsG2K0VvNOddz1NXVUVdXt2d91qxZibxPkt2GHweOkDRaUl/gbODOjGOW\nEBrtkXQwIZm8IqmfpP7R9v0I/W3zNLEHSXYHLpX4U8IGcbshO+dcsSVWQol6al1MaDWuAq4zsxej\nhnjM7BrgSuB6SU8Tktt3zez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       "text": [
        "<matplotlib.figure.Figure at 0x7554c10>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For some perspective, we can wrap our maximum likelihood estimator code in one function and then examine the variance of the estimator using our set of synthetic trials data. Note that this takes a long time to run!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ML_estimator(x_samples):\n",
      "    dL=sum((xk-a)/(1+(xk-a)**2)  for xk in x_samples)\n",
      "    a_x  = fmin_l_bfgs_b(S.lambdify(a,(dL)**2),0,bounds=[(-3,3)],approx_grad=True)\n",
      "    return a_x[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# run maximum likelihood estimator on synthetic data we generated earlier\n",
      "# Beware this may take a long time!\n",
      "v= np.hstack([ML_estimator(o[i,:]) for i in range(o.shape[0])])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vmed= np.hstack([np.median(o[i,:]) for i in range(o.shape[0])])\n",
      "vavg =  np.hstack([np.mean(o[i,:]) for i in range(o.shape[0])])\n",
      "fig,ax = subplots()\n",
      "ax.plot(v,'-o',label='ML')\n",
      "ax.plot(vmed,'gs-',label='median')\n",
      "ax.plot(vavg,'r^-',label='mean')\n",
      "ax.axis(ymax=2,ymin=0)\n",
      "ax.legend(loc=(1,0))\n",
      "ax.set_xlabel('Trial Index')\n",
      "ax.set_ylabel('Value of Estimator')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<matplotlib.text.Text at 0x9a2ca30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1ELC+wDOyVLOJTKN/zZKq3obj2SZV7XhIZalqI+zTKaifbqDS0JBx+4zg+FQL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       "text": [
        "<matplotlib.figure.Figure at 0x9bdc190>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above chart shows that the using the mean-based estimator jumps all over the place while the maximum likelihood (ML) and median-based estimators are less volatile. The next chart explores the relationship between the ML and median-based estimators and checks whether one is biased compared to the other. The figure below shows that (1) there is a small numerical difference between the two estimators (2) neither is systematically different from the other (otherwise, the diagonal would not split them so evenly )."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax = subplots()\n",
      "ii= np.argsort(v)\n",
      "ax.plot(v[ii],vmed[ii],'o',alpha=.3)\n",
      "axs = ax.axis()\n",
      "ax.plot(linspace(0,2,10),linspace(0,2,10))\n",
      "ax.axis(axs)\n",
      "ax.set_aspect(1)\n",
      "ax.set_xlabel('ML estimate')\n",
      "ax.set_ylabel('Median estimate')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.text.Text at 0x9a45d30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pQVXd4otF8W2Zcs5bSN5ZOZ4dCSOfVVKSyc6dveTkLGHtwdXs6dnCX8y6l/nF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\nWAzD8BwTFsMwPMeExTAMz/n/6lT0G+skdw4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9a2c910>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax = subplots()\n",
      "ax.hist(v,10,alpha=.3,label='ML')\n",
      "ax.hist(vmed,10,alpha=.3,label='median')\n",
      "ax.legend(loc=(1,0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.legend.Legend at 0x1aa258f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x9a27710>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Maximum A-Posteriori (MAP) Estimation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's use a uniform distribution for the prior of $\\alpha$ around some bracketed interval\n",
      "\n",
      "$$ f(\\alpha) = \\frac{1}{\\alpha_{max}-\\alpha_{min}} \\quad where \\quad \\alpha_{max} \\le \\alpha \\le \\alpha_{min}$$\n",
      "\n",
      "and zero otherwise. We can compute this sample-by-sample to see how this works using this prior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha  = a\n",
      "alphamx,alphamn=3,-3\n",
      "g = f(x_samples[0])\n",
      "xi = linspace(alphamn,alphamx,100)\n",
      "mxval = S.lambdify(a,g)(xi).max()\n",
      "plot(xi,S.lambdify(a,g)(xi),x_samples[0],mxval*1.1,'o')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1aacd610>,\n",
        " <matplotlib.lines.Line2D at 0x1aacd770>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wSvBFzh1mzYKxY2HMmDAl7/77h6TetSscfrja1EXykRK81Gj+fPjnP+H11+HV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\n4A0x2YuoAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1aa1dbf0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xi = linspace(alphamn,alphamx,100)\n",
      "palpha=S.Piecewise((1,abs(x)<3),(0,True))\n",
      "\n",
      "def slide_figure(n=0):\n",
      "    fig,ax=subplots()\n",
      "    palpha=S.Piecewise((1,abs(x)<3),(0,True))\n",
      "    if n==0:\n",
      "        ax.plot(xi,[S.lambdify(x,palpha)(i) for i in xi])\n",
      "        ax.plot(x_samples[0],1.1,'o',ms=10.)\n",
      "    else:\n",
      "        g = S.prod(map(f,x_samples[:n]))\n",
      "        mxval = S.lambdify(a,g)(xi).max()*1.1\n",
      "        ax.plot(xi,S.lambdify(a,g)(xi))\n",
      "        ax.plot(x_samples[:n],mxval*ones(n),'o',color='gray',alpha=0.3)\n",
      "        ax.plot(x_samples[n],mxval,'o',ms=10.)\n",
      "        ax.axis(ymax=mxval*1.1)\n",
      "    ax.set_xlabel(r'$\\alpha$',fontsize=18)\n",
      "    ax.axis(xmin=-17,xmax=17)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(slide_figure, n=(0,15,1));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1b6296d0>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Does the order matter?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,axs = subplots(2,6,sharex=True)\n",
      "fig.set_size_inches((10,3))\n",
      "for n,ax in enumerate(axs.flatten()):\n",
      "    if n==0:\n",
      "        ax.plot(xi,[S.lambdify(x,palpha)(i) for i in xi])\n",
      "        ax.plot(x_samples[0],1.1,'o',ms=10.)\n",
      "    else:\n",
      "        g = S.prod(map(f,x_samples[:n]))\n",
      "        mxval = S.lambdify(a,g)(xi).max()*1.1\n",
      "        ax.plot(xi,S.lambdify(a,g)(xi))\n",
      "        ax.plot(x_samples[:n],mxval*ones(n),'o',color='gray',alpha=0.3)\n",
      "        ax.plot(x_samples[n],mxval,'o',ms=10.)\n",
      "        ax.axis(ymax=mxval*1.1)\n",
      "        ax.set_yticklabels([''])\n",
      "        ax.tick_params(labelsize=6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Wfh9Qv/Sf0ZBK2GfvCmA18EGl1KqkY64EztVaLwP+D/A9LwT1ypBy6v3Idv1s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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1ae172b0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# use random  order for first 12 samples\n",
      "x_samples[:12]= np.random.permutation(x_samples[:12])\n",
      "fig2,axs = subplots(2,6,sharex=True)\n",
      "fig2.set_size_inches((10,3))\n",
      "\n",
      "for n,ax in enumerate(axs.flatten()):\n",
      "    if n==0:\n",
      "        ax.plot(xi,[S.lambdify(x,palpha)(i) for i in xi])\n",
      "        ax.plot(x_samples[0],1.1,'o',ms=10.)\n",
      "    else:\n",
      "        g = S.prod(map(f,x_samples[:n]))\n",
      "        mxval = S.lambdify(a,g)(xi).max()*1.1\n",
      "        ax.plot(xi,S.lambdify(a,g)(xi))\n",
      "        ax.plot(x_samples[:n],mxval*ones(n),'o',color='gray',alpha=0.3)\n",
      "        ax.plot(x_samples[n],mxval,'o',ms=10.)\n",
      "        ax.axis(ymax=mxval*1.1)\n",
      "        ax.set_yticklabels([''])\n",
      "        ax.tick_params(labelsize=6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RvP468OqrwJNPisVvU5nYctllYlIAtf3mEK8EhSw4WkgBlGwuAwMDwKc/DWzf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\n4qIzPi5GJFwu+SKCJKSSRBv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       "text": [
        "<matplotlib.figure.Figure at 0x1b629130>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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Wfh9Qv/Sf0ZBK2GfvCmA18EGl1KqkY64EztVaLwP+D/A9LwT1ypBy6v3Idv1s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\n",
       "prompt_number": 25,
       "text": [
        "<matplotlib.figure.Figure at 0x1ae172b0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using Monte Carlo Methods"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING (theano.configdefaults): g++ not detected ! Theano will be unable to execute optimized C-implementations (for both CPU and GPU) and will default to Python implementations. Performance will be severely degraded.\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$f(x \\mid \\alpha, \\eta) = \\frac{1}{\\pi \\beta [1 + (\\frac{x-\\alpha}{\\beta})^2]}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with pm.Model() as model:\n",
      "    th = pm.Uniform('th',lower=-pi/2,upper=pi/2)\n",
      "    alpha= pm.Uniform('a',lower=-3,upper=3)\n",
      "    xk = pm.Cauchy('x',beta=1,alpha=alpha,observed=x_samples)\n",
      "    start = pm.find_MAP()\n",
      "    step = pm.NUTS()\n",
      "    trace = pm.sample(300, step, start)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "c:\\Python27\\lib\\site-packages\\theano-0.6.0-py2.7.egg\\theano\\gradient.py:512: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: th\n",
        "  handle_disconnected(elem)\n",
        "c:\\Python27\\lib\\site-packages\\theano-0.6.0-py2.7.egg\\theano\\gradient.py:532: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: <DisconnectedType>\n",
        "  handle_disconnected(rval[i])\n",
        "c:\\Python27\\lib\\site-packages\\theano-0.6.0-py2.7.egg\\theano\\tensor\\subtensor.py:110: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n",
        "  start in [None, 0] or\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 16 of 300 complete in 1.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 17 of 300 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 18 of 300 complete in 5.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                7%                  ] 21 of 300 complete in 5.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 25 of 300 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 28 of 300 complete in 7.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 29 of 300 complete in 9.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             10%                  ] 32 of 300 complete in 10.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 35 of 300 complete in 11.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 37 of 300 complete in 27.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             13%                  ] 39 of 300 complete in 28.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 45 of 300 complete in 29.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           16%                  ] 49 of 300 complete in 30.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           17%                  ] 53 of 300 complete in 31.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          18%                  ] 56 of 300 complete in 32.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          19%                  ] 57 of 300 complete in 35.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 60 of 300 complete in 40.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         21%                  ] 65 of 300 complete in 45.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         22%                  ] 67 of 300 complete in 46.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         23%                  ] 70 of 300 complete in 46.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        24%                  ] 73 of 300 complete in 47.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 76 of 300 complete in 48.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 77 of 300 complete in 49.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       26%                  ] 80 of 300 complete in 50.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       27%                  ] 81 of 300 complete in 51.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       28%                  ] 85 of 300 complete in 52.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      29%                  ] 88 of 300 complete in 52.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      30%                  ] 91 of 300 complete in 53.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      30%                  ] 92 of 300 complete in 58.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      31%                  ] 94 of 300 complete in 59.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     32%                  ] 97 of 300 complete in 59.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     34%                  ] 102 of 300 complete in 68.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    35%                  ] 107 of 300 complete in 69.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    36%                  ] 108 of 300 complete in 80.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   37%                  ] 113 of 300 complete in 81.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  39%                  ] 119 of 300 complete in 82.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  40%                  ] 120 of 300 complete in 83.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  40%                  ] 122 of 300 complete in 83.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  42%                  ] 126 of 300 complete in 84.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 43%                  ] 130 of 300 complete in 84.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
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      },
      {
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      },
      {
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      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pm.traceplot(trace);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YnnWWWLk2bBDhdMopwBNPiPXbT2itXQts2dK9AK7ywgvSoaqulv1taACOPVY6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\nX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       "text": [
        "<matplotlib.figure.Figure at 0x1ffc1070>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}