{
 "metadata": {
  "name": "week6_tutorial"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Psych 216A Lecture 6: Model Reliability"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Previous lectures have covered how to specify a model, fit a model and\n",
      "test the accuracy of a model.  This tutorial will focus on using\n",
      "bootstrapping to quantify the reliability of the parameter estimates of\n",
      "our model.  By reliability we essentially mean putting error bars on the\n",
      "parameter estimates.  In tutorial 1 we used bootstrapping to put error\n",
      "bars on estimates of the mean and median.  In tutorial 2 we used\n",
      "bootstrapping to put error bars on correlation coeficients.  We will now\n",
      "see that this same principal can be extended to just about any other type\n",
      "of model.\n",
      "\n",
      "Written by Jason D. Yeatman May 2012. jyeatman@stanford.edu\n",
      "\n",
      "Translated to Python by Michael Waskom June 2012"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import seaborn\n",
      "seaborn.set()\n",
      "colors = seaborn.color_palette()\n",
      "import moss"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Reliability -- Linear Models"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the case of a linear model with 5 regressors (one of which is a column\n",
      "of ones for our offset term), we can use bootstrapping to assess the\n",
      "reliability of each parameter:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_obs = 100\n",
      "X = column_stack((randn(n_obs, 4), ones(n_obs)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "y will be created as a linear combination of the variables in the X and the weights will be random"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w = rand(5)\n",
      "noise = randn(100) * 5\n",
      "y = dot(X, w) + noise"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now pretend this was real experimental data that we collected and we can\n",
      "fit a linear model to estimate the propper weights on X to predict y with\n",
      "the ordinary least squares formula. This is equivalent to matlab's\n",
      "regress or polyfit functions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ols_fit = lambda X, y: dot(dot(inv(dot(X.T, X)), X.T), y)\n",
      "w_ols = ols_fit(X, y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The weights we estimated are similar but not exactly the same as the true\n",
      "weights. This was due to the noise in the data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bar(arange(5) + .1, w, .4, label=\"actual weights\")\n",
      "bar(arange(5) + .5, w_ols, .4, color=colors[1], label=\"estimated weights\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ACiXSAFCoHkf6sccey6WXXpr6+vq89NJLJz1u06ZNmTx5ciZOnJg1a9b09HQA0O/0ONKX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\n6v8B+S47jFYwI6AAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can quantify the reliability of our estimated weights with bootstrapping."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iterations = 1000\n",
      "w_boot = zeros((iterations, len(w_ols)))\n",
      "for i in xrange(iterations):\n",
      "    \n",
      "    # Get an index vector to sample with replacement \n",
      "    samp = randint(0, n_obs, n_obs)\n",
      "\n",
      "    # Resample data and model\n",
      "    samp_X = X[samp, :]\n",
      "    samp_y = y[samp]\n",
      "    \n",
      "    # Fit the model on this iteration\n",
      "    w_boot[i, :] = ols_fit(samp_X, samp_y)\n",
      "\n",
      "# Get the 95% confidence interval for each weight (across each column in the design matrix)\n",
      "w_ols_ci = moss.percentiles(w_boot, [2.5, 97.5], axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The bar() function expects errorbar coordinates to be relative to bar height\n",
      "# We have a convenience function in our plotting library to convert these\n",
      "ebar_coords = seaborn.ci_to_errsize(w_ols_ci, w_ols)\n",
      "\n",
      "# Plot the confidence intervals as error bars on our barplot from above\n",
      "bar(arange(5) + .1, w, .4, label=\"actual weights\")\n",
      "bar(arange(5) + .5, w_ols, .4, yerr=ebar_coords, color=colors[1], ecolor=\"gray\", label=\"estimated weights\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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fPK158663tBzTehys3+W33vqD7pi3VBkZmZZrsvq7HKk9rq2t0YULF1S+5IeWa4q0vxfB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\nbW/E+ET3iBkAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Reliability and Noise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice that the reliability of the estimates increases when we collect\n",
      "more data or have less noise in the data (higher signal to noise ratio)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = column_stack((randn(1000, 4), ones(1000)))\n",
      "w = rand(5)\n",
      "\n",
      "# Large sample high noise; N = 1000, noise std = 5\n",
      "y_large_n = dot(X, w) + randn(1000) * 5\n",
      "\n",
      "# Small sample low noise; high signal to noise ratio\n",
      "y_lownoise = dot(X[:100], w) + randn(100)\n",
      "\n",
      "# Small sample, high noise\n",
      "y_noisy = dot(X[:100], w) + randn(100) * 5\n",
      "\n",
      "# Bootstrap all three models\n",
      "n_boot = 1000\n",
      "w_boot1 = moss.bootstrap(X, y_large_n, n_boot=n_boot, func=ols_fit)\n",
      "w_boot2 = moss.bootstrap(X[:100], y_lownoise, n_boot=n_boot, func=ols_fit)\n",
      "w_boot3 = moss.bootstrap(X[:100], y_noisy, n_boot=n_boot, func=ols_fit)\n",
      "\n",
      "# The median of these bootstrapped estimates are the weights for each model.\n",
      "# You could also use the mean if you prefer.\n",
      "w_model1 = median(w_boot1, axis=0)\n",
      "w_model2 = median(w_boot2, axis=0)\n",
      "w_model3 = median(w_boot3, axis=0)\n",
      "\n",
      "# Compute the 95% confidence intervals on parameter estimates\n",
      "pcts = [2.5, 97.5]\n",
      "ci1 = moss.percentiles(w_boot1, pcts, axis=0)\n",
      "ci2 = moss.percentiles(w_boot2, pcts, axis=0)\n",
      "ci3 = moss.percentiles(w_boot3, pcts, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot both estimates against the actual weights. Notice the errorbars are\n",
      "much smaller when there was less noise or more data.  The intuition is\n",
      "that increasing the sample size or making higher signal to noise\n",
      "measurements will decrease the error on our parameter estimates"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "barx = linspace(0, 1, 6)[:-1]\n",
      "models = [w, w_model1, w_model2, w_model3]\n",
      "cis = [None] + map(seaborn.ci_to_errsize, [ci1, ci2, ci3], models[1:])\n",
      "for i, model in enumerate(models):\n",
      "    bar(barx + i, model, 0.2, yerr=cis[i], color=colors[i], ecolor=\"gray\")\n",
      "xticks([.5, 1.5, 2.5, 3.5], [\"model\", \"large N\", \"low noise\", \"noisy\"]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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333yzJKmhoUEfffSRZs6cqaysLP3iF7/Q5s2bL/h8U6ZM0ebNm+XxeCK+bfFk\n5cqVuueee5Senq4rr7xSV1xxhbZs2aIxY8Zow4YN2rdvn4YMGaLu3bursLBQmzdvVnZ29jn9OJ1O\nTZ06VZJ04403atOmTZIaP2/Tp0+XJM2YMaN571n61/LCiBEjNHnyZP3tb39TamqqJOn999/XokWL\nlJWVpVtvvVUnTpw470wHLs7tduumm26S3W5XTk6O1q1bp61bt+qHP/yhnE6npk2bphUrVpz1Oykp\nKerevbseeOABrVq1Sh07dpQkzZw5U2+++aakxmMppk2bZnx7Iok13X/q1KlT8/8nJiYqPT1dkpSQ\nkKC6ujrZbDZd6EDv8/3c7/dr3LhxzW8eRMa6deu0YcMGffLJJ0pNTVVGRkZz6Pbo0aO53bfXFpvG\nzO/3y263a/Pmzc1fmC7G4XDoqaee0iuvvGLhVsS/831+bDabevXqpbKyMq1atUpjx45VSUmJ3n33\nXaWlpTUH45mSkpKaT1FMSEhQTU1N82PBTsRYunSpNm7cqKVLl2ru3LnasmWL/H6//vjHP2rs2LEW\nbGX79e2/nxUVFZIax+R8Y9/07/Xr1+uTTz7Rm2++qTfffFPvvvuusrOz5fF4tG7dOvl8Pg0ePNjc\nhhjAnm6Ibr/9di1ZskQ+n0/vvfeesrOzlZCQoNtuu01LliyR3+/X22+/rdra2ub2Td/gJamkpIQj\nXSMgPz9fbrdbLpdL77zzzgWPCh83bpw+/fRTFRUVKT8/X59//rmkxj8QEyZM0J/+9Cf5fD4FAgHt\n3r37nN8/84/Gww8/rM8++0xFRUWR2ag4dPvtt2v58uXyer365ptvdODAAY0aNUqSdN1112nBggXK\nycnRmDFj9Oqrr7Y4BCdMmKDFixfL7/frjTfe0B133CHpX+MWCATk8XiUnZ2tefPmqaCgQDU1NZoy\nZYoWLlzYvN64Y8cOC7e6/UpMTNSoUaP0/vvvq6GhQYsXL26edWpSWVmpkydPavz48Zo3b5527tzZ\n/NiDDz6oqVOnNs9exBNC95++vSd05r9tNpseeughuVwuXXvttfrss8+a1/WmT58uh8OhwYMHa/v2\n7erbt6+kxrXGRYsW6YUXXtDVV1+tcePGnfeSmmidpvH5/ve/r7KyMg0aNEh///vfz/pWfOYYduvW\nTT/72c80btw43X///Ro5cqQuvfRSSY1HUxYWFmrEiBEaOnToOdNgTX019ZeQkKDHH3+c0A1B02t2\n1VVX6cExfQLSAAABH0lEQVQHH9Rtt92mJ554QosWLWpuM2bMGPl8PvXv319ZWVkqLS3VmDFjLtpf\n0/83/fvpp5/WkSNHlJWVpRMnTuinP/3pWW18Pp8eeOABXX311brpppv04osvqkOHDrrnnns0atQo\njR8/XkOHDtWcOXMi9VLEtfP9/XzllVf08ccfa8SIEeratat+9KMfnfV4eXm5Jk2apOHDh2vKlCnN\nB7xJjcs4paWlzQe8xZOwLgMJxJLKykqlpqbq5MmTysnJ0datW6N+HimAcy1btkxr164968tZvGBN\nF+3GrFmzlJubq44dOzYfKQmgbZk9e7a+/PLL5iPT4w17ugAAGMKaLgAAhhC6AAAYQugCAGAIoQsA\ngCGELgAAhhC6AAAY8v8Bc19xikvH/M0AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Model accuracy and noise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "While the reliability of a parameter estimate depends both on the number\n",
      "of measurements that are made and the signal to noise of these\n",
      "measurements, the same is not true about model accuracy.  We will explore\n",
      "this below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We will use the R^2 function from the Scikit-learn function\n",
      "from sklearn.metrics import r2_score\n",
      "r2_model1 = r2_score(y_large_n, dot(X, w_model1))\n",
      "r2_model2 = r2_score(y_lownoise, dot(X[:100], w_model2))\n",
      "r2_model3 = r2_score(y_noisy, dot(X[:100], w_model3))\n",
      "\n",
      "print 'Model 1 is reliable but not accurate. R^2 = %.2f' % r2_model1\n",
      "print 'Model 2 is reliable and accurate. R^2 = %.2f' % r2_model2\n",
      "print 'Model 3 is neither reliable nor accurate. R^2 = %.2f' % r2_model3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Model 1 is reliable but not accurate. R^2 = 0.10\n",
        "Model 2 is reliable and accurate. R^2 = 0.74\n",
        "Model 3 is neither reliable nor accurate. R^2 = 0.22\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Model reliability with correlated regressors"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now lets use bootstrapping to examine the effects of having correlated\n",
      "regressors. When each column (regressor) in the matrix is orthogonal the\n",
      "parameter estimates are much more reliable.  High correlations between\n",
      "the columns means that decreasing the weight on one column can be\n",
      "compensated for by increasing the weight on another column.  The result\n",
      "is that each estimated weight is very noisy and unreliable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Here are the weights\n",
      "w = rand(3)\n",
      "\n",
      "# Simulate data from 3 uncorrelated regressors\n",
      "X_orth = randn(100, 3)\n",
      "\n",
      "# Signal with no noise\n",
      "y_orth = dot(X_orth, w)\n",
      "\n",
      "# Add noise that with a std proportional to the signal std\n",
      "y_orth = y_orth + std(y_orth) * randn(100)\n",
      "\n",
      "# Simulate data from 3 correlated regressors.  To do this first we define a covariance matrix, S.\n",
      "cor = 0.8  # This is the correlation to induce between the variables\n",
      "S = eye(3)\n",
      "S[S == 0] = cor\n",
      "\n",
      "# Then simulate data that comes from a 3-D gaussian (mean 0) with this covariance matrix\n",
      "X_corr = random.multivariate_normal(zeros(3), S, 100)\n",
      "y_corr = dot(X_corr, w)\n",
      "y_corr = y_corr + std(y_corr) * randn(100)\n",
      "\n",
      "# Bootstrap the model fits for the correlated and uncorrelated data\n",
      "n_boot = 1000\n",
      "boot_orth = moss.bootstrap(X_orth, y_orth, n_boot=n_boot, func=ols_fit)\n",
      "boot_corr = moss.bootstrap(X_corr, y_corr, n_boot=n_boot, func=ols_fit)\n",
      "\n",
      "# Calculate the 95% confidence intervals on the 2 sets of weights\n",
      "pcts = [2.5, 97.5]\n",
      "ci1 = moss.percentiles(boot_orth, pcts, axis=0)\n",
      "ci2 = moss.percentiles(boot_corr, pcts, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the parameter estimates and 95% confidence intervals for the\n",
      "correlated and uncorrelated data. Notice how large the error bars are\n",
      "when the regressors are correlated. With correlated regressors you would\n",
      "need to collect much more data to reach an equivalent level of\n",
      "reliability."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "barx = linspace(0, 1, 4)[:-1]\n",
      "models = [w, median(boot_orth, axis=0), median(boot_corr, axis=0)]\n",
      "cis = [None] + map(seaborn.ci_to_errsize, [ci1, ci2], models[1:])\n",
      "for i, model in enumerate(models):\n",
      "    bar(barx + i, model, 1. / 3, yerr=cis[i], color=colors[i], ecolor=\"gray\")\n",
      "xticks([.5, 1.5, 2.5], [\"model\", \"orthogonal\", \"correlated\"]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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Shg0btHfvXg0aNEgDBgzQp59+qr/97W8h3ko014YNGzRy5EglJiYqKSlJI0aM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\nAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Reliability of complex models"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above scenarios of model reiability are slightly contrived.  In the\n",
      "real world we rarely know what parameters to include in a model.\n",
      "Assessing reliability and accuracy of models is essential for determining\n",
      "the most apropriate set of parameters to include in a model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Assume that this is the population of data\n",
      "x_pop = randn(1000) + 4\n",
      "noise = randn(1000) * 5\n",
      "y_pop = 1.5 * x_pop ** 2 + noise\n",
      "\n",
      "# And this is a random sample we collect in an experiment\n",
      "n = 10\n",
      "samp = permutation(arange(len(y_pop)))[:n]\n",
      "x_samp = x_pop[samp]\n",
      "y_samp = y_pop[samp]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When we plot the population and the sample data it is obvious that y is\n",
      "increasing as a funciton of X however with a small sample we can not\n",
      "reliably estimate the exponent on x."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(x_pop, y_pop, \"o\", label=\"population\")\n",
      "plot(x_samp, y_samp, \"o\", color=colors[2], label=\"sample\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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+KGhNnQqVRZm4eDIL5Yffx5R7Qgdds8EkMBcGKUgHwF+9y15FLy93JxhEHlDM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\nrkJggg==\n"
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will bootstrap the parameter estimates for two models.  Model 1 is a\n",
      "linear model and model 2 is a non-linear model with an exponent as a free\n",
      "parameter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import curve_fit\n",
      "modelfunc = lambda x, a, b, c: a * x ** b + c\n",
      "# Bootstrap the linear and nonlinear fitting procedures\n",
      "w_ols_boot, w_nonlin_boot = [], []\n",
      "for i in xrange(100):\n",
      "    \n",
      "    # Get the bootstrap index\n",
      "    boot_samp = random.randint(0, n, n)\n",
      "    boot_x = x_samp[boot_samp]\n",
      "    boot_y = y_samp[boot_samp]\n",
      "    \n",
      "    # Fit a linear model\n",
      "    w_ols_boot.append(lstsq(moss.add_constant(boot_x), boot_y)[0])\n",
      "    w_nonlin_boot.append(curve_fit(modelfunc, boot_x, boot_y, maxfev=100000)[0])\n",
      "w_ols_boot = array(w_ols_boot)\n",
      "w_nonlin_boot = array(w_nonlin_boot)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The parameter estimates for the non linear model are very noisy.  Because\n",
      "there is so little data to constrain estimates, they very substantially\n",
      "from one bootstrap iteration to the next. For the linear model on the\n",
      "other hand there are fewer parameters and they are more reliable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Visualize the reliability of the parameter estimates of the linear model\n",
      "ols_model = median(w_ols_boot, axis=0)\n",
      "pcts = [16, 84]\n",
      "ols_ci = percentile(w_ols_boot, pcts, axis=0)\n",
      "nonlin_model = median(w_nonlin_boot, axis=0)\n",
      "nonlin_ci = percentile(w_nonlin_boot, pcts, axis=0)\n",
      "ols_ebars = seaborn.ci_to_errsize(ols_ci, ols_model)\n",
      "bar(range(2), ols_model, 1, yerr=ols_ebars, ecolor=\"gray\", label=\"OLS\")\n",
      "nonlin_ebars = seaborn.ci_to_errsize(nonlin_ci, nonlin_model)\n",
      "bar(range(2, 5), nonlin_model, 1, yerr=nonlin_ebars, ecolor=\"gray\", color=colors[1], label=\"nonlinear\")\n",
      "xticks(arange(5) + .5, [\"slope\", \"constant\", \"slope\", \"exponent\", \"constant\"])\n",
      "legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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MAIAFCDIA+Fl5eLnKw4zTYyDI8B4yAPhJwyORanQkUqX1yyRJcfujJUklDY/pSMNjTo6G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\nIMgAAFiAIAMAYAGCDACABf4P6DsLKA87oWgAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Visualize model fits"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The code below provides an example of how to visualize a model's fit to\n",
      "the data including error bars on the model estimates.  This code can be\n",
      "generalized to any complex model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scatter(x_pop, y_pop, facecolor='none')\n",
      "l, r = xlim()\n",
      "xx = linspace(l, r, 200)\n",
      "# Loop over each bootstrap iteration and compute that models prediction for all of the x values\n",
      "y_model = []\n",
      "for i, w in enumerate(w_ols_boot):\n",
      "    y_i = dot(xx, w_ols_boot[i][0]) + w_ols_boot[i][1]\n",
      "    y_model.append(y_i)\n",
      "\n",
      "# Plot the linear prediction and transparent error bars\n",
      "pcts = [16, 84]\n",
      "plot(xx, median(y_model, axis=0))\n",
      "lin_ci = moss.percentiles(y_model, pcts, axis=0)\n",
      "fill_between(xx, *lin_ci, color=colors[0], alpha=.2)\n",
      "\n",
      "# Now derive the nonlinear predictions and plot\n",
      "y_model_nlin = []\n",
      "for i, w in enumerate(w_nonlin_boot):\n",
      "    y_i = modelfunc(xx, *w)\n",
      "    y_model_nlin.append(y_i)\n",
      "plot(xx, median(y_model_nlin, axis=0))\n",
      "nlin_ci = moss.percentiles(y_model_nlin, pcts, axis=0)\n",
      "fill_between(xx, *nlin_ci, color=colors[1], alpha=.2);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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NpvVz220Lht67kiqkt7d3KKhTqfTQ7GZN14dCWtN1vF4fBw+1YRjG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\nIo5JUAshhBBx7P8DBNqHKMH7qHkAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Also note the distribution of parameter estimates for the non linear\n",
      "model.  Extreme outliers are relatively common on the exponent.  Notice\n",
      "that in the code above we plotted the median fit rather than the mean\n",
      "fit.  Sometimes the mean can be outside the error bars!  This is an\n",
      "instance when the mean is a poor estimate of the central tendency."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scatter(x_pop, y_pop, facecolor='none')\n",
      "plot(xx, mean(y_model_nlin, 0), label=\"mean\", color=colors[3])\n",
      "plot(xx, median(y_model_nlin, 0), label=\"median\", color=colors[4])\n",
      "legend(loc=\"best\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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KM2FOMQR0Xz6PA2vty2jDYkicch8qlVyhHbFZ1Gtqajh58iQlJSV8+ctfJi8v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\n8Xq9+Hw+5s2bT09PN01NjSx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R4PP5AIiNjaO31/aZfkVHGzAYDPT09ODxDH7ypUSDyzVA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\n"
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the histogram of parameter estimates for the non linear model.\n",
      "Note that the distribution of parameter estimates across bootstrap\n",
      "iterations is highly non-gaussian."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(9, 9))\n",
      "plot_type = [\"slope\", \"exponent\", \"constant\"]\n",
      "for pi in range(3):\n",
      "    subplot(3, 1, pi + 1)\n",
      "    hist(w_nonlin_boot[:, pi], 25, color=colors[pi])\n",
      "    title(plot_type[pi]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ycqWkpOjAgQOaO3eu3fUCAIAwFtK5l6FDh2rnzp1nbXc4HFqzZk2riwIAAJ0T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\nGEsb/wJqtiHHu4dNpAAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the histogram of parameter estimates for the linear model.\n",
      "Note that the distribution of parameter estimates across bootstrap\n",
      "iterations is roughly gaussian."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(9, 6))\n",
      "plot_type = [\"slope\", \"constant\"]\n",
      "for pi in range(2):\n",
      "    subplot(2, 1, pi + 1)\n",
      "    hist(w_ols_boot[:, pi], 25, color=colors[pi])\n",
      "    title(plot_type[pi]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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//vmaPHmyHnjgAe3fv1/19fXatm2bpk+frtWrV2vz5s3av3+/li9frhkzZvjV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\n"
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Which model is more accuracte? This is a question for cross validation."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}