{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Frequentism and Bayesianism V: Model Selection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*This notebook originally appeared as a [post](https://jakevdp.github.io/blog/2015/08/07/frequentism-and-bayesianism-5-model-selection/) on the blog [Pythonic Perambulations](http://jakevdp.github.io). The content is BSD licensed.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Jake VanderPlas is a Senior Data Science Fellow at the University of Washington's eScience institute\n", "Other interesting articles in that area:\n", "- https://healthyalgorithms.com/2009/08/25/mcmc-in-python-pymc-for-bayesian-model-selection/ (read the comments also)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here I am going to dive into an important topic that I've not yet covered: *model selection*.\n", "We will take a look at this from both a frequentist and Bayesian standpoint, and along the way gain some more insight into the fundamental philosophical divide between frequentist and Bayesian methods, and the practical consequences of this divide.\n", "\n", "My quick, TL;DR summary is this: for model selection, frequentist methods tend to be **conceptually difficult but computationally straightforward**, while Bayesian methods tend to be **conceptually straightforward but computationally difficult**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Fitting vs Model Selection\n", "\n", "The difference between *model fitting* and *model selection* is often a cause of confusion.\n", "**Model fitting** proceeds by assuming a particular model is true, and tuning the model so it provides the best possible fit to the data. **Model selection**, on the other hand, asks the larger question of whether the assumptions of the model are compatible with the data.\n", "\n", "Let's make this more concrete.\n", "By *model* here I essentially mean a formula, usually with tunable parameters, which quantifies the likelihood of observing your data.\n", "For example, your model might consist of the statement, \"the $(x, y)$ observations come from a straight line, with known normal measurement errors $\\sigma_y$\".\n", "Labeling this model $M_1$, we can write:\n", "\n", "$$\n", "y_{M_1}(x;\\theta) = \\theta_0 + \\theta_1 x\\\\\n", "y \\sim \\mathcal{N}(y_{M_1}, \\sigma_y^2)\n", "$$\n", "\n", "where the second line indicates that the observed $y$ is normally distributed about the model value, with variance $\\sigma_y^2$.\n", "There are two tunable parameters to this model, represented by the vector $\\theta = [\\theta_0, \\theta_1]$ (i.e. the slope and intercept).\n", "\n", "Another model might consist of the statement \"the observations $(x, y)$ come from a quadratic curve, with known normal measurement errors $\\sigma_y$\".\n", "Labeling this model $M_2$, we can write:\n", "\n", "$$\n", "y_{M_2}(x;\\theta) = \\theta_0 + \\theta_1 x + \\theta_2 x^2\\\\\n", "y \\sim \\mathcal{N}(y_{M_2}, \\sigma_y^2)\n", "$$\n", "\n", "There are three tunable parameters here, again represented by the vector $\\theta$.\n", "\n", "Model fitting, in this case, is the process of finding constraints on the values of the parameters $\\theta$ within each model.\n", "That is, it allows you to make statements such as, \"assuming $M_1$ is true, this particular $\\theta$ gives the best-fit line\" or \"assuming $M_2$ is true, this particular vector $\\theta$ gives the best-fit curve.\"\n", "Model fitting proceeds without respect to whether the model is capable of describing the data well; it just arrives at the best-fit model *under the assumption that the model is accurate*.\n", "\n", "Model selection, on the other hand, is not concerned with the parameters themselves, but with the question of whether the model is capable of describing the data well.\n", "That is, it allows you to say, \"for my data, a line ($M_1$) provides a better fit than a quadratic curve ($M_2$)\".\n", "\n", "Let's make this more concrete by introducing some data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Selection: Linear or Quadratic?\n", "\n", "Consider the following data:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "data = np.array([[ 0.42, 0.72, 0. , 0.3 , 0.15,\n", " 0.09, 0.19, 0.35, 0.4 , 0.54,\n", " 0.42, 0.69, 0.2 , 0.88, 0.03,\n", " 0.67, 0.42, 0.56, 0.14, 0.2 ],\n", " [ 0.33, 0.41, -0.22, 0.01, -0.05,\n", " -0.05, -0.12, 0.26, 0.29, 0.39, \n", " 0.31, 0.42, -0.01, 0.58, -0.2 ,\n", " 0.52, 0.15, 0.32, -0.13, -0.09 ],\n", " [ 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ,\n", " 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ,\n", " 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ,\n", " 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ]])\n", "x, y, sigma_y = data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get an idea of what we're looking at, let's quickly visualize these points:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set() # set default plot styles\n", "\n", "x, y, sigma_y = data\n", "fig, ax = plt.subplots()\n", "ax.errorbar(x, y, sigma_y, fmt='ok', ecolor='gray')\n", "ax.set(xlabel='x', ylabel='y', title='input data');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our central model selection question will be this: **what better fits this data: a linear ($M_1$) or quadratic ($M_2$) curve**?\n", "\n", "Let's create a function to compute these models given some data and parameters; for convenience, we'll make a very general polynomial model function:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def polynomial_fit(theta, x):\n", " \"\"\"Polynomial model of degree (len(theta) - 1)\"\"\"\n", " return sum(t * x ** n for (n, t) in enumerate(theta))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the ``theta`` variable is of length 2, this corresponds to the linear model ($M_1$). If the ``theta`` variable is length 3, this corresponds to the quadratic model ($M_2$).\n", "\n", "As detailed in my previous posts, both the frequentist and Bayesian approaches to model fitting often revolve around the *likelihood*, which, for independent errors, is the product of the probabilities for each individual point.\n", "Here is a function which computes the log-likelihood for the two models:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy import stats\n", "\n", "def logL(theta, model=polynomial_fit, data=data):\n", " \"\"\"Gaussian log-likelihood of the model at theta\"\"\"\n", " x, y, sigma_y = data\n", " y_fit = model(theta, x)\n", " return sum(stats.norm.logpdf(*args)\n", " for args in zip(y, y_fit, sigma_y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both the Bayesian and frequentist approaches are based on the likelihood, and the standard frequentist approach is to find the model which maximizes this expression.\n", "Though there are efficient closed-form ways of maximizing this, we'll use a direct optimization approach here for clarity:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy import optimize\n", "\n", "def best_theta(degree, model=polynomial_fit, data=data):\n", " theta_0 = (degree + 1) * [0]\n", " neg_logL = lambda theta: -logL(theta, model, data)\n", " return optimize.fmin_bfgs(neg_logL, theta_0, disp=False)\n", "\n", "theta1 = best_theta(1)\n", "theta2 = best_theta(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can visually compare the maximum-likelihood degree-1 and degree-2 models:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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U8qryufTjXXxiSQolulLzchttO3q5daeTUyDBTgH42rVvlKr629Hig/P8vB+h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\nyx6unvv/n5ytbMj+FJPJxOOJ40jp+OObXuTXlk2f/gyRkUE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xfit = np.linspace(0, 1, 1000)\n", "fig, ax = plt.subplots()\n", "ax.errorbar(x, y, sigma_y, fmt='ok', ecolor='gray')\n", "ax.plot(xfit, polynomial_fit(theta1, xfit), label='best linear model')\n", "ax.plot(xfit, polynomial_fit(theta2, xfit), label='best quadratic model')\n", "ax.legend(loc='best', fontsize=14)\n", "ax.set(xlabel='x', ylabel='y', title='data');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The crux of the model selection question is this: how we can quantify the difference between these models and decide which model better describes our data?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Naive Approach: Comparing Maximum Likelihoods\n", "\n", "One common mistake is to assume that we can select between models via *the value of the maximum likelihood*.\n", "While this works in some special cases, it is not generally applicable.\n", "Let's take a look at the maximum log-likelihood value for each of our fits:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('linear model: logL =', 22.010867006612543)\n", "('quadratic model: logL =', 22.941513586503998)\n" ] } ], "source": [ "print(\"linear model: logL =\", logL(best_theta(1)))\n", "print(\"quadratic model: logL =\", logL(best_theta(2)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The quadratic model yields a higher log-likelihood, but this **does not** necessarily mean it is the better model!\n", "\n", "The problem is that the quadratic model has more degrees of freedom than the linear model, and thus will **always** give an equal or larger maximum likelihood, regardless of the data!\n", "This trend holds generally: as you increase model complexity, the maximum likelihood value will (almost) always increase!\n", "\n", "Let's take a look at the best maximum likelihood for a series of polynomial fits (linear, quadratic, cubic, quartic, etc.):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TJz6DXq9n/PjnOXr0OKrLLIwJMGbMWMrKyhg//mlMJhPNm7fgvfc+\nxN29usf49dff5P3332XEiHvR6Zzp0KET06e/XadzcXNz4803Z/Lhh7P5/POPCQ0N4623ZtGsWYvr\nbyjhcJKSEq76/NKl8wEYPfrxeh1jf2IOy35MorjMRJMAdx4ZGkvz0IuLKJ1XWFnEr+f2sPPcnpoC\nDmEeIdwW2o2uQR1xr2eVu+tlKSlB4dYYkqdSLlVP0wE50p1jR7zT7WgxS7x183tSLks2JlJcbiIi\nyIOxw1oREVS39R2kjW3P0WIOCKjf2iC3Ckf6XdpaVVVVzZpMAQF6Bg26k/vvH8Hw4TduoQt7cLTP\ngMZkq7bp27cnJ04cu+j51q3bsnXrTqD+CVNhqZFlmxL5/WQeWo2ae3s1ZUj3iEsWH7IqVhIKTrI9\n4zeO5B1HQcFF40LX4I7cFtKVcH3YZQs4NNa/m7RpUzEU5HPgtu71Th4bW32vU9LDJMQtqMRg4qsf\nk9hzIgetRsX9tze77Ie2EEI0pEOHDjJp0rPMnfs5rVu3Yc2aNZw7l0G3bj3sHZoQTJw4udYcpvMm\nTJhUr/0tXTofRYHwdkP5bmsyFUYLMeHePDI0lmDfi3uGSk1l/Ja5jx0Zv5FXWQBAuD6MPmE96BLU\nEZ3mxpkvZCkpviVKioMkTELcUhRFYW9CDss2JVFWUUXzUE8eHdbqiuW/hRCiIbVv34Gnn36eN954\nhaKiQsLDmzB9+ltERDS1d2hC1MxTmj59GtnZ2cTGtmbChEn1nr9UXuVEYpE/Wzcm4qrT8siQGPq0\nD0V9Qe+QoiikFJ9ie8YuDuYcwaxYcFI70TOkK33CehDpGd4g59aQrEYj1ooKTD4NW0H3RiUJkxC3\niKIyI0s3Vg8FcNaqGdW/BQO7hKNWy4KtQojGNWLEKEb8sc6UDDsTN5r4+OGUlRUB9Z+nZLZYWb/r\nNHtzmqCgonNMAA8Nisbb488CJxXmSvZkHWBHxm+cK88CIMgtkD5hPege3Ak3O81NqgtzUXX73AoV\n8kASJiFueoqi8OuRLJZvOYnBaCYm3JtHh8USdI2rhgshhBDi6pIzilm8IYGMvHKc1RaivfN4Nr5/\nzfZsQy7b0nfyW+ZejBYTGpWGzoHt6RPWgxbezRp0cVlbMRdXJ0wmnSRMQggHl19cyeIfEjiaVoDO\nWcPoO6Pp2zGs1lAAIYQQQly/CqOZldtS+PlABgrVC6Wbs3agVStYFSsnCk6yNX0Hx/MTAfDWeXFn\n5B3cFtoNT2fHKppjLioEpIdJCOHArIrCtoPnWPFzMkaThTZRvjwyJAZ/r0uvUSSEEELYwvWW4HYU\nB0/msXRTIoWlRkL83HhkSCzR4d4sWraNLLdi/rX7PXIMeQA092pKv/DetPdvg0Ztv4Xhr4elSHqY\nhBAOLKfQwKINCSScKcJVp+WxYbH0bhfiEF38QgghhCMpLjPy1eaT7E3IqbWWYaGpgO+S/suB4FQs\naivaCg09grvQN/w2IvRN7B32dTs/h8l0lUWnbxaSMAlxk7BaFTbvT2fVthRMZisdWvgzenAMPvpb\n48NMCCGEaCyKAtsPneObn5IxGM00D/PkkcExlGozmX9sEcfyE1FQcFI0hBb78exdz6J39rB32A3m\nfMJ0z4OP4OTra+dobE8SJiFuApn55Sxcf4KUjBI8XJ14dFgs3VsFSa+SEEII0cAMZi2JhQFs3ZCA\ni7OGvw9qjntILovTvqipdtfMK5J+TXpxdNNe1KhuqmQJ/pjDpFKh9fS0dyiNQhImIRyYxWrlh91n\nWLPjFGaLla6xgTw0KBpP91tjTLEQQgjRWMwWKxv3nGFvdhOsqGnXUk9U20J+yl1CcUIpapWaLkEd\n6B/ep2btpOPss3PUtmEuLkKj16PS3hqpxK1xlkLchM5kl/Ll+gROZ5fi6e7M6Dtj6BwTYO+whBBC\niJtOWmYJizYkcDanDGeXcnwikjjjV0xyhgkXjY7+4X24I7w3vi4+9g7V5hRFwVxUhHNQsL1DaTSS\nMAnhYMwWK+t2nuL7XaexWBV6tQ3mfwa0xMPVyd6hCSGEEA7FYiinMiUF49kzmHJzMOflYzVW0jYn\nC6tazdn8OZw2ObG/yIkKHxdCO5VRqDlNiQq8tV7cFTWIXqHdcNXeOlVorRUVKEYjWm9ve4fSaCRh\nEsKBpGWWsHD9CTJyy/HR63hkSCxxzf3sHZYQQgjhMIznMijbv4+y3w9gPHumuoLDhTQaXACVxUrF\n0UMEAkMBcqA4Xc3pUHfyQ0J5/OEXHbYs+PU4X/BBEiYhxA3FVGVhzY40fthzBkWBfh1CGXFHC1x1\n8l9YCCGEuBpLRQWlu36laNtWTBnpAKi0WlxbRuPaMhqXqGY4BQbi5B9AmRnenv89+a4lePin4FNV\nSkCRmTYFLgSllxB3shTlZCJZJR/jH/8AujDHLxN+LSzF1QmTxksSJiHEDeJkehEL1yeQXWDA38uF\nx4bG0qrpzV/CUwghhLheVbm5FGz6gZKdv6IYK0Gjwb1jJ/RduuIe1wGN659D6RRFYfvRs6w49DOW\nlik46yoxoyYquCcDI/sS4h6EYjazYe4sgtPPoTr4O+WHDuJ1e1/8HxiBxs3djmfaeMyFhQBovW/+\n+VrnScIkxA3KaLKwclsKW/ZX3wkb2KUJD9zeHJ3zrdf9L4QQQlwLU24OBd+vo2TXr2CxoPXxxWvo\nMLz69EXr5XXR68/kFTBv1/cUOCegCq1CY1UTVOrNs4P/t1YhB5VWS35gAPkB/sR36EbeiuUUb9tK\n+ZHDBI99ArfYVo15mnZRVZAPgJPfrXPzVhImIW5AJ04V8OWGBPKKKwnydWPssFhaNrl1ur6FEEKI\n+jAXF5G/5j8U/7odLBacgoPxu/te9F27o9JcfMOxoKKIRfs2kFx5GJW7BY3ViT7BfSn7PR0nq+by\nVe9UKjzi2uPeug0FG74nf+0a0t97F7/77sf3rntu6nUQzQUFAGh9b5051JIwCXEDMVSa+XZrMtsO\nnkOlgqE9IvhbryicnaRXSQghhLgcq8lE4Y8bKVj/PYqxsjpRuuc+9F27oVKrL3p9riGf1Yk/cqjg\nIKisqKw6Onn14u8dB+Lq5MLS/fPrdFyVVovfPX/DvW07zn3+Cfn/WYUpM5OgRx9D7XRzrolY08Pk\nKz1MQohGdjglj8U/JFJYaqRJgDuPDWtFVMitsYK2EEIIUR+KolC6dzd5332LuSAfjYcevxEj8erT\n95I9Slnl2XyfupkDuYcBBavRjUhVe57qMxgfD7erHm/16u94771ZZGdnM3/+AiZOnEx8/HBcopoR\nMe11zn3yIaW7d2EpKSb0uQk2OGP7Mxfko3ZzQ+1y65RSl4RJCDsrMZhY9vUBftp3Fo1axb29mnL3\nbU3Rai6+IyaEEEIsXVrd+zF69ON2jsS+TFlZ5Px7CYYTx1FptfgMGYbvsLvRuF2c+Jwry+KHU1vY\nn3MIAKtBj2tRDI/edgdxzeq26Pvq1d/x1FNjax6fOHGs5nF8/HC0np40eeFFMv/vM8oP/k7Gh3NQ\nB/hgvUTi5qgURaEqvwCngLq12c1CEiYh7KTCaGbT3rP8sOcMRpOFyGA9Y4e1IjzQw96hCSGEEDcs\na1UVZ5avIP3blShmM+7t4gj4+8M4BwRe9NqMskw2pG3m99wj1e8t98R8rjkDWnYm/s5rK6T0wQez\nL/n83LnvEx8/HAC1kzOhTz9L5rzPKDuwH92eIibu2FarN8qRWQ2G6iGPt9BwPGiEhGnmzJkcOHAA\ni8XCk08+yaBBgwDYvn07TzzxBAkJCRe955133uHQoUOoVCpefvll2rVrZ+swhWg0VWYrWw9msG7n\nKUoNVejdnHhkWGu6RvuhucQ4ayFE46vLdWj27NkcPHiQpUuX2iFCIRxffXrKDAknyF62mKqsLDTe\n3gSOegiPzl0uKrJwtjSDDWmbOZR3DACVwZvKs80I00Xx2N9a0TT4ykPeLxVTUtLF31kv9bxKq2V3\nUBAFmefoExLKi3EdefP3fbV6oxxVTcEHv1un4APYOGHavXs3ycnJLF++nKKiIuLj4xk0aBAmk4l5\n8+YRGHjxnYC9e/dy+vRpli9fTkpKCtOmTWP58uW2DFOIRmG1Kuw6lsV/tqeRX1KJi7OG+/pEMahL\nOBFNfMjNLbV3iEII6nYdSklJYd++fTg5OdkpSiFuLebSEvJWfFNdJlylIuSuYbgNuafWOkoAp0vO\nsuHUZo7knQDApcqf4tRINOWBPNC7GYO6htd7yHt0dCwnThy75PN/9cGHc0hNSmBuz94MCY8gp8LA\nvITjtXqjHNGfBR8kYWowXbt2JS4uDgBPT08qKipQFIXPP/+c0aNH8+677170nl27djFw4EAAmjdv\nTklJCeXl5bi73xqLgYmbj6IoHEzOY9W2VDLyytFqVNzZNZy7ekaid7s5K+gI4cjqch169913mTx5\nMh9++KG9whS3sLKyW+cGm2K1UvLrdnK/W4G1vBxdRCRBYx4lvGtcrRuNacVn2HBqM8fyq3t7fDUh\n5CWGU1jgQ6tIX8aMiiHI5+pFHa5k4sTJteYwnTdhwqSLnktKSsBisTBlzy4+792PMdGxJBYX8etl\neqkchfmPhOlWKikONk6Y1Go1rn9k/t9++y19+/bl9OnTJCcnM378eGbMmHHRe/Ly8mjbtm3NYx8f\nH/Ly8iRhEg4p6WwR321NITmjGJUKercL4W+9o/DzcrF3aEKIy7jadWj16tX07NmTkJAQe4UoxC3B\neC6DnKWLqTiZhErnQsD/PIh3/4G1qt+dLc1gXeomjuZX9yhFuEdSfqop6WkuuLs48dCwlvRqF9wg\n6yKd7xmaPn0a2dnZxMa2ZsKESZfsMTrfG1VsMvHy3t+Y16cf0zp2ZkZGxnXHYU9V+dLDZDObN29m\n1apVLFiwgBdeeIHXXnutzu9VFMWGkQlhG2eyS1n1SyqHU6o/WDpFBxB/ezPC/CXxF8LRXHgdKi4u\nZs2aNSxcuJBz587JNUqIK7hcCe6rsVaZKPh+LQUb1oPFgnvHTgQ++HCtQgNni8+x9Mh/OPhHMYdm\nnk3xKY9j17YqLFaFbq0CeXBgNF7uDTuSIz5+OGVlRcCV515d2BuVVlrCOwf3888u3ZnWui1WoxG1\nTtegcTWWP+cwSdGHBrV9+3bmzZvHggULKC8vJy0tjUmTJqEoCrm5uYwePbrWhNnAwEDy8vJqHufk\n5BBQh9KFAQF6m8RvK44WLzhezPaINzOvnH//kMC239MBaNfcn0fuakVM5NU/WBytfcHxYna0eMEx\nY3Z0V7oO/fbbb+Tn5/P3v/8do9HI2bNnmTFjBlOnTr3qfuV3eXnSNpd3pba5kdtt+fLllyzB7enp\nyqhRowBQq6t7fS48j6KDh0j5fB6VmVk4+/vT7MnH8evetWZ7ZmkO3x77nl9P70VBoYVvU3r49+P7\njaUcyy3H39uVZx6Io2vrYJud26Xi/qsnn3wMT09XJk+eTFZWFnn+fpRGt0CflEzZutU0f/oJm8V3\ntdiuR2ZpEajVhLQIv+Q6VzcrmyZMZWVlzJo1i0WLFqHX69Hr9WzcuLFme//+/S+qLtSrVy8+/vhj\nRo4cybFjxwgKCsLtEvX0/8qRJswHBOgdKl5wvJgbO97iMiP/3XmKXw6ew2JViAjyYHi/5rRp6otK\npbpqLI7WvuB4MTtavOB4Md/IX96uxZWuQ4MHD2bw4MEAZGRk8NJLL9UpWQLHuk41Jkf7d96YrtY2\nN3K7/fOfb17y+X/96y0GDLgLqC6GBNXnYS4tIfebryn9bReoVHgPGoz/3+KxuriQm1tKfkUBG05t\nYXfWfqyKlUjvJvQP7s+xwxq++CETFTCwcxPib2+Gq05r07a5MO4rGTDgLiZPzgSqe6OsVSbO/OsN\nsjb8gLplKzzi2tskPlv+nzKcy8LJ14+8AoNN9m9r9b1O2TRhWr9+PUVFRUycOBFFUVCpVMycOZPg\n4Oqs/8LxpJMmTWLGjBl07NiRNm3aMGrUKDQazTUN3xOisRkqzfyw5zSb9p7FVGUl0MeV+29vRpfY\nQNQNMF5aCNH4LnUdWr16NXq9vqYYhBC2tnTpfNRqFQ89NM7eodRLXUtwoygU7/iF3G+/qS7qENmU\noDGP4hLZFIAiYzEbT/3Er+f2YFEsBLsFclezO9FbmvLpysMUl5kIC3Dn0SGxNA/zsvFZXR+1kzMh\nTzzNmbfeIPvLBbi88SZazyuXN7+RWI1GLMVF6Fq1sXcojc6mCdPIkSMZOXLkZbdv2bKl5uf333+/\n5udJky6uNiLEjcRUZeGnAxl8v+sU5ZVmvDycGdU/it5xIfUuVyqEuHH89ToUExNz0WvCwsJYsmRJ\nY4UkhEOpSwlut7IyIk+mkv3Lr9VFHUY9hHf/AajUakpNZWw6/TPbM3ZRZTXj7+rHXVGDaO7Wiq83\nJ3MgaR9ajYr4PlEM7RHpMNdeXXg4/vcPJ3fFcnK/XkbIU8/YO6Q6q/pjqLJTHabK3GwapeiDEDcL\ni9XKr0eyWLMjjcJSI246LcP7NWdA5ybonG6dsbxCCCHElVypBLelrIy8/6yi7f6DqACPjp0JePAh\nnHx9qTRXsuX0drac2YbRYsJH582wqIF0DerEr4ezeW3rHiqMFto08+PvA1oQ4ud4xZS8B95J6b69\nlO7dg77nbXjEdbB3SHVSlZsDgFPAxeuo3uwkYRKiDhRFYX9iLqt+SSWrwICTVs3QHhEM6xGJu4ss\nXCmEEEJc6JIluMf/P+7w9iVt2hSs5eVUurlyqnkz/vbs85itZram/8qGtM2UVZWjd/Lg3mZD6RXW\nnbxCI7O/PkRSejGuOi1jhsTwwIAY8vPL7HyW9aNSqwl65DFO//N1cpYtwe2fMahdXK/+Rjuryjmf\nMEkPkxDiL46fKuC7rSmcyipFrVLRr0Mo9/SKwkfvmCVBhRBCiMZwYQnuB7r3IffrZeScPYvaxYWA\nkaP4PvMMVrWKfVm/szZ1I3mVBeg0ztwVNYj+4X3QqpxZv+s063aewmxR6BwdwN8HReOj19VUqnNU\nurAm+A4dRsG6teStXkXggw/ZO6Srqsr7I2EKlB4mIcQf0jJLWLktheOnCgHo1iqQ+D7NCPK9vpXC\nhRBCiFuFa7mB8LRTpG/bAYDnbb3xf2A4Gk8vCr/9kDOeeew+fhKNSkO/Jr0Y0nQAemcPUjKKWbTh\nEBl55Xh5OPPwoBg6x9xcPRu+d91D6d69FP20Ga/efdCFR9g7pCsy5eQC4OR/c/0e6kISJiH+IjO/\nnNXb09iXUH0npU2ULw/0bUbTYMepZCOEEELYU1VhIflrVtNu3wFUgGvLaPxH/A+uzZpzuuQsaw6u\nINPSECkAACAASURBVNE/A/j/7N13YFRV2vjx75RMeic9hIRAEiDU0Lt0kKqAKAqWXVDXd0H97bur\nri67q68KqKhgW3ERLIhIKErHQu9ICYGQQHovk2RSJlPu7w/WrJgAAZJMyvP5B2bm3nOfO0nm3mfO\nOc+B3n49mNR+LG0cvakwmvl8VwLfn0hHAYb3DGL6sHCcHFreLavaTofv/bPJWPYGuV9+TvCf/nJN\nBemmxpSfi9rFBU0dlvtpaVreb58Qt6mwpJLNB5LZfyYLq6IQFuDG9GHt6RTaulazFkIIcfvWrPkY\nuLruTmtkKS+jaPs2inbvRKmqosLJibSwdkxc+L/kVeTzxbnPOJl7BgD3SidCStrwyIgHAPg5MZ/P\ndl6ksMRIgLcTc8dFEdHWw5an0+Cco7vi3L0HZad/xnDiGK69+9o6pFopVivm/Hx0wW1tHYpNSMIk\nWj1DhYmth1PYcyIdk9lKgLcT9wwNp1dEmyb9TY8QQgjRVFjKyijavRP97p1YKyrQeHjQ5v7ZbL6S\ngEljYV3CJvZnHr666KxrW6aEj+fodz8CUFxWxZe7Ezgan4tGrWLyoFDuHhCKnbZ5lAq/Uz4z76c8\n7hx5677CuWt31PZNb460WV+EYjaja4Xzl0ASJtGKGass7D6RxtbDqVQYzXi62jN1cBgDu/qjUbeO\nD2khhBDiTlgMhquJ0p5dVxMlF1fa3DsTjxEjsWjVZOYfIcO1EEvGZXwcvZkcPp6ePl1RqVQcUX4k\nu9yFv/7rMGWVZsID3Xh4fBRBPi62Pq1GpfPzw2PUGIq2b6Voxza8J0+1dUg1mHJygNZZUhwkYRKt\nkNliZd/pTDYfSKa4rApnBy33jejAiF5B2GllLSUhhBDiZiylpRTt2Yl+9y6slZVoXF1pM30mHsNH\noLK350TuaTYnbaPAvQitVc30jpMZEtQfrfrqrWdOUTk/FwSgNzpir1OYPTqCu3oGNfvqd7fLe+Ik\nSg4doHD7VtyHDUfr3rSGIlZlZQKgCwiwcSS2IQmTaDWsisLR+Bw27r1Crr4CezsNkwaGMrZvSIuc\nTCqEEKLliY1dz3vvvUdeXh5r165j4cJnq9c8agxV2VkU7dpJyaEDKFVVaFzdaDNpCh7DR6C2t+dy\ncQobzm3hSkkqGpWGgFJPgkq9uGvUYODql5Y7j6Wxaf8VTGZHvB3KeO7R0Xi5OTTaOTRFagdHvCdN\nIfez1RR8uxm/2XNsHdI1jFlZAOgCAm0ciW3IXaJo8RRF4dyVQr75MYnUXAMatYqRvYKZOCgUd2ed\nrcMTQggh6iQ2dj3z5z9a/Tg+Pq76cUMmTYqiUHHxAkU7t1N25jQAWm9vPEeNwX3ocNT29uRXFLDx\n3Nec+k9Bh54+XZkSPoHt38RWt5OcXcKqrRdIzTXg5mRHhGsWPo5lrT5Z+oX74KEU7dpB8d6f8Bw1\nBp2fv61DqmbK/k/C5C89TEK0OIkZxXzzYxIX0/SogAFd/JgypD2+Hk1/RW0hhBDi15Yte6PW599+\n+80GSZgUs5nS40cp2rkDY2oKAA7t2+M5ZhwuPWNQaTSUmyrYfulbfko/gFmxEOoWwj0dJhLuEVrd\njsWqYu2eS+w6noaiwOBuATiXn+f//rmInJwcVq5c2eg9ZU2RSqulzbTpZH2wgvzYDQQ+/qStQ6pm\nzMpE6+XdJAtSNAZJmESLlJJdwsqNZzl1KR+A7uHe3DMsnLa+rWsiqRBCiJYjIeHCLT1/uyxlZRTv\n/RH997sxFxWBSoVLTG88x4zDMbzD1W2sFvalHWBr8i7KTOV4OXgyJXw8Mb7dr6kwW1jpyEV9Gyqz\n0vD1cGTuuEgunPqe+U82fk9Zc+AS0xuHsPYYjh+l8so4HMLa2zokLBUVWPR6nLpE2zoUm5GESbQo\niqLw1feJ1d9idQh2Z/qw8Ba/joMQQoiWLyIiivj4uFqfrw9Vubnod++k+MA+FKMRlb0DHqNG4zFy\nNLpfVUeLL0xg/aUtZJfl4KBxYGr4BIYHD8JOY1e9TWl5FWv3JHK6IAAVChP6t2PyoFB0dhoen9u4\nPWXNiUqlos29M0hf+jp533xN8LP/a/MlTqqyWvdwPJCESbQwP5zKYOexNIJ8nLl3WDjdw71t/kEj\nhBBC1IeFC5+9Zg7TLxYseOa221QUhcrERIp2bcdw6iQoClpPLzwmTcF96DA0Ts7V2+aVF/BN4hbO\n5p9HhYrBgf2Y2H4srjqXa9o7fD6HL3dfwlBhwtWukkiPfKYPH1m9TWP1lDWUhl6U2CmqE07R3Sg/\nd4by83E427hnp3r+UiutkAeSMIkW5EpWCWv3XMLF0Y6XHx+EYjLbOiQhhBCiSVIsFgwnT1C0azuV\nly8DYN8uFM8x43CN6Y1K+99bxEpzJTtSfuD71L2YFQsdPMKY3nEKbV2vrZiWr69g9Y6LnLtSiM5O\nzawRHci6sJPfVgpv6J6ylqDNPfeSeu4MBZs24NS5i02//K1q5QUfQBIm0UKUVZp4f+M5LBaFeZM7\n08bDkby8UluHJYQQQtSb+ij6YK2spHj/Pop278Ccnw8qFc49el6dn9Qx4pobc6ti5Vj2KTYlbaW4\nqhRPew+mdbibXr7drt3OqrD7eBob9l2mymQlOsyLh8ZG4uPhyJqLNWNoiJ6ylsYhpB0uMb0xnDhO\n2dnTuHTrYbNYjBnpAOgCg2wWg61JwiSaPUVRWPltPPnFlUweFEp0mLetQxJCCCHq3Z0MZTPr9ei/\n343+x++xlpejsrPDffiIq+Wr/WuWr04uSWV9wmaulKRip9YyIXQUo9sNR6e5djmO1JxSVm27QHJ2\nKS6OdswdG0X/Ln437BH5JblbtOgFcnJyiIrqzIIFz7TI+Ut3MnzPe/JUDCdPULAxFueu3W3Wy2RM\nS0Xj7oHWzc0mx28KJGESzd72o6n8nJhP51BPJg8Ks3U4QgghxB2JjV3P0qVLyMnJ4aOPPq4uuX07\nQ9mMmZkU7dhGyeGDYLGgcXXFe8o03Iffhda15g1wsbGUzUnbOJx9HIBevt2Y1uFuvBw8r9muymRh\n84Fkth9JxaooDOjix30jO+LmVLf1DadNm47BoAcafk5Qc2UfFIxr7z6UHjtK2c8ncekZ0+gxWAwG\nzIWFOEV3bfRjNyWSMIlmLSFNzzc/XsbDRce8SV1Q/3agtBBCCNGM3Ghx2lsZymbMSKfw282UHj8G\nioKdvz+eY8bh1n8gal3NpMZsNfNj+gG2XdlNpcVIkEsAMzpOpqNneI1t41OK+HT7BXKLKmjj7sCc\nsZFEt5fRHQ3Be/JUSo8fI3/TRpy790SlVjfq8Y1pqQDYtw1p1OM2NXVKmKxWK+fOnSM9/eoYxuDg\nYKKjo1E38g9NiF8rKavig03nAHh8SjRuznX7VksIIYRoqm40T+nHHw8C8NJLz5GXl1frUDZjWhoF\n327CcOJqD5F9SDu8J02+4c12QlEiX13cSHZ5Ls52TszqcA+DAvuiVl27fVmlia++T2T/mSxUKhjT\npy3ThrTHXqepj1MXtdAFBOLarz+lhw9hOHkC1959GvX4xrQ0ABwkYbo+q9XKypUrWbVqFYGBgQT8\np5xgZmYm2dnZPPzwwzz66KOSOIlGZ7UqfLg5Dr2hihnDZZ0lIYQQLcPN5ilNmzad7OyrN7FPPPF0\n9etV2Vnkx37z30QpNAzvSVNw7nb9uS96YzGxid9xPOdnVKgYEjSASe3H4mzndM12iqJw7EIuX+y+\nRElZFW19XXh4fBRhATef0yLD7e6c96QplB49QsHmWFx6xTRqL1N1D1OIJEzXNW/ePLp06cK3336L\np+e1Y1eLiopYtWoV8+fP51//+leDBinEb20+cIX4lCJ6dGjD2H6t+49YCCFEy3Gr85TMxXoKNm+i\neN9PYLXiENYe78lTcYruet1EyWK18GP6Ab67shOjpYp2bm2ZFTGNELfgGtsWllTy2c4Efk7Mx06r\nZvrwcMb0aYtWI1+WNxadnz9uAwZRcmAfpceO4tavf6MduzItFZVOh52vX6Mdsym6YcL0xz/+kW7d\nuqEoSo3X7O3tefrppzlz5kyDBSdEbc5dKWDLgWTauDvw2MROqGVhWiGEEC1EXecpaSwWCjZvpHDH\nNhSjETs/f9rcOwOXnr1uWE3tUtFl1iVsJLMsG2etE/dGTmJAYJ8aw++sisIPJzNY/1MSxioLUSEe\nzB0fhZ+n03VaFg3Je+JkSg4fpGDzRlx790GlafhhkFaTiaqsTBxC2jX63Kmm5oYJU7du3QC4//77\nef3112nXrh0Ax44d46WXXmLbtm3V2wjRGApLKvlo83k0GhVPTI3G2cHO1iEJIYQQ9eZmJbcVRcG3\nSE/HtEwKfj6Hxs0N7xn34T546DWLzf5WsbGU2MTvOJZzEhUqBgX2ZXL4eFzsnGtsm5FnYNX2CyRl\nlODsoOWBCVEM7hpg08VTWzs7Hx/cBw2heO+PlB45jNvAQQ1+TGNqClgsOIRJBeI6FX14+umnWbhw\nIdOmTSMzM5OzZ8/y7rvvNnRsQlzDbLHywaY4DBUmHhwTUaex00IIIURj+XU58I8/XlldDvxW/VJy\nW61WMXv2Y9XPV+Vkk/vFZ3S9nIJVpcLr7kl4jZ+A2sHxum1ZrBb2Zhzi28s7qbRU0tY1iPsiphHm\nXnM4u8ls5btDyXx3KAWLVaFvJ1/uHxWBuxRVahK87p5EycH9FGzZiGvffjdMkOtDZVIiAA7hHRr0\nOM1Bnd7pfv36sXTpUh544AE8PDxYu3ZtjTlNQjS0b35KIjGjmL6dfLmrZ+tdbVoIIUTTc6Ny4He6\nIKtiNlPw3RaKtn139f9uLlxsG8zD0+694X6Xi1NYe3EDGYYsHLWO3BcxjcFB/WoMv4Ory3R8uv0C\nWQXleLra89DYSHp0aHNHcYv6ZeftjduQYRT/sIfiA/vxGDa8QY9X8Z+EybG9JEx1Spg++OADtm3b\nxvvvv09eXh5z5sxh3rx5TJo0qaHjEwKAkwl57Diahr+XE3PHRcmwACGEEE3KjcqB30nCVJmaQvYn\nH1OVnobW0xOf+x5gz9F9cIPrYLmpgk2Xt7E/4zAA/f17M7XDBFx1LjW3rTSz/qckfjyVgQoY2SuY\ne4a1x9FelupsirzvnkTJgX0UfrsJt4EDUds1TO+foihUJCWicXdH20YS5zr9NeTn5/PVV1/h4OAA\nQJ8+ffjnP/8pCZNoFLn6ClZ+F49Oq+bJadHyIS6EEKLJuVk58FulsloJTEknde8/wGLBfehw2sy4\nD42jIxzbX+s+iqJwMvc0X1/aTGmVAX9nP+6PvIcOHrXPQTmZkMdnOy+iN1QR1MaZueOj6BDkflvx\nisah9fDAY8QoirZvpfiHH/AcM7ZBjmMuLMSi1+PSM0a+pKaOCdNf//rXax67urpisVgaJCAhfs1k\ntvBe7FkqjGYeu7sTwT41vx0TQgghbO1Wy4HfSFVONl1OncbZUIbWywu/uY/i3CX6hvvkVxTy1cVY\nzhdexE6tZVL7cYwKGYpWXfNWr6jUyBe7EjiRkIdWo2LqkDAm9G8npcKbCa9xEyj+6QcKt36L+9Ch\nN5zDdrv+O38pvN7bbo7qlDBt2rSJV199leLiYgDUajX9+zdeDXjRen25+xKpOQaGdAtgUNcAW4cj\nhBBC1Kqu5cBvpuTQQXI+W42zsZI8fz/6v7Doaq/SdVisFvak7WXrld2YrCaiPDtyX+Q0fJ1qDqOy\nKgp7T2fy9Q9JVBjNdAx25+HxUQR416yUJ5oujYsLnmPGUbAplqLdu/CeOLnej1GecBEAx44R9d52\nc1SnhGn16tVs2bKFZ555hg8//JDNmzfj5CR1+EXDOhSXzY8/Z9LW14XZo+UPVgghRNN1s3LgN2Ot\nrCT3izWUHDyA2sGBhE6R6P19GVRLsvTL+piXi1P48sI3ZJZl42rnwoNR04nx61HrEKqsgjI+3X6R\nhDQ9jvYa5oyNZGiPQFnLsJnyHD0G/Z7dFO3YhsfwEWhc6ncETvn5ONQODjiESklxqGPC5Orqio+P\nDxaLBScnJ2bNmsXDDz/M5Mn1n9EKAZCRX8an2y/goNPw5NRodHYNv0CbEEIIcSd+KQcO8NBDv6vz\nflU5OWSueJuqzEzsQ8MImPcEh3Zs5noD5CxqKzk+pbx54j0UFAYF9mVq+ASc7Gp+mW22WNl2JJUt\nB5IxW6z0ivBh9ugIPF3tb+cURROhdnDEa8Ld5K1bS+GObfjcO6Pe2jbl52HKzcG5R89GWSC3OahT\nwqRWq9mzZw8BAQG8++67dOjQgezs7IaOTbRSxqqr85aqTFaenBqNn5f0ZgohhGiZys6dIeujD7CW\nl+MxcjQ+M+677vo6V4s6nCGxfT5mrfWmRR2SMotZte0CGXlluLvoeHB0BDGRvg15OqIRuQ8fQdGu\nHej37MJz5Gi0Hh710m55/HkAnDp3qZf2WoI6JUxLliwhLy+P559/nmXLlnH+/HlefPHFho5NtEKK\norB6x9V1IEb1DqZ3lHywCyGEaHkURaFo23fkx36DSqPB75Hf4T5o8HW3L6rUs/biBs4VXEClBt88\nF54bvqDWog4VRjMb9l7m+xPpKMDwHoFMHx6Ok4NdA56RaGxqnQ6vSVPIXb2K/Nhv8H/ksZvvVAeG\nM6cBcO5840IjrUmdEiZvb2+8vb0B+Oc//9mgAYnW7afTmRyKyyE80I2Zd8lCaUIIIVoeq8lEzqpP\nKD1yCK2nJ4FP/g8OYe1r31axsj/jCJuStlJpMRLp2QHriWLsTdpak6XTifms2XmRwhLjf9YujCQy\nxLOhT0nYiPugIej37Kbk4H487hqJQ2joHbVnNRopjzuHLiAQnb9//QTZAtR54dqVK1diMBiueT4+\nPr5BghKtU0p2KV/suoSzg5bHp0RLeVMhhBAtjqW8jMwV71Jx8QIO7cMJ/MP/oHWvfShVhaaKZSc/\nJKn4Co5aRx6MmkH/gN58cHhZjW2Ly6r4cncCR+Nz0ahVTBwYyqSB7bDTyhyUlkyl0eA76wHS31hM\n7trPafvn5++ovfLz51CqqnDp2aueImwZ6lxWfOPGjfhLpikaSHmlifc2nsVssfLUPV3xdnewdUhC\nCCFEvTIVFJDx9htUZWbi0jMG/9/PR63T1djOYrWQ4VJIulsBSrFCd59o7ouYiru9W41tFUVh/9ks\n1n2fSFmlmfaBbjw8LopgX1m3sLVw6tQZ5569KDt1EsOxo/jePeq22yo9fgwA5x6SMP1anRKmjh07\n4u/vj+Y2KmUsXryYkydPYrFYmDdvHj4+PixevBitVou9vT2LFy/G0/O/XcVHjx5lwYIFdOzYEUVR\niIyMrLFwrmhZFEVh5Xfx5OkruXtAO7qFe9s6JCFEK/fqq69y+vRpVCoVzz//PF27dq1+7fDhw7z1\n1ltoNBrCwsJ45ZVXbBipaC6MaamkL3sTS7Eej1Gj8Zl5Pyp1zZEUaaUZfB7/NWnu+dhZNMzt/gA9\nfbvW0iLkFpXz6faLxKcUYa/T8MCojozoFYxa3TxKhd9KJUFxYz4zZlF+9gy5674kZPiA22rDUl6O\n4eQJ7Pz8cAiTcuK/VqeEafLkyUyaNIno6OhrkqZXX331hvsdOXKExMRE1q5di16vZ9q0aXTv3p0l\nS5YQFBTE8uXL+frrr5k3b941+/Xt25e33377Nk5HNEc7j6Vx6lI+USEeTB0if6BCCNs6duwYKSkp\nrF27lqSkJF544QXWrl1b/frf/vY3Vq9ejZ+fHwsWLGDv3r0MHTrUhhGLpq4iKZGMt9/EWlGBz333\n4zl6bI1tqiwmtiXvZnfqT1gVKz5lboSW+taaLCkKZFf58OLKo5jMVrqFe/PQmEgZndGK6Xx98bp7\nEgWbYkn+dA3uM2bfchulx4+imEy4DRxc61perVmdEqbXX3+dKVOm4Ofnd0uN9+nTh27dugHg5uZG\nRUUFy5ZdHXerKAq5ubnExMTU2O+XBdlEy5eYXsz6H5Nwd9Yxf3IXNLV82yaEEDdS3wnLoUOHGDXq\n6pCW8PBwSkpKKCsrw9nZGYBvvvkGl/8sEunl5YVer6+3Y4uWp/xCPBnvLkMxmfB/9Pe4DRhYY5tE\n/RU+v/A1ueX5eDt4cn/kvRzfurfWnqLk7BIuVERhMNnj5qThsbs70SfKV25wBV7j76b0+DFyduzC\nrmsvnKI61XlfRVEo/uF7UKlq/R1t7eqUMIWEhPDUU0/dcuNqtRrH/6xQ/fXXXzNs2DAA9u3bx8sv\nv0yHDh2YMmVKjf2SkpJ48sknKS4u5g9/+AMDB8oPriUqKa/i/U3nsCoK8yd3wd1FFtETQty61atX\n849//IPJkydz7733EhQUdEft5efnEx3933K6np6e5OfnVydMvyRLubm5HDx4kIULF97R8UTLZThz\nmqz3l6NYrQQ8/gdce137JXGFuZJNSdvYl3EIFSruajuYiWFjcdDac5y912xrrLKwcf9ldh5LQ1Hs\n8Xcq5fnfT8DFUUqFi6tUWi3+Dz9K6qsvk71qJe1e/Dua/3xu3Uz5+TiMaam49umLnZdMjfitOiVM\n3bt355133qFXr17XDMkbMKBuYyR3797Nhg0bWLlyJQBDhgxhx44dLF26lA8//JD58+dXb9uuXTue\neuopxo8fT1paGnPmzGHXrl1or7OI2y98fFzrFEtT0dzihfqN2WpVWB57mKJSI3MmdGJI75B6a/sX\nze09bm7xQvOLubnFC80z5sb28ccfU1hYyI4dO/jLX/6CTqdj+vTpjBkz5rbm3v5WbaMeCgoKeOKJ\nJ1i0aBHu7u51akd+ltfXkt6bX3qFVJfOkfXeu6jUajr99Tk8e/W8Zrsz2fF8cPwz8ssLCXYL4PE+\nDxLRpn2Ndnx8XDl5MZf31p8mp7CcAG9n/NWJeDlUEhbi1Xgn1gS1pN+beuPTHev0e0hft57Cz/5N\np+f/XOtcuV9TFIXsHd8B0H7WdFzkfa2hTgnTsWPHrvkXQKVS1Slh2rdvHx999BErV67ExcWFnTt3\nMmbMGADGjBnDihUrrtnez8+P8ePHA9C2bVvatGlDTk7OTb8xzMsrrcupNAk+Pq7NKl6o/5g3H7jC\nyYu5dAv3ZmhX/3p/P5rbe9zc4oXmF3NzixeaX8y2vHnx8vJi0qRJaLVaVq9ezSeffMKKFSt4+eWX\n6dGjxy215evrS35+fvXj3NxcfHx8qh8bDAZ+//vf8+yzz9b5i0NoXtepxtTcfs9vxmpV8Mwv4OKS\nN1HZ6Qj840LMbTtUn2OluZLYpK3szziMWqVmXOhIxoWOxE7RXvM+WK0KZkXD/31yhENx2ahVKsb3\nD2HyoDDWrT2L1dq6f6da2u9NfQqZNZOCM3EUHTvOxU+/xHvi5BtuX3L0MCXn43Hu0ZMKd18qWvD7\nervXqTolTGvWrKnxXFFR0U33MxgMLFmyhFWrVuHqejXAFStWEBISQlRUFGfOnCHsN1U4tmzZQkpK\nCk899RQFBQUUFhbe8twp0bSdTy5k074reLvZ87uJnVHLuGshxB04evQo69ev5+jRo4wdO5Zly5YR\nHh5Oeno6Tz31FBs3bryl9gYNGsTy5cuZOXMmcXFx+Pn54eTkVP36a6+9xiOPPMKgQYPq+1REC+BR\nUEiH8xdQ6XQEL3wWx44dq19LKErks/ivKagsIsDZjzmd7iPELbhGG4qikF3uQmKxN6bMbNr5u/Lw\nuCja+cs3/+LmVBoNAfOeIPXlRRRs3IDGxQWP4SNq3dZUVETel1+g0mrxmXl/4wbajNQpYarN7Nmz\n2bp16w232bp1K3q9noULF6IoCiqVihdffJFFixZhZ2dXXVYc4JlnnuG1115jxIgRPPvss9x///0o\nisKiRYtuOhxPNB9FpUY+2hyHWq3iialdZey1EOKOvfXWW8yaNYuXX34Z3a/WtAkODq4esXArevbs\nSZcuXZg1axYajYaXXnqJ2NhYXF1dGTx4MJs3byY1NZV169ahUqmYNGkSM2bMqM9TEs1UWdw5OsbF\no6hUBP3x6epkqdJsZFPSVvb+Z67S2HYjGB82Cjt1zfubfH0Fq3deJL7IF52dhpnDwhjdJ1iKIolb\nonVzI/iZP5H2+v+R+9lqzMXFeE+acs3wPIvBQOaKd7CUluAzazY6X18bRty0qZTbLEk3fvx4tm3b\nVt/x3Lbm1C3bHLuR6yNmi9XKki9OkZBezAOjOjKqd9t6iq6m5vYeN7d4ofnF3NziheYXs8wnuLHm\n9LNsTM3t9/x6yuPPk/HOW1jMZi527cKUP/4/AC4VJbEm/msKKgvxd/ZjTqeZtHOref2zWhV2H09j\nw77LVJmsdAn1ZOEDMWis1hrbrlnzMdC61zFqKb83DeHX740xI4PMd5dhys/DoX17PMeMRxcQgDE1\nhYLNGzHl5eE2cDB+jzzWKiotNuiQvNq0hjdV1K8NP10mIb2Y3lG+jIypOQRBCCGEaI4qLieRsfxt\nUBQSunSixNMDo6WKTUnb+Cn9ACpUjGl3FxNCR2GnqTmyIjWnlE+3X+BKVikujnbMGRvJgC7++Ho7\nS1Ig7oh9UBAhL7xEzuerMRw/RtYHv6odoFbjNWEi3lPvkfv6m7hhwnTo0KHrvlZZWVnvwYiW69Sl\nPLYdScXP05FHxkfJH6YQQogWoSork4x33kKpqiLwyac4fO4UJbpy/u/oW+RXFODn5MtDnWYS5l6z\nGmyVycKWg8lsP5KKxarQv4sfs0Z2xM1JV8uRhLg9GldXAh//A8a0NAw/n8Ss12Pn7Y1Lr97o/P1t\nHV6zcMOE6b333rvua3e6zoVoPfL0Faz8Nh47rZonp3XF0V7mpAkhhGj+TIWFpL+1FKvBgN/cR9B1\n60py2g6ynfWoKlSMChnGxLAxtfYqxacU8en2C+QWVeDt5sCccZF0bS/r34iGY9+2LfZtG246REt2\nwzvX5cuX33R9ieLi4jqvQSFaH5PZyvsbz1FuNPPI+Cja+rrYOiQhhBDijlkMBjKWLcVcWEib976q\njQAAIABJREFUe6aj796eZceWkeuix8Fkxx/6z6O9e7sa+5VVmlj3fSL7zmShUsGYPm2ZOiQMB518\nmShEU3XDkivz58/n4MGD1339wIEDPP744/UelGg5vvr+EsnZpQzq6s+Q7oG2DkcIIYS4Y1ajkYx3\nl1GVmYn7yNEcirRj6YkV5Jbn42/woFtuuxrJkqIoHLuQywv/OsK+M1kE+7jw1zm9mTWy4y0lS7Gx\n61m6dAl/+tP/Y9iwAcTGrq/v0xNC/MYN/0LfeecdXnzxRV577TWGDBlCQEAAAFlZWezbt4/AwEDe\neeedRglUND9H43P4/mQGwT7OPDgm0tbhCCGEEHdMsVrJ+uh9KpMSsYvpyafhBaSknMbT3oM5nWcS\n4dmhxj6FJZV8tjOBnxPz0WrU3DusPWP7hqDV3Fqp8NjY9cyf/2j14/j4uOrH06ZNv7MTE0Jc1w0T\nJl9fXz788EPOnz/P/v37SUpKAiAgIIDXX3+dTp06NUqQovnJKijj39suYK/T8MTUaOztNLYOSQgh\nhLhjeV99SdnpnzG2D+KDiByMBjP9/GOYETEZR63jNdtaFYUfTmbwzU9JVFZZiArxYO64KPy8nK7T\n+o0tW/ZGrc+//fabkjAJ0YDq1AfcuXNnOnfu3NCxiBbCaLLw3sZzGKssPD6lCwHezrYOSQghhLhj\nRXt2od+zC4OXE2t6GbHTufBQ5P309O1aY9uM/DI+3XaBxIxinOy1PDw+iiHdAu6oSmxCwoVbel4I\nUT/qlDBFR0djsViueU6j0RAaGsrf/vY3+vTp0yDBieZHURQ+23GRjLwyRvQKom8nP1uHJIQQQtwx\nw+mfyV37BRUOatYNdqRjQGdmR03H3d7tmu1MZivfHUrmu0MpWKwKvaN8mT2qI+4u9nccQ0REFPHx\ncbU+L4RoOHVKmJ577jl0Oh2jRo1CURT27NlDaWkpvXv35uWXX2bdunUNHadoJvadyeLAuWzCAly5\nb0RHW4cjhBBC3DH95YtkffAuVrXCtuFtuDvmXgYH9qvRW3QpXc+qbRfIKijH09Weh8ZE0qNjm3qL\nY+HCZ6+Zw/SLBQueqbdjCCFqqlPCtH37dtasWVP9eMaMGTzyyCM8+uijaLVSBlNclZpTyue7EnB2\n0PLElGjstLc2mVUIIYRoauIvH8e47H0cTRZOjA3nsQlP4Ot0bRJUXmnmm5+S+OFUBipgRK8g7h0W\nXu/rDv4yT2nRohfIyckhKqozCxY8I/OXhGhgdfpLNhqNfPnll8TExKBWqzl79iwFBQWcPn26xlA9\n0TpVGM28t/EcJrOVJ6ZG08bD8eY7CSGEEE2UyWJic/xm/D7dhm+5hYJRMdx/75No1NcWMTqVkMea\nnRfRG6oI8HbikfGd6BDccOtTTps2HYNBD8BDD/2uwY4jhPivOiVMixcv5t133+WLL77AarUSHh7O\n4sWLMZvNvPLKKw0do2jiFEXh31vjyS2qYHz/EHp0qL/hB0IIIURjyzRk8+9zn9NzewK+RWY0A/rQ\n/74nrxmCpzcY+XxXAicu5qFRq5gyOIwJ/dvJ6AohWqA6JUyhoaG88cYbFBUVoVarcXdvuG9ORPOz\n+0Q6xy/mEdHWg3uGtrd1OEIIIcRtURSFnzIOEpv4HTGni+mQbsQhMpK2c+dXJ0tWRWHf6UzW/ZBE\nhdFMhyB35o6PIqiNVIQVoqWqU8J04sQJ/vznP1NWVoaiKHh4eLBkyRK6dq1ZRlO0LkmZxaz7PhE3\nJzsen9IFjVq+WRNCCNH8lFYZ+Cx+HecKLtA5S6H/2TK0bdoQ9PhTqP4zXzuroIxPt18kIU2Pg07D\nQ2MiGNYzCPUdlAoXQjR9dUqY3nzzTd577z0iIiIAOH/+PK+88gqff/55gwYnmjZDhYn3N57DqijM\nn9wFj3oomSqEEEI0triCi6yJ/4rSKgO9rYEMPhgPOh1Bf/gjGldXzBYr246ksuVAMmaLlZ4d2zB7\ndARebg62Dl0I0QjqlDCp1erqZAmuLmSr0WhusIdo6ayKwr+2nKewxMi0IWF0CvWydUhCCCHELTFZ\nTGy6vI0f0vajUqBDvifDfs7AbDQS8PiT2LcNISmzmE+3XSA9rwx3Zx2zR0cQE+lzRwvQCiGalzon\nTDt27GDQoEEA7N27VxKmVm7roRTOXi4gOsyLuweG2jocIYQQ4pZkleXw77gvyDBk4efki99le3qd\nTMKs1+M1cRJ23Xrxxe4E9hxPRwGGdg9kxl3hODvY2Tp0IUQjq1PC9Pe//51//vOfvPjii6hUKrp3\n784//vGPho5NNFHxKUXE7ruMp6s9v5/UWcZuCyGEaDYURWFfxiE2JH6LyWpmcGA/7u04iUPbFuGu\n1+PcvQeZ0UNY8/ERCkqM+Hk68vD4KCJDPG0duhDCRm6YMD3wwAPVXc6KotChQwcADAYDf/nLX2QO\nUytUbDDy4eY41CoVT0yNxtVJZ+uQhBBCiDoprTLw+YWvOZsfj7OdE490eYDuPtGUHDxAQEYm5Y5O\n7A0cysH159CoVdw9oB2TB4Vip5VRNUK0ZjdMmBYuXNhYcYhmwGK18uHmOErKqpg1ogMdgqS8vBBC\niOYhoSiRVXFfUlxVSqRnB+Z0vg8Pe3cqLl8mZ/W/qdJo+cJ3JPmX9IQFuPHw+Cja+rrYOmwhRBNw\nw4Spb9++jRWHaAY27rvChVQ9MRE+jO7T1tbhCCGEaObWrPkYtVrF7NmPNdgxLFYL25L3sD15DyqV\niqnhExgZMhS1So1Zryd9+dtYzRZiA0ZQpHPn/hEdGRkTjFotw82FEFfVaQ6TEMfjc/juUAq+Ho48\nMqGTVAcSQgjR5BVV6ll1/ksS9VfwdvDkkS6zCXMPAcBsNHJ+8VIcSor5wTuGYi9P+nqkM7rPKBtH\nLYRoaiRhEjdVUFzJm1+cQKtR8+S0aJwc5NdGCCFE03Y2/zxr4tdRZiqnh09XZkdNx8nOEYDkrBLO\nv/s+HXLTuegRTo8503E68R3yXaAQojZy5ytuyFBh4v1N5ygtNzF3XCQhfq62DkkIIYS4LrPVzKak\nbXyftg+tWst9EdMYEtQflUqF0WRh074r5O3ayei8eEo9/Bj+4jO4ujtz6aStIxdCNFWSMIlalZRX\nsfNoGntOpmOssnBXTDBDuwfaOiwhhBDiuvLKC/gk7nNSS9Pxc/Lh0S6zCXa9eu2KSy5k9fYLOGYm\nMyvvGIqzK92e/zN27s42jloI0dRJwiSuUVxWxY4jqXx/Kp0qkxV3Zx1TB4dx39hO6IvKbB2eEEII\nUasTOT/zxYVvqLQY6ecfw8yIqTho7TFUmPhqzyUOnMvGw1zK3IJ9qDVq2j71R+y8vGwdthCiGZCE\nSQBQVGpk+5FUfvw5A5PZioeLjunD2jG0eyA6Ow12WrWtQxRCCCFqqLJUsf7SZg5kHkWn0TGn0330\nC4hBURQOx2Xz5Z5LlJabaN/GnvuSd6MYK/Cd8zCOHTvaOnQhRDMhCVMrV1hSydbDKew9nYXZYsXL\nzZ67+7djcLcAWahPCCFEk5ZpyOaTuM/JKsshyCWAx7rMxs/Zl/ziCtbsSODs5QJ0WjUzhren28kt\nlGVn4n7XSDyGDrd16EKIZkQSplYqX1/B1sMp7DuThcWq0MbdgYkDQxkY7Y9WI71JQgghmrYjWSf4\n8uIGTFYTw4IHMi38bjQqLbuOpbFh72WMJgudQz2ZMzYSzYHdFJw8gWNEJL733W/r0IUQzYwkTK1M\nblE53x1K4eC5bCxWBV9PRyYOCKV/Fz9JlIQQogVas+ZjAB566HdNus26qrKY+DphEwezjuKgcWBu\n9Cx6+nYlLdfAqm2nuZJVgrODlgfHdGJgtD9lP58ic+MGtF7eBDzxB1Ta5n/rY4v3XYjWrPl/aog6\nyS4s59uDyRyOy8GqKPh7OTFpYCh9O/uiUUuiJIQQounLLc/j43OfkWHIoq1LII9FP4SHzoNvfkpi\n+5FULFaFfp39uH9kR9ycdRgzMsj6+CNUOh2BT/0RraubrU9BCNEMScLUwmXkl/HdwWSOxOegKBDU\nxpmJA0PpE+WLWi0r9AkhhGgeTuWe5bP4dVRajAwK7MeMjpO5nGHgzW1HySmqwNvNnofGRtItvA0A\nFoOBzOVvoxgrCZj/JA4h7Wx8BkKI5koSphYqPdfAloPJHL+QiwIE+7gweVAovSJ9UMtS5kIIIZoJ\ns9XMxsSt/JC+H53ajrmdZ9HFoyuf70xk7+ksVMCo3sHcM7Q9DrqrtzWKxULWR+9jysvFa8JEXPv0\nte1JCCGaNUmYWpiU7FK2HEzmZEIeAO38XJk8KJTuHdtIoiSEEKJZKawsYuW5z0kuScXfyZfHoh8k\nM13NX78+QnFZFcE+zswdH0V4oPs1++WvX0f5+Ticu3XHe+o9NopeCNFSSMLUQlzJKmHLgWR+TswH\nICzAjSmDQ+na3huVJEpCCCGamXP58aw+/xVl5nL6+PVkXNDdfL0jmVOX8tFq1NwztD3j+oXUKFik\n/+lHinbtQOcfgP/v5qOSebpCiDskCVMzl5hRzJYDyZy9XABAhyB3Jg8OpUuolyRKQgghmh2L1cK3\nV3ayM+UHtGotsyLvwZQdxD8+OUVllYXIth7MHR+Fv5dTjX3LzseR+/lq1C4uBP7xaTRONbepTWzs\nepYuXUJOTg4ff7yShQufZdq06fV9akKIZqrBE6bFixdz8uRJLBYL8+bNw8fHh8WLF6PVarG3t2fx\n4sV4enpes8+rr77K6dOnUalUPP/883Tt2rWhw2x2EtL0bD5whfPJRQBEtvVg8qBQotp5SqIkhBB3\n6EbXoYMHD/LWW2+h0WgYOnQoTz75pA0jbVmKjSX8O+4LLukv08bBi8nB09nxQzGJ6ZdwtNcyd1wk\nQ7oH1jrE3JiZSdb7y1Gp1QT94Y/ofH3rdMzY2PXMn/9o9eP4+Ljqx5I0CSGggROmI0eOkJiYyNq1\na9Hr9UybNo3u3buzZMkSgoKCWL58OV9//TXz5s2r3ufYsWOkpKSwdu1akpKSeOGFF1i7dm1Dhtls\nKIrChVQ9Ww5c4UKqHoDOoZ5MGhhKZIjnTfYWQghRFze7Dr3yyit88skn+Pr68uCDDzJ27FjCw8Nt\nGHHLkKi/wspzn1FSVUo37y54l/Tjg7VpWKwKMZE+zB4dgYeLfa37mktLyHz3LawVFfj/bh6OHSPq\nfNxly96o9fm3335TEiYhBNDACVOfPn3o1q0bAG5ublRUVLBs2TLg6s1/bm4uMTEx1+xz6NAhRo0a\nBUB4eDglJSWUlZXh7OzckKE2aYqicD65iM0HrnApvRiA6PZeTB4YRodg95vsLYQQ4lbc6DqUlpaG\nh4cHfn5+AAwbNozDhw9LwnSbDIZSFBR+SNvPhsRvARjaZiSnj7hxpCATDxcdD42JpGeEz3XbsJpM\nZK54F1NeHl4TJ+PWf+AtxZCQcOGWnhdCtD4NmjCp1WocHR0B+Prrrxk2bBgA+/bt4+WXX6ZDhw5M\nmTLlmn3y8/OJjo6ufuzp6Ul+fn6rTJgUReHs5QI2H0jmcmYJAN3DvZk0KIz2gbL4nhBCNIQbXYfy\n8/Px8vKqfs3Ly4u0tDRbhNkiWFVWMvyLibu0GRc7Z0IqhrFzqxWFCu7qGcS9w8Jxcrj+rYpitZKz\naiWViZdw7dsP7ynTbjmGiIgo4uPjan1eCCGgkYo+7N69mw0bNrBy5UoAhgwZwo4dO1i6dCkffvgh\n8+fPv+6+iqI0RohNiqIo/JyYz+YDyaRklwLQs2MbJg8Ko52/q42jE0KI1uVG16HWeI2qL59v+oxj\nLgk4u7lTmW1CyYvhRIWVAG8n5o6LIqKtx03byF+/jtIjh3EI74DfI4/d1hzehQufvWYO0y8WLHjm\nltsSQrRMDZ4w7du3j48++oiVK1fi4uLCzp07GTNmDABjxoxhxYoV12zv6+tLfn5+9ePc3Fx8fK7f\nFf8LH5/mlUjUFq/VqnDoXBZf7brIlcwSVCoY1D2Q+0ZFEBZo+6F3LeE9bsqaW7zQ/GJubvFC84y5\nubvRdcjX15e8vLzq13JycvCtY3EBW/0s1WpVvR//Ttt8c+1y9mlO4hzoTvFFO3QlYyg3W+je1sTf\nF4zATqu5aRsZsZso2rkdx+Bgui76K3ZutxfLvHmP4ObmyLPPPkt2djbR0dE899xzzJo167baq2/y\nGXB98t5cn7w39atBEyaDwcCSJUtYtWoVrq5Xf3ArVqwgJCSEqKgozpw5Q1hY2DX7DBo0iOXLlzNz\n5kzi4uLw8/PDqQ5lQfPyShvkHBqCj4/rNfFarQrHL+ay5UAyGfllqIB+nf2YOKAdQT4ugO3P77cx\nN3USb8NrbjE3t3ih+cXcUi7QN7oOBQUFUVZWRmZmJr6+vvz444+88UbtRQN+y1Y/S6tVqffj326b\nVsXKd5d3clgVh9rOjvILEehK2lOYeYEzu1aQ7OfO03PG3rSdkkMHyF61Gq2nJ/7/8zR6I3AH5zdy\n5N08+2wWAA899DvA9tddaH6fAY1J3pvrk/fm+m73OtWgCdPWrVvR6/UsXLgQRVFQqVS8+OKLLFq0\nCDs7u+qy4gDPPPMMr732Gj179qRLly7MmjULjUbDSy+91JAh2pTFauXo+Vy+PZRMVkE5KhUM6OLP\nxIHtCPBufXO2hBCiKajtOhQbG4urqyujRo3ib3/7G888c3W41sSJE2nXrp2NI24eDKYyVsV9SXxh\nAmaDBvOVgZj1Wi7s/5CU09sBhYTirJu2U3buDNmrPkHt5ETQwmex8/Zu+OCFEK1agyZMM2fOZObM\nmTWer61M+Jtvvln9/18uRC2V2WJl/5ksvj2UTG5RBRq1isHdArh7QDv8POu2yJ4QQoiG89vrUGRk\nZPX/e/fuLctd3KLUknT+dXY1hUY9Vr0PpqRuZCec4tyeD6k0FFRvd7NCCxWXEsh87+paS4FPLcA+\nKLihQxdCiMYp+iD+60JKEZ9+dJicwnI0ahXDegQyoX87fDwcbR2aEEIIUe8OZh5j7cUNWKwWTBkd\nUGe3I8a/kr8v+b8a296o0ELF5SQy3n4TxWIh8ImncIqIvO62QghRnyRhakQms5WPvztPsaGKu3oF\nMaFfO7zdHWwdlhBCCFHvTFYzay/Ecjj7GIpZS1VSDH4me8L9Mnh0zqMEun7CSy89R15eHlFRnVmw\n4JnrLhRbmZJMxltLsRqNBMx/EpcePRv5bIQQrZkkTI1o7+lMCkuMTB0WzuQBMuZdCCFEy6Q3FvP2\nsU/IrcrCWuaKW+4AHpkQw7G931RvM23adLKzr65h9cQTT1+3LWN6GulvLcVaWYn/7+bh2rtPg8cv\nhBC/JglTI6kyWfj2UDL2dhruvasjpsoqW4ckhBBC1NmaNR8D/60idz3ncpL419nVmNUVWAoCGeEz\njqnjOqKz03DsFo9ZcfkyGW+/gbWsDL+HH8Ot34DbjF4IIW6f2tYBtBY/nMqg2FDFqN7BeLja2zoc\nIYQQrUBs7HqWLl3Cn/70/xg2bACxsesbrE1FUVh9dBfvn/0XJlUFrvpuPDfkUWYOj0Jnd/N1lX6r\n/EI86W8sxlpejt8jv8N98JA7jl0IIW6H9DA1gsoqM98dSsHRXsPYviG2DkcIIUQrEBu7nvnzH61+\nHB8fV/34enOFbubUqVN89tmaGm2WVkG8cxElTpdQrHYMdJ3EA3cNrF7g9lYZzvxM1vsrUKxWAh5/\nEtcYGYYnhLAd6WFqBHtOpGOoMDG6d1tcHO1sHY4QQohWYNmy2hfUffvtN2t9vi727Nl9zWOVSk3E\nkGkctE+gxOkSOrM7C7s/yYMDBt12slS87ycyV7wLKhVB/7NQkiUhhM1JD1MDK680s/1IKs4OWsb0\nkd4lIYQQjSMh4cItPV8XOTk51f938wmj14zf4d0vD7W9nhD7jiwY8hAOdrdX/VWxWsnfsJ6i7VtR\nOzsT9NQCHDtG3HasQghRXyRhamA7j6VSVmnm3mHtcXKQt1sIIUTjiIiIIj4+rtbnb5efnx85eQVE\nDJhFxzF9sQ8/DyoruT9lsnzR66hUt9erZDUayV75EYaTJ7Dz8yfoj0+j8/O77TiFEKI+yZC8BmSo\nMLHreBquTnaMjJHVyIUQQjSehQufrfX5Gy0OezNDx93PsLlvE3VPZxw6nsNSVcWBJVt5oMfU206W\nnCoqSX3l7xhOnsAxMoqQ5/4qyZIQokmRLo8GtONoKhVGCzPvCsNBJ2+1EEKIxvNLYYdFi14gJyfn\npovD3oihwkR8kQ9lbYLx7HAajXsBpZnFZMcmsmj+otsuIuFXWERUSjpVViseI0fjM+M+VFq5Xgoh\nmhb5VGogJWVV7D6ejruLjrt6Bdk6HCGEEK3QtGnTMRj0wM3XT6qNoigcjc/li90JGBRwjD4I9pV4\nVDrTm3Ae+ebD24rLUlpK7pefEX0lFbNafbUSXu++t9WWEEI0NEmYGsjWwykYTRamDw/H/jbWnxBC\nCCFsqaC4kjU7L3ImqQCddx6OoadQNFbGtRtB0cE0VNzGEDxFwTO/gOSXXsBSWkKxsxNxoSF0lmRJ\nCNGEScLUAIpKjfxwKgMvN3uGdg+0dThCCCFEnVmtCntOprPhp8sYTWYCO2VT5HoalVVFh4IAJo0Y\nx5qDH99yu8aMDKLOxuFepMeq1dJmxn3sSYqH25z7JIQQjUUSpgaw9VAKJrOVSQNDsdNKXQ0hhBDN\nQ3qugVXbL3A5swQnRxWd+qeSbIzHw96dtmnuOJtuvWS4KT+Pwm3fUbxvL+5WK3pPD3o88798d/gg\n773/Pnl5eaxdu46FC5+97blQQgjRkCRhqmcFxZX8dDoDHw8HBnUNsHU4QgghWgFLWRnmwkKslZUo\nZhMqnQ61zh6Nmxsoyk17cUxmC1sOJrPtcCoWq0LPzq6U+R8m2ZBGO7e2zO86l82X191STJXJyei/\n30XJ4UNgtWLn5885Hy/0Xp5kHD7I/PmPVm8bHx9X/ViSJiFEUyMJUz3bcjAZs0Vh8qAwtBrpXRJC\nCFH/zCUlGE4cp+zcGSqTr2ApLr7utn1UKowO9qQXFGMfFIQuMBj7oGB0AQGo7e25mFrEqu0XySks\nx8vNnvHDPfihaBNFBj29/XowO2oGOo1dneIy5edh+PkUJQcPYExNAUAXEIjXhIm49u3H/i/+DcCy\nZW/Uuv/bb78pCZMQosmRhKke5eorOHA2Cz8vJ/p3kTUkhBBC1K+q7CwKtmym9PhRsFgA0Hp54xTd\nDTufNqgdHFFptSgmE1ajEUuxnuxLF7GvNFJ+7izl587+tzGVikond9IVFzrr3BjeMYw23Z1Zn7qF\nEjsLk8PHM6bdXdddX0lltWLMzMCYmkJFUhIVCRepyki/+qJajXPPXrgPGYZzdFdU6mu/QExIuFBr\nm9d7vjHcThVBIUTrIAlTPdqy/woWq8LUwWFo1NK7JIQQon5YjUbyN25A//1usFjQBQTiPmw4Lt17\nYufjc8N996y5WqDhgWmzMGZmUJWRQXrcJfIvXcGjoogOVj0dyoFj5+EYPAIoajV27ltIdduL2t4e\nlUZLZHYGaquV5KQX6Zmbg11VFSn7DlYfR6XV4hTdDZeePXHp0ROtu8d1Y4qIiCI+Pq7W54UQoqmR\nhKmeZBWUcTAumyAfZ/p08rV1OEIIIZqhNf9Jbn7d21GVlUnmB+9RlZGOnY8vbWbch0vPXtft+bke\njYsLxoBQPjtr5JQBtMERTBoYyvBObuw4vpbc5AsElGnppg7ArsyIpaSEqqxMlKoqAH5Jf8xVJhSV\nilJ3N4K79sA+MAiH8HDsQ9qhtqvb0L2FC5+9Zg7TLxYseOaWzkkIIRqDJEz1ZNP+KygKTB0chlpK\npAohhKgHFZcukfHOm1grKnC/awQ+M2ehttPdcjuKAj+cymD9j4lUGC1EtPVg7rhIHF3MvH9mNSna\nNNrHRDGy6xzcdK6/2VcBi4UvPluJVa3moTm/r07sej9UM+mpi1/mKb300nPk5eURFdWZBQuekflL\nQogmSRKmepCea+BYfC4hfi70irjx0AghhBCiLsrjz5Px7jIUsxn/x36P24BBt9VOmcmOi/o2/Ljj\nIo72WuaMi2Ro90DSStN599inFFeV0M8/hvuj7sVOXfO2QKVSgVaLVXNni7DHxq5n6dIl5OTk8PHH\nK1m48Fn+93//jFqtYvbsx+6obSGEaEiSMNWDjfuvoADThrS/5SESQgghxG8Z09LIWP4OWK0EPvk/\nuPToecttmC1Wth5K4VhuMAoqYiJ8eGB0BJ6u9pzKPcun59ditpqZGj6BUSHDGvT6FRu7vtYy4g8+\n+BAxMb0a7LhCCFEfJGG6QynZpZxMyKN9oBvdwr1tHY4QQohmzq6qiox330IxVhIw/8nbSpYSM4r5\ndNsFMvLL0KktRHjk84d7RqAoCjtTfmBT0jZ0Gh3zu82la5vON23vt71DMTG96Nmz7nFdr4z4nj27\nJWESQjR5kjDdodh9lwGYNlR6l4QQQtRu2bJldRt2piiEX0jAXKTHe9q9uPbpe0vHqTCa+eanJH44\nmYECDO8ZhCV7P1q1gtlq5quLsRzMOoaHvTtPdHuEYNfAm7ZZW+/QLxXuHnqobnFdr1x4Tk5O3RoQ\nQggbkoTpDiRlFHMmqYCIth50budp63CEEEI0c34ZmbgX6XHu1h2vCRNvad+fL+WzZudFikqNBHg7\nMXdcFBFtPVizZh9mlYUVpz8hoSiRtq5B/7+9O4+rqs7/B/6698JlX2RVFoEwtUwMyxUbUtGEptIK\nxQW0nCy3NJcZMVNLG0zURh+OP2LC/DrqMOKCaI6mmY6KgkWJmmQICMq+KjuX+/n9wUiScAGFe7jw\nev6jcJb7Oh8u9/A+77PgPY8ZsDSwaNF6NXWHWqqp24jb2/OZhUTU8bFgegz13aUX3NhdIiKix1Kd\nlYmeKWmo0deH/fS3W7xfKSmtwp6Tv+JSUi4Uchle9XLFy8Ncoa9X9zzASkU1kqzvoLLzyVYMAAAf\n3UlEQVSoBh42/TCj32QYKFp+p7226A41dRvx0aN9WrwOIiKpsGB6RL+kF+HntCI87doNfXqyu0RE\nRI9OCIHcyD2QC4HkJ93Rz6L57o8QAucSs/DvU8kor1LB3cEcM3z7wtHWtH6em8VpuGqbAZWiFqOd\n/4Dxvfwgl7Xuwept0R26f7vw1as/RE5OTv1txEtLi1uVhYhICiyYHoEQAgf/e7+79ITEaYiISNeV\n/fQjyq9dRXE3SxTZNH8DoZzCcvzfsSQkpRfDQKnA1DG9MdLTEXL5b12pS9k/Ytf1vVDJa+FWZIfX\nR7XuFL/72qo7NGHCm/UF0v0H895/nhMRUUfGgukR/JxWhBu3S+Dhbg13x5adA05ERNQYoVIh79//\nAhQK3Or1BKDhVDxVrRrH49MRcz4NNSo1BrhbI/ClPrAyN/xtfULgP2kn8XXqCRgqDNErrzssq0we\nOV9j3aGBAz1bdZc8IiJdxoKplYQQD1y7xO4SERE9npLzZ1GTnwdLnzGorKlocr7UrLvY8Z8kZOSW\nwtxYHzNffgqD+to1uNapRq3C7uv7cCknAVaG3TDb4y18e/DIY2f8fXeInSEi6kpYMLVS4s0CpGTe\nxXO9beHS3UzqOEREpMOESoXCr49Apq8PK9+XgZh9D81TVV2Lg2dTcOL7DAgBjPDogYkje8HUSL/B\nfKU1ZQhP3ImbJalwNe+Jdz2mw1xpVn/6W1tqj3USEXVULJha4X53SQbgtRfcpI5DREQ6ruT8OagK\nC2DpMwZ6FpYPTb+aUoCdx39Bfkkl7CyNMH1cHzzlavXQfDnlefh/l7cjr6IAnnYeCHpqEpQK/Yfm\nIyKi1mPB1AoJN/KQnlOKwU/ZwemBuxARERG1llCrUXTsa8j09GA1zq/BtLvl1Yj89ldcvJYDuUwG\nv6EueNXLFUp9xUPruVmchi8Sd6BMVY6XXEbhj0+MbfWd8IiIqGksmFpILQSiz6VCJgNeG8HuEhER\nPZ6yxMuoycuD+Yg/QM+y7vEUQgA5FaZY8Y84lFbUwLW7GWb49kVP+8ZPAU/ITcT//RwJtVBjal9/\nDHcYpM1NICLqElgwtdCl67m4k1cGr2e6o4f1o99tiIiICACKv/sWANDtf7fnziuuwOWC7iiqMoZS\nvxYBo3ph9PNOUMgf7hYJIXAq4ywOJn8NpUIf7/afjqet+2g1PxFRV8GCqQVq1WpEn0uFQi7DK+wu\nERHRY6rOzkL5tasw6t0Heo5OOB6fjoNnU1BdYwwrg3L85a3RsLU0anRZtVBj/6+Hcfr2eVgozTB7\nwEw4mzloeQuIiLoOFkwtcPFaDnIKy/GHAQ6wa2IHRkRE1FLFp08BAFTPeWHtzh9wK/seTI304W6a\nDXuj0iaLperaauz4ORKX866ih4k95gx4G1aG3bQZnYioy2n3gmn9+vVISEhAbW0tZs2ahf79+yM4\nOBgqlQr6+voIDQ2FtfVvTzWPj4/HggUL8OSTT0IIgT59+mDFihXtHbNJqlo1Ys6nQk8hwyvDXSXL\nQURE2qFSqbBs2TJkZmZCoVAgJCQETk5ODeY5evQovvrqKygUCgwZMgQffPBBi9cvVCrcvXgBNYYm\n2HCpBiqoMKyfPSaNfhKH9u9scrl71aX4InEHUu+mo7elO97pHwRjfR7EIyJqb+1aMMXFxSE5ORmR\nkZEoLi7GhAkTMHToUPj7+8PPzw+7d+/G9u3bsXTp0gbLDR48GJs3b27PaC12/koW8oorMXqgE6wt\nDJtfgIiIdNqRI0dgYWGBDRs24Pz589i4cSM+//zz+umVlZXYsGEDjhw5AmNjY0ycOBGvvvoq3N3d\nW7T+pFOxUJSW4ieLp2BpYYSgl/rgmSescfDgPmzYEIqcnBx8+WUEFi5cjAkT3gQA5Jbn4e+XtyO/\nogCD7Adi2lNvQk/Ok0SIiLShXT9tBw0aBA8PDwCAubk5KioqsGLFChgZ1R0Rs7KywvXr1x9aTgjR\nnrFarEalxuHYNOjryfHycBep4xARkRZcuHAB48ePBwAMHz4cy5cvbzDd0NAQMTExMDY2BgBYWlqi\nuLi42fWWVtRg76lk2HxzEn0BmA4djjWvDYGBUoGDB/fh3Xffrp/3+vVr9V8PGDUIXyTuQGlNGca5\njMIfn3gJMpmsjbZWWoGBf4KtrRny8u5JHYWIqEntWjDJ5fL64igqKgre3t4wMam7w5xarcaePXsw\nd+7ch5a7efMm5syZg5KSEsydOxfDhw9vz5hN+u/lTBTercLYQc6wNDWQJAMREWlXfn4+rKzqHg4r\nk8kgl8uhUqmgp/fbLtPUtO5ZfL/88gsyMzPx7LPPalxnTrkJVvzjIqrvlWJ++W3ArgdefXNEfeHz\nt79tbHS57cf+D+7dElAr1Jjc53WMcBzaFptIREStoJV+/smTJ3HgwAFEREQAqCuWli5diqFDh2Lo\n0IYf/i4uLpg3bx58fX2RkZGBoKAgnDhxosGOqjG2to0/o+JRVVarcPTiLRgqFQh8uR8szdq2YGrr\nvNqga5mZt/3pWmZdywvoZmZdEhUVhX379tUXLkIIJCYmNphHrVY3umxaWhqWLFmCjRs3QqF4+IGy\nD7paYAelXi3edquGIlUNF18f2NmZ10+/cSPpoWV6jXsGzv59IZcrsHjYuxjo8ExrN69NyeV1Y/Q4\n78mm1sH3edM4Nk3j2DSNY9O22r1gOnv2LMLDwxEREVF/RC44OBhubm6Ndpfs7e3h6+sLAHB2doaN\njQ1ycnLg6Oio8XXaup1/LC4dRfeq8PIwF9RUViOvsrrN1q2Lpx/oWmbmbX+6llnX8gK6l1kXd9D+\n/v7w9/dv8L3g4GDk5+ejT58+UKlUAPDQQbvs7GzMnz8foaGh6NOn+ecfWRuWY8n0UajZsQ3lAORP\neTT42fbu3RfXr1+r+0IGDJg2DL1fHoCae9VYOGQBnPWdJH8vqNV1p8s/To7G1qFr73Nt4tg0jWPT\nNI5N0x51P/Xw0/DaUGlpKUJDQxEWFgYzs7qAMTExUCqVmDdvXqPLHD58GFu3bgUAFBQUoLCwEPb2\n9u0Z8yH3u0tGBgq8NLinVl+biIik5eXlhWPHjgEATp06hSFDhjw0z4cffohVq1ahb9++LVrnP9dN\nw/TXx6D052sw6OkCfRvbBtMXLlwMAJDryTFkvg96vzwAd28X4kUxCD3NnBpbJRERaUm7dpiOHj2K\n4uJiLFy4EEDdqQ7Z2dkwMzNDYGAgZDIZevXqhZUrV2LRokVYt24dRo0ahcWLF2Py5MkQQmD16tXN\nno7X1r794TZKK2rw2gg3mBrpa/W1iYhIWn5+fjh//jymTJkCAwMDrFu3DgAQHh6OIUOGwMLCAgkJ\nCdiyZQuEEJDJZHjrrbcwcuTIJtepVqthXVwMuRBINzTE728jNGHCm1ChFtE5x2DZ2xZl6SV4xdIH\nE8cHtOOWEhFRS7RrJTJx4kRMnDixRfNu2rQJAKBUKhEWFtaesTQqr1ThWFw6TAz1MOZ5Z8lyEBGR\nNORyOUJCQh76/qxZs+r//+OPP7Z6vd49HAAA204cxwt/Dm4wraTqHpIds2BpYYtuFSb4PPBTKBU8\nYEdE1BHwIQ6/882ldJRVqvCG9xMwNuTwEBHR4zNQKDDUzh637t3DmWsNbyqRW56HrT9FoKCyEHZl\nFnArtuu0xVJg4J+kjkBE1Grteg2TrimtqMGJ7zNgZqyP0c/xnHEiImobntY2MNTTw9nsTPTu/dt1\nT7fuZmDjD9tQUFkIP7cxcCu2gwyd4xlLRESdBVsoDzgen46KqlpMGuUGQyWHhoiI2sYQu7qbF13M\nzcGCv64HAFwr+AVfXtmJGrUKAX1exwuOQ/HPc19KGVMjdoeIqKtiVfA/d8uqceL7DFiYKjHSU/Mt\nzImIiFpjqF13VKhrMWftOoyf8Cbisn7ArqQoyGVyvNM/EANspX3GEhERNY0F0/8cvXgL1TVq+L/o\nCqW+5gcQEhERtYazqSlMnvWEx+v+OHHrNKJvHoWRnhHe85iBXpZuUscjIiINWDABKLpXhe9+vAMr\ncwP8YYCD1HGIiKgTMu73DA4kH8GpjLOwNLDA3AEz4WDaXepYRETUDBZMAL6+kIYalRqvDHeFvh7v\ng0FERG3vqDIVsRk30N3YDvOe/RO6GVpKHYmIiFqgyxdMBSWV+O/lTNhaGsKrfw+p4xARUSdUZKaP\n2KobeMLCFe95zICJvrHUkYiIqIW6fMF0ODYNqlqBV73coKdgd4mIiNreoRfN0N/mabzdb2qnfcYS\nEVFn1aULptyicpy/koXuVsYY1o/nkRMRUfswldnhnWcCoZDzpkJERLqmS7dUYs6noVYt8NoIN8jl\nfFAgERG1D5d7tiyWiIh0VJctmLIKynDhWjYcbU0w6Ck7qeMQEREREVEH1GULpkPnUiEEMH7EE5DL\n2F0iIiIiIqKHdcmC6XZuKeKv58LF3gwDe9tIHYeIiIiIiDqoLlkwRZ9LBQCMf8ENMnaXiIiIiIio\nCV2uYLqVfQ8JN/Lg7mAOD3drqeMQEREREVEH1uUKpoNnUwAA4//wBLtLRERERESkUZcqmJLvlCDx\nZgF6O1viaZduUschIiIiIqIOrksVTNH/6y5N4LVLRERERETUAnpSB9CWX9KL8HNaEfq5dkOfnuwu\nERFRxxMY+CepIxAR0e90iQ6TEAIH//vbtUtEREREREQt0SUKpp/TinDjdgk83K3h7mAhdRwiIiIi\nItIRnb5gEkLU3xlvwgvsLhERERERUct1+oIp8WYBUjLv4rnetnDpbiZ1HCIi6oIWLlwodQQiInpE\nnbpgut9dkgF47QU3qeMQEREREZGO6dQFU8KNPKTnlGLw0/ZwsjWVOg4REREREemYTlswqdUC0WdT\nI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "degrees = np.arange(1, 10)\n", "thetas = [best_theta(d) for d in degrees]\n", "logL_max = [logL(theta) for theta in thetas]\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(14, 5))\n", "ax[0].plot(degrees, logL_max)\n", "ax[0].set(xlabel='degree', ylabel='log(Lmax)')\n", "ax[1].errorbar(x, y, sigma_y, fmt='ok', ecolor='gray')\n", "ylim = ax[1].get_ylim()\n", "for (degree, theta) in zip(degrees, thetas):\n", " if degree not in [1, 2, 9]: continue\n", " ax[1].plot(xfit, polynomial_fit(theta, xfit),\n", " label='degree={0}'.format(degree))\n", "ax[1].set(ylim=ylim, xlabel='x', ylabel='y')\n", "ax[1].legend(fontsize=14, loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see in the left panel that the maximum likelihood *value* always increases as we increase the degree of the polynomial.\n", "Looking at the right panel, we see how this metric has led us astray: while the ninth order polynomial certainly leads to a larger likelihood, it achieves this by **over-fitting** the data.\n", "\n", "Thus, in some ways, you can view the model selection question as fundamentally about comparing models while correcting for over-fitting of more complicated models.\n", "Let's see how this is done within the frequentist and Bayesian approaches." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fundamentals of Frequentist & Bayesian Model Selection\n", "\n", "Recall that the fundamental difference between the frequentist and Bayesian approaches is the [**definition of probability**](http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/).\n", "\n", "Frequentists consider **probabilities as frequencies**: that is, a probability is only meaningful in the context of repeated experiments (even if those repetitions are merely hypothetical).\n", "This means, for example, that in the frequentist approach:\n", "\n", "- *observed data* (and any quantities derived from them) are considered to be random variables: if you make the observations again under similar circumstances, the data may be different, and the details depend on the generating distribution.\n", "- *model parameters* (those things that help define the generating distribution) are considered fixed: they aren't subject to a probability distribution; they just *are*.\n", "\n", "On the other hand, Bayesians consider **probabilities as degrees-of-belief**: that is, a probability is a way of quantifying our certainty about a particular statement.\n", "This means, for example, that in the Bayesian approach:\n", "\n", "- *observed data* are not directly considered as random variables; they just *are*.\n", "- *model parameters* are uncertain quantities and thus subject to probabilistic description.\n", "\n", "This difference in philosophy has real, practical implications, as we will see below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Some Notation\n", "\n", "Before we continue, a quick note on notation.\n", "For the below discussion, it is important to be able to denote probabilities concisely.\n", "We'll generally be writing conditional probabilities of the form $P(A~|~B)$, which can be read \"the probability of A given B\".\n", "Additionally, I'll be using the following shorthands:\n", "\n", "- $D$ represents observed data\n", "- $M$, $M_1$, $M_2$, etc. represent a model\n", "- $\\theta$ represents a set of model parameters\n", "\n", "With this in mind, we'll be writing statements like $P(D~|~\\theta,M)$, which should be read \"the probability of seeing the data, given the parameters $\\theta$ with model $M$.\n", "I'm playing a bit fast-and-loose with discrete vs continuous variables, but the meaning should be clear from the context." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Fitting\n", "\n", "In the model fitting context, the difference in philosopy of probability leads to frequentist and Bayesians dealing with different quantities:\n", "\n", "- frequentists look at the *likelihood*: $P(D~|~\\theta, M)$\n", "- Bayesians look at the *posterior*: $P(\\theta~|~D, M)$\n", "\n", "Note the main distinction: frequentists operate on a **probability of the data**, while Bayesians operate on a **probability of the model parameters**, in line with their respective considerations about the applicability of probability.\n", "\n", "**Frequentists**, here, have a clear advantage: the likelihood is something we can compute directly from the model – after all, a model is nothing more than a specification of the likelihood given model parameters.\n", "By optimizing this likelihood expression directly, as we saw above, you can arrive at an estimated best-fit model.\n", "\n", "**Bayesians**, on the other hand, have a slightly more difficult task.\n", "To find an expression for the posterior, we can use Bayes' theroem:\n", "\n", "$$\n", "P(\\theta~|~D,M) = P(D~|~\\theta,M) \\frac{P(\\theta~|~M)}{P(D~|~M)}\n", "$$\n", "\n", "We see that the posterior is proportional to the likelihood used by frequentists, and the constant of proportionality involves ratio of $P(\\theta~|~M)$ and $P(D~|~M)$.\n", "$P(\\theta~|~M)$ here is the *prior* and quantifies our belief/uncertainty about the parameters $\\theta$ without reference to the data.\n", "$P(D~|~M)$ is the *model evidence*, and in this context amounts to no more than a normalization term.\n", "\n", "For a more detailed discussion of model fitting in the frequentist and Bayesian contexts, see the previous posts linked above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Selection\n", "\n", "Similarly, when comparing two models $M_1$ and $M_2$, the frequentist and Bayesian approaches look at different quantities:\n", "\n", "- frequentists compare the *model likelihood*, $P(D~|~M_1)$ and $P(D~|~M_2)$\n", "- Bayesians compare the *model posterior*, $P(M_1~|~D)$ and $P(M_2~|~D)$\n", "\n", "Notice here that the parameter values $\\theta$ no longer appear: we're not out to compare how well *particular fits* of the two models describe data; we're out to compare how well *the models themselves* describe the data.\n", "Unlike the parameter likelihood $P(D~|~\\theta, M)$ above, neither quantity here is directly related to the likelihood expression, and so we must figure out how to re-express the desired quantity in terms we can compute." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Model Selection: Bayesian Approach\n", "\n", "For model selection, in many ways Bayesians have the advantage, at least in theory.\n", "Through a combination of Bayes Theorem and probability axioms, we can re-express the model posterior $P(M~|~D)$ in terms of computable quantities and priors:\n", "\n", "First, using Bayes' Theorem:\n", "\n", "$$\n", "P(M~|~D) = P(D~|~M)\\frac{P(M)}{P(D)}\n", "$$\n", "\n", "Using the definition of conditional probability, the first term can be expressed as an integral over the parameter space of the likelihood:\n", "\n", "$$\n", "P(D~|~M) = \\int_\\Omega P(D~|~\\theta, M) P(\\theta~|~M) d\\theta\n", "$$\n", "\n", "Notice that this integral is over the exact quantity optimized in the case of Bayesian model *fitting*.\n", "\n", "The remaining terms are priors, the most problematic of which is $P(D)$ – the prior probability of seeing your data *without reference to any model*.\n", "I'm not sure that $P(D)$ could ever be actually computed in the real world, but fortunately it can be canceled by computing the *odds ratio* between two alternative models:\n", "\n", "$$\n", "O_{21} \\equiv \\frac{P(M_2~|~D)}{P(M_1~|~D)} = \\frac{P(D~|~M_2)}{P(D~|~M_1)}\\frac{P(M_2)}{P(M_1)}\n", "$$\n", "\n", "We now have a means of comparing two models via computable quantities: an integral over the likelihood, and a prior odds for each model.\n", "Often the ratio of prior odds is assumed to be near unity, leaving only the well-defined (but often computationally intensive) integral over likelihood for each model.\n", "More on this below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Model Selection: Frequentist Approach\n", "\n", "For model selection, frequentists are working with the quantity $P(D~|~M)$.\n", "Notice that unlike Bayesians, frequentists *cannot* express this as an integral over parameter space, because the notion of a probability distribution over model parameters does not make sense in the frequentist context.\n", "But recall that frequentists can make probabilistic statements about data or quantities derived from them: with this in mind, we can make progress by **computing some *statistic* from the data for which the distribution is known**.\n", "The difficulty is that which statistic is most useful depends highly on the precise model and data being used, and so practicing frequentist statistics requires a breadth of background knowledge about the assumptions made by various approaches.\n", "\n", "For example, one commonly-seen distribution for data-derived statistis is the [$\\chi^2$ (chi-squared) distribution](https://en.wikipedia.org/wiki/Chi-squared_distribution).\n", "The $\\chi^2$ distribution with $K$ degrees of freedom describes the distribution of a sum of squares of $K$ independent normally-distributed variables.\n", "We can use Python tools to quickly visualize this:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4G5eH+RNPPMHSpUtZtmwZKSkpp7333nvvsWTJEpYvX86f//xnV5fiNsP7BwJw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7AAAg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\ny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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import stats\n", "v = np.linspace(0, 8, 1000)\n", "for k in range(1, 7):\n", " plt.plot(v, stats.chi2.pdf(v, k),\n", " label=\"k = {0}\".format(k))\n", "plt.legend(ncol=2)\n", "plt.gca().set(title='$\\chi^2$ distribution',\n", " xlabel='x', ylabel='p(x)', ylim=(0, 0.5));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The key observation is this: if we can somehow *transform our data* into a single statistic $S(D;\\theta,M)$ which we expect behaves like the sum of squares of normally-distributed values, then we can analyze the likelihood of this statistic in terms of this $\\chi^2$ distribution, and use this as a proxy for the model likelihood $P(D~|~M)$.\n", "\n", "In the case of our linear and quadratic model likelihoods $M_1$ and $M_2$ above, the models are built on the explicit expectation that for the correct model, the observed data $y$ will be normally distributed about the model value $y_M$ with a standard deviation $\\sigma_y$.\n", "Thus the sum of squares of normalized residuals about the best-fit model should follow the $\\chi^2$ distribution, and so we construct our $\\chi^2$ statistic:\n", "\n", "$$\n", "\\chi^2(D;\\theta,M) = \\sum_n\\left[\\frac{y_n - y_M(x_n;\\theta)}{\\sigma_{y,n}}\\right]^2\n", "$$\n", "\n", "Coincidentally (or is it?), this statistic is proportional to the negative log likelihood, up to a constant offset, and so for model *fitting*, minimizing the $\\chi^2$ is equivalent to maximizing the likelihood.\n", "\n", "With this statistic, we've replaced an *uncomputable* quantity $P(D~|~M)$ with a *computable* quantity $P(S~|~M_S)$, where $S = \\chi^2$ is a particular transformation of the data for which (under our model assumptions) we can compute the probability distribution.\n", "So rather than asking \"how likely are we to see the data $D$ under the model $M$\", we can ask \"how likely are we to see the statistic $S$ under the model $M_S$\", and the two likelihoods will be equivalent *as long as our assumptions hold*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Frequentist and Bayesian Model Selection by Example\n", "\n", "Let's use the ideas developed above to address the above model selection problem in both a frequentist and Bayesian context." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Frequentist Model Selection: $\\chi^2$\n", "\n", "We introduced the $\\chi^2$ statistic above, and now let's take a look at how this is actually computed.\n", "From our proposed models, we explicitly expect that the residuals about the model fit will be independent and normally distributed, with variance $\\sigma_y^2$.\n", "Consequently, we expect that for the correct model, the sum of normalized residuals will be drawn from a $\\chi^2$ distribuion with a degree of freedom related to the number of data points.\n", "For $N$ data points fit by a $K$-parameter linear model, the degrees of freedom are usually given by $dof = N - K$, though there are some caveats to this (See [The Dos and Don'ts of Reduced Chi-Squared](http://arxiv.org/abs/1012.3754) for an enlightening discussion).\n", "\n", "Let's define some functions to compute the $\\chi^2$ and the number of degrees of freedom, and evaluate the likelihood of each model with the $\\chi^2$ distribution:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "chi2 likelihood\n", "('- linear model: ', 0.045524434063728803)\n", "('- quadratic model: ', 0.036256174893796296)\n" ] } ], "source": [ "def compute_chi2(degree, data=data):\n", " x, y, sigma_y = data\n", " theta = best_theta(degree, data=data)\n", " resid = (y - polynomial_fit(theta, x)) / sigma_y\n", " return np.sum(resid ** 2)\n", "\n", "def compute_dof(degree, data=data):\n", " return data.shape[1] - (degree + 1)\n", "\n", "def chi2_likelihood(degree, data=data):\n", " chi2 = compute_chi2(degree, data)\n", " dof = compute_dof(degree, data)\n", " return stats.chi2(dof).pdf(chi2)\n", "\n", "print(\"chi2 likelihood\")\n", "print(\"- linear model: \", chi2_likelihood(1))\n", "print(\"- quadratic model: \", chi2_likelihood(2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have found that the likelihood of the observed residuals under the linear model ($M_1$) is slightly larger than the likelihood of the observed residuals under the quadratic model ($M_2$).\n", "\n", "To understand what this is saying, it is helpful to visualize these distributions:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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mj69erVFXF93nFqItHn30Cd55561WN89pi5kz7yYzM5Orr55MQcFkgsEAjz76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\nZqDoQQJ+Cmjuaubbpi3o2vHNVVOjaGyUYC+ESA02LYugGcA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "for degree, color in zip([1, 2], ['blue', 'green']):\n", " v = np.linspace(0, 40, 1000)\n", " chi2_dist = stats.chi2(compute_dof(degree)).pdf(v)\n", " chi2_val = compute_chi2(degree)\n", " chi2_like = chi2_likelihood(degree)\n", " ax.fill(v, chi2_dist, alpha=0.3, color=color,\n", " label='Model {0} (degree = {0})'.format(degree))\n", " ax.vlines(chi2_val, 0, chi2_like, color=color, alpha=0.6)\n", " ax.hlines(chi2_like, 0, chi2_val, color=color, alpha=0.6)\n", " ax.set(ylabel='L(chi-square)')\n", "ax.set_xlabel('chi-square')\n", "ax.legend(fontsize=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see visually here how this procedure corrects for model complexity: even though the $\\chi^2$ *value* for the quadratic model is lower (shown by the vertical lines), the characteristics of the $\\chi^2$ distribution mean the *likelihood* of seeing this value is lower (shown by the horizontal lines), meaning that the degree=1 linear model is favored." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Significance of the Comparison\n", "\n", "But how much should we trust this conclusion in favor of the linear model?\n", "In other words, how do we quantify the **significance** of this difference in $\\chi^2$ likelihoods?\n", "\n", "We can make progress by realizing that in the frequentist context *all data-derived quantities* can be consistered probabilistically, and this includes the difference in $\\chi^2$ values from two models!\n", "For this particular case, the difference of $\\chi^2$ statistics here also follows a $\\chi^2$ distribution, with 1 degree of freedom. This is due to the fact that the models are *nested* – that is, the linear model is a specialization of the quadratic model (for some background, look up the [Likelihood Ratio Test](https://en.wikipedia.org/wiki/Likelihood-ratio_test)).\n", "\n", "We might proceed by treating the linear model as the *null hypothesis*, and asking if there is sufficient evidence to justify the more complicated quadratic model.\n", "Just as above, we can plot the $\\chi^2$ difference along with its expected distribution:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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N3HPPPTz88MN0dnayevVqN+OIC0KhGB0DIV59o4Z9bW1exxERyUmulvmLL75I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\n5ZVuRhEREfEl18tcRERE3OW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "chi2_diff = compute_chi2(1) - compute_chi2(2)\n", "\n", "v = np.linspace(0, 5, 1000)\n", "chi2_dist = stats.chi2(1).pdf(v)\n", "p_value = 1 - stats.chi2(1).cdf(chi2_diff)\n", "\n", "fig, ax = plt.subplots()\n", "ax.fill_between(v, 0, chi2_dist, alpha=0.3)\n", "ax.fill_between(v, 0, chi2_dist * (v > chi2_diff), alpha=0.5)\n", "ax.axvline(chi2_diff)\n", "ax.set(ylim=(0, 1), xlabel=\"$\\chi^2$ difference\", ylabel=\"probability\");\n", "ax.text(4.9, 0.95, \"p = {0:.2f}\".format(p_value),\n", " ha='right', va='top', size=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see where this observed $\\chi^2$ difference lies on its expected distribution, under the null hypothesis that the linear model is the true model.\n", "The area of the distribution to the right of the observed value is known as the [*p value*](https://en.wikipedia.org/wiki/P-value): for our data, the $p$-value is 0.17, meaning that, assuming the linear model is true, there is a 17% probability that simply by chance we would see data that favors the quadratic model more strongly than ours.\n", "The standard interpretation of this is to say that our data are *not inconsistent with the linear model*: that is, our data does not support the quadratic model enough to conclusively reject the simpler linear model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Other Frequentist Approaches\n", "\n", "Recall that a primary purpose of using the $\\chi^2$ statistic, above, was to prevent mistaken selection of very flexible models which *over-fit* the data.\n", "Other qualitatively different approaches exist to limit this overfitting.\n", "Some important ones are:\n", "\n", "- [The Akaike Information Criterion](https://en.wikipedia.org/wiki/Akaike_information_criterion) is an information-theoretic approach which penalizes the maximum likelihood to account for added model complexity. It makes rather stringent assumptions about the form of the likelihood, and so cannot be universally applied.\n", "- [Cross-Validation](https://en.wikipedia.org/wiki/Cross-validation_%28statistics%29) is a sampling method in which the model fit and evaluation take place on disjoint randomized subsets of the data, which acts to penalize over-fitting. Cross-validation is more computationally intensive than other frequentist approaches, but has the advantage that it relies on very few assumptions about the data and model and so is applicable to a broad range of models.\n", "- **Other sampling-based methods**: the classical frequentist approach relies on computing specially-crafted statistics that fit the assumptions of your model. Some of this specialization can be side-stepped through randomized methods like bootstrap and jackknife resampling.\n", "For an interesting introduction to this subject, I'd recommend the short and free book, [Statistics is Easy](http://www.morganclaypool.com/doi/abs/10.2200/S00295ED1V01Y201009MAS008) by Shasha and Wilson, or the extremely approachable talk, [Statistics Without the Agonizing Pain](https://www.youtube.com/watch?v=5Dnw46eC-0o) by John Rauser.\n", "\n", "We will not demonstrate these approaches here, but they are relatively straightforward and interesting to learn!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian Model Selection: the Odds Ratio\n", "\n", "The Bayesian approach proceeds very differently.\n", "Recall that the Bayesian model involves computing the *odds ratio* between two models:\n", "\n", "$$\n", "O_{21} = \\frac{P(M_2~|~D)}{P(M_1~|~D)} = \\frac{P(D~|~M_2)}{P(D~|~M_1)}\\frac{P(M_2)}{P(M_1)}\n", "$$\n", "\n", "Here the ratio $P(M_2) / P(M_1)$ is the *prior odds ratio*, and is often assumed to be equal to 1 if no compelling prior evidence favors one model over another.\n", "The ratio $P(D~|~M_2) / P(D~|~M_1)$ is the *Bayes factor*, and is the key to Bayesian model selection.\n", "\n", "The Bayes factor can be computed by evaluating the integral over the parameter likelihood:\n", "\n", "$$\n", "P(D~|~M) = \\int_\\Omega P(D~|~\\theta, M) P(\\theta~|~M) d\\theta\n", "$$\n", "\n", "This integral is over the entire parameter space of the model, and thus can be extremely computationally intensive, especially as the dimension of the model grows beyond a few.\n", "For the 2-dimensional and 3-dimensional models we are considering here, however, this integral can be computed directly via numerical integration.\n", "\n", "We'll start, though, by using an MCMC to draw samples from the posterior in order to solve the *model fitting* problem.\n", "We will use the [emcee](http://dan.iel.fm/emcee) package, which requires us to first define functions which compute the prior, likelihood, and posterior under each model:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def log_prior(theta):\n", " # size of theta determines the model.\n", " # flat prior over a large range\n", " if np.any(abs(theta) > 100):\n", " return -np.inf # log(0)\n", " else:\n", " return 200 ** -len(theta)\n", "\n", "def log_likelihood(theta, data=data):\n", " x, y, sigma_y = data\n", " yM = polynomial_fit(theta, x)\n", " return -0.5 * np.sum(np.log(2 * np.pi * sigma_y ** 2)\n", " + (y - yM) ** 2 / sigma_y ** 2)\n", "\n", "def log_posterior(theta, data=data):\n", " theta = np.asarray(theta)\n", " return log_prior(theta) + log_likelihood(theta, data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we draw samples from the posterior using MCMC:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import emcee\n", "\n", "def compute_mcmc(degree, data=data,\n", " log_posterior=log_posterior,\n", " nwalkers=50, nburn=1000, nsteps=2000):\n", " ndim = degree + 1 # this determines the model\n", " rng = np.random.RandomState(0)\n", " starting_guesses = rng.randn(nwalkers, ndim)\n", " sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[data])\n", " sampler.run_mcmc(starting_guesses, nsteps)\n", " trace = sampler.chain[:, nburn:, :].reshape(-1, ndim)\n", " return trace\n", "\n", "trace_2D = compute_mcmc(1)\n", "trace_3D = compute_mcmc(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The output is a trace, or a series of samples which by design should reflect the posterior distribution.\n", "To visualize the posterior samples, I like to use seaborn's ``jointplot`` (for 2D samples) or ``PairGrid`` (for N-D samples):" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ptO7YudJOwccslAGEZggkKxtpM2WQZMBkMyrXq31Pk/XBqPg8QnKoTKGfuv+b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mYwGDAa+Tu9X/iFX+B73/sev/qrv/qkDm+NTxirw5mupYWDcL5nkcbKl9f02QWuNpaiCMrjWnL9\nQg/5YEYvi+hnEZNFhakNSSTRSmKMQQhvF6GDNYYU0E0U1kFlLFmiQm/G+xoJCf1ORD/VaCWD9p6n\nsDeLvnOWB4cT9raH3mq90/cMvP1bbGxskvQ2OD1VbI56GGNw5ZjdnV26nYQ0iZjnpWfeDbsUpaHX\n0WgpOTias72RMa9rQDDqxSjpg1AcK2aLkm4W87c/esAir9keZdx+MGXYjzF2ydS7tT8j1j6TGfYS\n0ljTyTy1/nRW8u69MRe2umgpmc5LNgcJSvmyXVlbqtqhpJdxskCWKFRQDJfroLPGY8QTC0oHBwe8\n8sor7fONjQ0ODg7odrtsbm4ym8149913uXjxIn/zN3/DL/7iLz6pQ1vjU4DV4Uy3YrHeWjXEmuSc\nz83mpVe+BjqZJo5TXsziNvHaP55TW58ZZYlXNZjMC6aLumWLgSCONZN5RbWo6WURsRZc3unw9p0J\nAL00Yrqo2BykOKCovAfEW7dP/XcnkkVRcO/gFB2lICMoxxzu3+Vw/y7XXvgnFLWgn8QcnRxxOlnw\nlS89S20VUkgOb+5DmTPspkyDkvruRkZeWQ5Pc06mfoj3+l7flw97CZFW5KXlZDLl/vGCW/szvvz8\nFtaCcS4wHiVJ7BXC370/odeJSWPNc5eHRJEfOP7RO0cUlSVLIjppxKI0PHd5SBprimADAlDV3mtq\nOq/opNrPca2xxmPGJ0Z0eJgC/C//5b/kD/7gD9je3mZnZ+dcivDD+Iu/+Au+853vfFyHuMYniKai\n9zA5ojaWWV55qwsl0VqSOE+OMMZhnaGuHQhIIsm1iwMeHM4QUqKUJIkkF7c77J/klLVBIry6hPM0\n6yTMMi3yiiRKSW9oytqwu9Hh/tGMo3EJznF7f8a8MGwNM3qZJtKeGTjopkgpuX3/BN3d5sp1Qbfb\nR6cdIl0Sx5pLlxK6nYyTmcFWE26++SOqyjLYuc54OidSEq0009mCOI6pKksv1aSxZP94TjfTIHQY\n6I3pdiKU8lp501lJrxPjnM9srPPsxyZ++Hkvx4/fO2FrmNHNFJd3+5RVzbW9vhdnLQ23HkzZHCa4\nUMKUaml/nqWaOgw8y6D6UFuHC27DTQmvKYdKKc6UD9d4f3zQmvZJs+8axt3jZNqdhycWlHZ3dzk4\nOGifP3jwgJ2dnfb517/+db7+9a8D8Cd/8idcvnz5Q/f52muv8dprr53ZduvWLb75zW8+pqNe45PA\nkrX1qJhqXhqq2iuJK9HYXyz7KbVxGB+TvLOqEgz6KfOgIj4I8z7DXsxpyD7iWDGd10jhTfGabfPc\nEMeaC1sdrPNzUVXtB10XZc3xuEBKwaAbUxnHha0Bp7MSjKUsCk5nNb3+Lovawbxmo5dycLpASsUw\n63M6qxjfv8lb77znj23nOieTnF4nYVx5ltWVvZjTWRlIHTF5WZKlUTtcuzVMqY0jSzWnk5Jq7rO5\nsrIhWPjrksbKB6TKIqUnd/j+WoIUgmcuDoOXlcMYR1EZ5osaHXpVEs+STGJJpP3j1dtGew5TpaGP\nf5QbzDU8PmhN+yTZdw8z7h4X0+48PLGg9I1vfIPvfOc7fOtb3+IHP/gBe3t7dDqd9vXf+Z3f4V/9\nq3+FlJLvfe97/P7v//6TOrQ1PiZYa5eN8oa08FP0H853Pv3gz0shMLgV1W1vwdDAGIuSaqnmvfI9\nkfZBzBiHDOre4PtMSkpiLYkjhTGGSHmtt06qiaOw4IuwDymIAlU90pI4VhRVDUIiJXRSRaSgtJCk\nGVkao6TCtV5Elk6ign2Ep9J3sogkVt6or/DSSg3zsLE6jyNPn69qPxAbaYmw3o9JCJ85SSFBNKQF\nQt9oaVMh5dLOwlj3yAJhrGt/y4aib1e2nTcM7WDl9UeD1JoI8dHwSbLvPm7G3SqeWFD66le/yssv\nv8yv//qvo5TiT//0T/nLv/xL+v0+r776Kr/2a7/Gt7/9bYwx/O7v/m5Leljjs4kyGPMJQEcS50AJ\n1955/6zopNobzAnRWqRHeqmZ15HeRlwI/5537415996UQSei24mYzkv6nYjD0xxEIAxoyfYwpdeJ\nkFJQhB6VcY53744pasflnQ7jWUU3VRSl4JnLQ7QWnExK8tKwM0qRQpBGCuPgS89fZqN/jBUaa43X\n5tMabMFbb73Nnffgf/5n/z3dqy8zGg554+YBJ9OSfkdx994xcaR57pnrOASbwxSBDwh1XfH/vXHM\n7laXOIp4686YLz+/xWRWoSSMul4eadSLWZR+8d8epSSRn+FyoZy2M1JsjzKMsSzyipNJwUbfi+Aq\nJdpsqDKGSCnqYOC3KA1KllzY6mCs/50XpcE5GHQipJRn1N4hKHM4kCHztdaX+8CzGNcxaY1VPNGe\n0u/93u+def7iiy+2j1999dWWnbfGZx8NVcG1/wPuMS0+kVZtlahh0Am31F+LI9WWjuq6oXj7xbG2\nlpNp7gkUCKT0n+mmEVp7mZ5ISz+DE2wxYOlRJIRfuK3xKuSTuQ+Ao37CZFYhJdjav6/TSZktarTS\ndNKIyjj63QSEL3c15cnhxibxg4UXnI2i9gp2s5h5YXzQDedTBar4ZJqTpSCVYjwtaEz9JlLQzWKm\n85Io0kEOKFwj4drMcNiNz3o/CU+tl/jekWc7OpwFK2zIxsKRPUTBb56KsG9Tm9BLkqhzNPFqY99X\nT2+NNdaKDmt8LIi1IlKuNc6z1p47PPuzoNVdC4HIL/Ae1jqUFOHu3PGFayMubHfQSiKAm/cn1CV0\nEsXWqIMQgkVehdkc11o15GXFojBc2OrSyTwVPI0rDk5ytHIcjQtOpz4jeenGBgKBNY5bBwVKemuI\ng5OcrUFKJ9UUpaHfi0miHf7FP9vgzoMJb9+ecGXPB5Yvv3iV2aIkLx1fu7DN1rCDE5DMKybziiRS\n5GVN7YLe3Sxn7uY8f22XRW5wznJnf0xZGV68vo1xPqu8vNPj3tGMYSfGWIeQgktBgLasPd3bWsv2\nKPPqFAL6mUZKyaKoKSuLsY5uptAqopdZtFatjUiWaOIoWKUD87xqJaW6mUJJccaHaZE3Q9C03lhr\nrLGKdVBa42PBw/0jpR4t2632GT5o28Pbl3+Xry2/eCn02gzdZrF+pOmuo6VjrJQ+83FuOThqjMWE\n7CiOJNb6bKkImYoN/R7/3C+81rm29FeWYX/WtSSLSEmv1FAL8ioQAcSyXKi1xpUVSeyzKn/dfNZW\nVhVFVWMtJEowL2oo/FBsYX0J7nRaNBefurbM87od0vUzWA6MCyoLtP0n8KaJ4fKduXnw/SBaO3rf\ndwrXzaemSMmZm4IGrbLDym+3Ouj80/YYn3Y8Kfbdw7p28Hi17T4M66C0xicCP5Rp0MrfTTeK0iaQ\nI5oFrRmk9Tg/YJ2B86VDGxrwUgpk08y3ljTSQO312mjmoPx/QnpyQx1Uw5NYsshrHhzN2d3osDNM\ncRZOZwVpqhn24lZyJ0sUz14ZUhlLXhg6iZdHUlLQ70Yo6VlrvSyiMobtYUptHbEWdNMY8KQF8My4\nXibQWjJdWHqZYjZbIF1Fv9tF64g959XPD44n7G4NGHR6IDwlfLYog7GfJz50swghHJ1EkcS6VYk4\nOMnRkWTQiZnnNf2uP5eqNgi806/WkkgritoQa0VdWaIIlISy8srkTdZkAzkCPIGiIUEUlUEpSaRk\nKEXaVgVjjY+OJ8G+ez9dO/h4GXerWAelNT4RzPPaN+6lo9eJgTDXEsposW6YWg/59pyzr4ddUWtj\n28VROC99UwvHZO4VxUeDFPB37db4QBc3fSoF80mOxS+yb9zyw7EXt3uMBhnDfsp/ff0uaay5uhex\nKAzHk4Iv3rhIHCk2+in/7z/sM+wlZInm9v6M8azipRsboUdTce8wByF58fqIvDQIHIvSa/p1Bdw7\nWnA6K7m806WuHePxKT98w9PGv/mNn6O2/j72h2/e4/BkzjOXR6RJQr8b8+69MYvC0EkdZVExXVT8\n4sterqubKnY2ugD85L0T3r47QQh49Z9e9aW8qiaONLPccHiyYFEauqnmwlaXqnJUVYWxQGFIgu2H\nUoJO4vtgJ5PCB3Qt6GX+Nx3PypCtGbYGCXGkiZu22Ro/FZ4E++5JsuzeD+ugtMYngjTWLIqKOHgA\n2RVR1qZ6tNorAlayoKapvvTsqWqLdV7VWgpPqmiyIF8ycmSJlyrqZ56hN1nUmNqSJpp+N6aqvRL2\nzijj/tGMXifm+atDTk4LtBRUdU1RGvY2Mg5Oc65fHHA6LShKQ1nVWOt46/apz/bwqtyDTsTWKCNL\nNEenCw7GOTpkYdN5gRAilN0Ew35CN9XkpSWNfWZhjOPyhS2ctRhrSROvLHFyOqWbaUb9jFE/85p1\n1rKz0eHe4ZQk8hT2JFFM5yVxJDmZFEwWNRc3MrpZxKgfc223R6Qli7zi/mFFtxPRDbYUSnqjxEZj\nT4ilZ5L3bJKMpwZTOzpZRJZoZnnVEk2kgE6isa4ijuT7lmbXWGMV66C0xicCrSVdGbX9izr0NqTw\nIqVwtv8gQwBqeharzfO6XvZGnG6ERJfCqlVZe3+mSDHqxUgpmec18yCfs7MRk8SaWNu2Z5QmEXlV\nsD3MuL7nyxbTecU894aBLz+7hVKSfidmHjyffvjOAW/e9i6z3TSiqByX9nokkVdf2D8puHe4QEnB\nha0OpzPvGHvvaO6PY7ODMY7tUcp0XpGXhn7XZ2OXL10gibzg68HRKTfvHAHwy7/0xdCvM4xnfgD4\n4naf6aLyg72d2EsqzR2ns4p7RwtPynCOL93YYHOQAbAoDNOFz6x2N/384PYwa6WIIuX7ULWxbQ9M\nIHA4alOSpRqtJYNufCbwaC09028djNb4iFhrf6zxiWG1ob6q5P3RsNJrEmc2fwjOkiX844cfnC0J\ntm63ctn+bRr/Qiwzu+ZFuRTSRrjlEG7zPh0GbFc/o+TyNER4DrRki0jJVr5HhuPQIVA0n5LtvkS7\nz+ZAmmAuGx44Zy9be7xieb4W9+jrK59x73uxH93ue4NnB5nXWOM8rDOlNT4V0Epg7HIxBr84tjMw\nK4w7FywkrHWkiSIKFOWG2GCMaTMeHWaO/Hf4gdCyNkiJV9xWkjSoLwghSGPFdFGFrCoJrytqYxj2\nEmbzirys2RyknM5KisqSRJrTWUEWK67sdIIArKSuDVmsUFoRa8GFL1/kb3+8z3hWYqxle5iSJZph\n19O1a+OQEvaPFiRBFuitO6f83Be2uXFxgBTw4Dhns3+RbhpTVI737k+5stfn8HRBpCRX93psDjP+\n/u1Dbt6dcDopuHZhwOFpzqgfc2WnTyfVLcuurGq6WcyFrS5JlLeKFML5zFD3hDcDjDXHkwJQpPiM\nqaotnVTTD3RzKZalVRXmx5aDtI7prOJwnHNlt0cnXTeWflp8XOy7Vbbdk2TZvR/WQWmNTwWklDw8\nxtSwuh7e5nDLMp5bBhwC69zYZTBrhk2F8AGq2eYcbS9JiqURnZSSKpAf0lijIxk08bzo6qAnyGo/\nx6OUwJXeiXUyqwDBoJswL3x5a9SL21JXr5NgrePKdpcfzj1hYGuYUlR+RqhR4rbGUltHOS+ZzH3Z\nsRf6NQCDbsR0UXP90hb3j+cY6ziZ5F7zzxi2R51WAHWWeyX08azEhWs06PlSWhZ7/mFVN06/Xjmi\n0cwTIdsx1pKmEVL4fdbG+CzShEHlwKhzLmgOhiGyNttqfyc4nuY4B0VpyBJ9JltdGwF+OD4O9t15\nbLsnxbJ7P6yD0hqfOSgpSBMdlLAfXcQaDTtrG1kbi1aqVR7vpJra2LYM1hAqnHNMF16kdZpX3D+Y\nIaXg6l6PspQ4V3IyyYPzbBLYdJYf3TxmPC3ZGCQMujH9DsE2AnqZpt9NvG/RpGRrI+MXejFxpMhi\nzXheUlaWjYFfyHXwO3rn7hgpFa88s8nOKMNYy2xRU1SWUS9m2Eu4cWnA//n92/zwnWMubXf4wtUR\ndw+nFIXheFxwaavD0aTg1v6MF6+NeP7yCCUFp7OC+0eGjV7M7maHeV7R7ySkaW4R/uQAACAASURB\nVEwSWfZPFlS1JYklRWl569YpV/Z6dDN/3W7uzzDGsTlIOJ5aZnnNxsArisdaEkUq2KV7O3fr/MzY\nMxeHTOclSaypjA0SQ+IMoUUExfc1HsXHwb77NLDtHsY6KK3xmYMQAj/mcv7iJYTwRY6wuGml2oWu\nuRGPVjT4GkKFb+T7x4u8CjYP4JzACZjlJbMwCFtVvuNSlN7vyDpQK6XCSEuq2pKmDWkDrPAlOiVl\nS36ItGyzpGEnCoZ6ltOZvyNuFMoXuWE6r3D4oNpQ3ud57d1vpaAyjsoYpvOSRVFTG8tkXgZr88SX\nLitLWQZiSBBe9ddItMfZnLcUQZi1rFsJobysWYRMEATW4jX1mjKrFGdKrf63Wv5OWRYFIdfl73WG\n8r+OR0891kSHNZ56hImoMLjrt/XSmCxWdFJNs2wmkSaJVeh/WaSANJZsDlOSIDobaUkcSZTwlGpj\nlvssSoOWgk6qgxOuoJ/FdEOP53haIIW3hxj2YnqZZrIoUVKQJP5YtBIcnCwAH3P7nZhOcM1NIkmi\nfTktTRS9LGLUi+mkmir4Hwl8PyhSPnBHyhMkxrMS51w4JxXsLYxnQ2qvRNFIOMXa+1Ip5dUcmkFZ\n8MSMhjZeVcaTG0L/z+//bMnOlwpZ2fbx/c5rfDawzpTW+FzCZ0sfrU8hpWCWLzOAJJJkmxnDXkRe\n2bbnpLVic5AymRd+pkr4HtTLz27x4NiXvKRwLfHCOcssN0wXcw5Pc/LScHW3Sy94Nl3ayFBKUdaW\nv/ovb+McvHBtyDw3CDwle/+kIIkUWRIRack798Y8OFow7I3Z7KdsDVIubXUoKsuDowW7mxndzBsD\n3j6YIYTgn//cJeJIcXAy587+HAd87aUdhv0Uay13j+ZUleXSVocsjUgiSV7WjBc1xli2NzocTUqK\nwznTeYUS8NyVIVqrduC5tpBE/jrP5lXrBtxNFDKwVzrBTl4EXl8jBOVlj9Y9pTU81kFpjc8tzlvg\nrLUty2+Vkh4rSSVtYJH5zzUSQnlpl9Rt1ahwV/Q7MWXlbRuu7HS5eW/CaJAhnGOW10SRQpSGojK4\nUCabLmrSWBHHism8ot8VaAXPXhpw896ENIkoS0OWxWSpZrqo6GYRSgjK2jLqJewfLxh2Y9JEMVtU\n1NYHwGE3JtaKWVFTGUsceQbg7QdTrl3okyURm4OEk2lJHTyUtJIMOzGH45x+JwYB80VNXniSRZou\nCQkq2Eykiaa2Dmlt2w+qast8UbLRT4kiicVRVhYddAOFIPSZbFsuXfVXWrIsH/v/DT43eBzsu4d1\n7T4NbLuHsQ5KazxVqE0gNViIV/59R5FioESbLQkBSit0pCjrvA1kWnuZnFEvecTiO4l121Mq61nI\nnPA9J+vN/SaLiqIyXNnrUUxLDsc503nFl5/f5kLIeC5ud73qtoMv3dgIVh2O8cLLJP3cF3ZapW2l\nfE9qe5gw7Kc4B+NJwem0REtJbmreujNmY5CyPcrY3uhwcadHVTvysqaXedLEld0ecaQpK8Obt8fU\nxnJlp0e/k7TXQyvJ9ihDSkleWlzwIjHWcjRe+HPMNBtZShwpb2cfsqB20NksSQ16ZSC62bZWfXh/\n/GPZd++na/dJs+0exjoorfFU4dx528ZJdWXb2XVR8PBA6HkMMSkefZ8Xhm326V831vsUwUOq2iv7\nbDY3hAxrHDbsSGkJgVzQfNqXGM+eZVUvNQBXD9fPcp0VFVQhwHplc/vI8TRn9rB6dPN1zTlK4anm\n/vo9WpI7r2X0YW2kdaDy+Mey7z6NTLvzsA5KazxV8CQF197BNwu7s5ayMhhj0VquyB8ZIi1QFuJY\nhUXZi44a47MEHOSV4faDCYNeShorellMXlaMegOSWHPr/pTZomJzkHJpu8ewF3E0LshzQxJJqtqR\nBqXSRW7QWnJxO+PidsZ4VlFWhs1BQlFZJA7pFHeP5tw9mHHj4tCXBMMc1sYgJYoUm4MEYxy392e4\nQOJohnqNhe+/ccCVvR6Xtnu8d2/M3laXoqwZ9hLysubwZE6aKLaGGWksOTwtmIXBYm/xboiUoChr\ntJJkifJad9a2rMDNQdoGPGO8tmAzWFsb6wd1Wd4QNFTy5vexwWgxUuKx+XGt8enGOiit8VRBSdmq\nRji3LBs19u3gF24VBkVr42dtokS2i6sOOkLW1m12cmd/xrywWJezPeoQx4o01VjruHZhwM27E4z1\nFO8re30ADk8LEN4+fJbX3mZDSBZliagML9244mnZxlPP0zgijR15aTidV/zw5gkAw15EEmvKwLBL\nY82l7R5R6ImN+gmzRU1e1iSR/yd/93DG/mnOwTinl8U4YP9kAUEjUApBXhrywrAZVNUPT3NqYz17\nL+x7UdQthfzKbp84UsyLipOpn/cy1hFHPsDkjT6hdQjlLdJVsCl5RHw3oCmHGvcknITW+DRgHZTW\neKohhL+DVyv9IYcvYUVKolJJbb2XUFUbP1Pk/DzOLIie9rKIq3s9Dk9yZKBHZ7EkjjV5UbPIDV99\nYYf7RzOSWDOZ5VTGobWkl2m6WURtHHf2p0QqIksVL13fpJNo7h5Mee/BFITg9LRgPC/ZGnofp3/6\n0i5RJLl2YdAGVYcjryreuz+h29Fc2ukx6Pr+VxSCTVUbru316aaaWCvKytDvRPTSCOP8cSxyw/ZG\nwsXtDou8Qkjh+2jeeAqtJNNF6V8Tgt2NzKusG8sir0kiRRp72nte1tw9mFHV3gqjrB1JpNjd7Cz1\n/sKDxk24QRQyW7XOkp4arIPSGk8thAhzO+EWfTUwSSFa6SPlmnJTTRXeXBZ1S2Qgi9BK0utELEqD\nsY4k1oEW7h1f40hxYbtLWVmmeU1R+qyh8ZKKtF/sK1Nzba/P1tCrd++f5IyDmvid/SnWeTsJ8JnV\nC1c3vEWHdJS1H8Kta8tkUZFXhr3NHuA/U1QW4/wCX9WWzUFCXlqKyrCXdloW3eFpgQO+ONogbVx7\ngzpGlixdcavK+uCqBJ1Ac88L077eybwK/PF4wXjmMyevUL50s111E/aF0bMOw/6/dU8Jfjb23adN\n1+6jYB2U1niq0fQtHrFlP6OQLdrBT9lQm8Nrq8OgXkPOv2adQwW9OCWDWGxDrRZ+QW48hxAgEXRS\n1SoxNMSCTqKRwjvbdjPNbFEjA+tuVWIpiSVV5RUl4kj5Idjw11uh2+CwK1pKtpKSOPIDr8ZYpPQu\nwEmsKErDbFG1JIPmeKQEaf0+G/dYFURyG+feBtZ4kdYoEt4byi4VwhvFcK28E62U8n3t0dcByeOn\nZd99GnXtPgrWQWmNpxaNWGllvFV4I3pq3aPloqI0oWcDZe1ZcVoJtFZUoRHvRUa9lM+isKSxQIYM\nKi9qEqkpqwWHpz5ruHqhz6ATY4yhm0Vcvzjg7btjskSzKGt6nYiXn9vGAfcO51zc7pNGgkEvxRhL\nlmqUhH43ppNGVCPD6aQgCr5RzgnmeU1VG05nFf2OZrOfoIUMzr6CxDYUdsusqHhwtADnGHQj7h7O\nEQKevzJqA7PSCiW979TmMCOOPNvuaFJ61fMsAlF599pxwbAbEWvNpe0OJ/OKSCmKoqIyjrfvjLkY\nZJS0EnTSaB2APgA/Lfvus8K2exjrQu0aTxWcc63kDbD0FhJNP0M8EpBWCRFKSV9qwxv5yYcWUaWW\nzD2tlxpwTWmwn8WowCzzA6pehqcteSVq+Rnp1bd3hpn3YFKCrZEv6xW1oa48waChlRvjMEG6Z9RL\nQnnMD7v6U10ea9mqpwuU9sfz45sn5EWNUpLdDW/0V1euJRscjougxOCvm1tlyVnLLC9DBuQzL/BE\nh+Z9SaC3J7F6ZEjWrHymgQ1uu2s8XVhnSms8VWjmf5qexqAT+3JZmFM6bybGOogjnxmtqhD40pNj\nuvAlFeP8JE8SK3rB6mKRV4wrg5SSXqKIo5RRP+FvfvSAd+6OGc8KwAeHQbBk72URo75nvBnrGA1S\nfv6lXe4dzLAO7h9PePvOBC0Fv/DyHqczz3Y7mRQYY7i000MpyeYoIQs0824akZc1tYPptGCe1wy6\nEb2uVzv/L//tFq+/ecDeZpfXvvVV4kgx6idUteX+0ZyTacFsUXM6Lbiw1cU5yAs/CCyFP855XjOZ\nVRjrh2W3hv4cKmOx1g8oKwFSam/HkUZIKShKQ208A7Hf8b28pQ8TCOyaDv4UYR2U1niqIcRHn39Z\nfV/jQbQav1ZDWZNtNU19v201U2mynGZ41LVZwSrhoknRfC/IP66CknjFst9SVHW7z2bo1a0kGSpQ\nsDFuJfsQrbPtPK8x1lO8ozDvpJVsB3AbX6pV48VWhNW6dkjXrsx+tcexPI2lWrsU7TU8bx636Xut\nXIL2O9clvs831kFpjacKS2WCR7d90Gf8nbtFCulLVji0FGGbf1+sFUVYxBelp0Wb8LpSog02Sgsu\n7/aYLioubGReq66yYL0it1/1HXXtmC0KokizyCtvsw6Mugm7o5o0UWjp99tNUiIlKSsTSpCeXFHV\nBgfcPZjSSSPft3ERkTJkaUQn8YKwL1zboKgMl7Y75IWXM1JSEIVgliW+5DZbGPrdmk6i221RJMHB\nZFFRVjYopSuMtURakQZLj8q4MPclMMaSl8YP/SqJNZZ54Weptgapt/oIquQCX8orax/B40g+lZnT\nR2XfNYy7zwrb7mGsg9IaTxXOlQf6EFM5KQV540GEbXs0eWmCvpu3TFdKoirDeO4X50VetyWo7UGK\nFCKw6+DahQHdVCOlYDovuXlvggW2egmRVlSV5eB0gbWOYlwEZ1uvv6eU5IVrw7bE19DKe92YqjIt\n225eGCgMN++OOZkWbPYTXri+QaQTLmw3vkaOWZ5zebfPS9c3UEoynpde2TuwBxelD2BKK+Z5zZ39\nGV96ZgMhFP1ejFa+VzRbjCmMQStBr+MHctNYBx08x1HoSZWVD9xFVZHGiijyrMN7h3PADyeniS87\nprFXXJ8tlsrjGzr+mX//zzI+CvvuYcbdZ4Ft9zDWQWmNNQJWZYcaS4UGSazAeetzrQS18QOgxi6t\n2U24s++kmkVeE0cSgSFN/QJrjA30Z4ja/fh+1vYo42SSs8grbGTJK4MxhkgKNjY7dJOKeVGRxIqT\nacGFzS6Rlhye5uwfz8lSzWxeUZSGUT8CJ0giHxx2N/b4uzf2kVIwnhZkqebotPYOsGHgNVaQJRqH\nL9WdTnPSSEHIupSEQTflRBZkiQ4mh5bTqSWJFXGk6GSayngPpem8pN+JqIOKw3RRUVQ1caTodSLK\nyrAoDKfTwntChQHk40mOlJ4mnsa6HaZNExVS2sZN2LW/U2Mm+HnHR2HffVYZd6tYB6U11ljB+5Xx\nlJRkK5RlGQY6hXA4tVIQFIIkUtS1z6K6WdTe9S8qL0ukZUMfF1Slz2w6acQi95YTeVm20j1b2x0i\nrRgNJEz8V1zbG7RCrUVpyEvDeFq0DrZ+uNaXybZHnkV3eafHnYMZR+OCTfyM1KLwNHeA3d1eCAaO\noqrbc26uiM/KBDuBlWec1+gra1+G62YxQkjSWJOHGafN4HY7ni0dezf6EXEgPCwKQ1X7HlccRWwO\nMrTyZok62KqvXv9OshyqbXpYD5di1/js4+krzK6xBk1D/v07SatWCo1q9urd+IfdmZ9R03arrX7/\nsHm18VkCP5jq/y6HUJv9CET7ul2hTrdeR3I5TGtbWfIlGaHJ+qRcJSC49nsaYoEUS0LGKkV7Vc18\n5SRX/zyCVpH9vIFYKZckkRXiRHvdPkw6fI3PLZ5opvTnf/7nfP/730cIwR/90R/x5S9/uX3t3/27\nf8df/dVfoZTilVde4Q//8A+f5KGt8RTBGEMdfPsiLc/K2rQGdARLby/Nk8YPseIIqtdhsW6sxpu1\nNE28KoLPPAxaSa8+bn3ZTwjBySTn3uGcfjdiY5BxeafH4WlOHKnApHPe/bb0qt7dNOZ4suC9/ZzN\nQUK/E7E9SpktKjpZxCKvmM4r/z0C6tpx696YLIuYzP1w69ULfTb6Ca+/dcj+0YJIS3Y2Ml/C0wqh\nBL1uzGJReRUIJdBSMJlXDLrxMlOUPiOTovLOs8aLwSolSWJ//U6nJYNuFHpLyvePArNPSsGon1CW\nhjTRbTkuTRR17UuC73utgyBug6ehdPc04YkFpb/+67/m5s2bfPe73+XNN9/kj//4j/nud78LwHQ6\n5d/+23/Lf/7P/xkhBN/+9rf5u7/7O77yla88qcNb4ylCO6t0zmtNMNLBWM+s0J7V2XXyTDblrEVp\n1S6uUkqU8v0max1G+FmbKBJtpnI6Lb34q3HtYj3sxZS1I1OSRHu6unN+yFYpSai2eYZcolFKsjFI\nMdZ5VQcTJHv8mVLWlsnhHBD0uxE7owwhvOyPwxMiOqkOgcUQK40Svnxmaxt6OMHTKUgnwZIenyS6\n1fFrdOviSEHozVXGb1PB2mI1gCgpSGN/U2CMgUDPT2L5CPnEPfRYrOwDfCb3YYSVzzo+iH33WWfc\nreKJBaXvfe97vPrqqwA899xzjMdjZrMZ3W6XOI5JkoTpdEqWZeR5/plu1K3x6UXjpYR1j2Q+1jkO\nT3Oq2luLd1Ltm/qBVl3WXi28gacrO4rKUQRHVa1k048nDZ5D89zgKuimXnaoti4QDiIGvYhRL20N\nAONOTF7WzHNDWTvKqiQva4QUxFpxYbPLLCvb4Z8sUUgpOZnm/PCdY8rKcOPSgE6sUFLx4GRBURl2\nRxmbww6n05LaWEb9lH4notvx7Ln7RzOOxwVJrNgYJEgp2OgnjHreeXZe1DTFxLRRnQCyOKaTNKaA\nEmcdSeKDUln7DLGZhfJitl6R3VrHwemCqrYMOrHPWIHkocC1eq3bkmaY2ZKi0S5c/rbqcxyY3o99\n93lg3K3iiQWlg4MDXnnllfb5xsYGBwcHbVB67bXXePXVV0nTlF/5lV/h+vXrT+rQ1njqIELf5qG7\ncetW5HcalWraUtHDy51/XeLcoz2eVSuGZtEU0u/FOduqjWdptBIcRfu3yQxqY9uhVxfiYax9sPMB\n1n92PCtbJW4tRVtSmweCQZb6f+q1da1vVCeNWjq3MX4AtihNG0Q6iV7pRQmsbc7Bo527WpkZimPZ\nPo/CNilX3Xf9X+uW17rpZ/kM6P1FWc9kWatv+YDe4OcJ78e++zww7lbxibHvVpvM0+mUf/2v/zX/\n8T/+R7rdLr/1W7/Fj3/8Y1544YUP3Mdf/MVf8J3vfOfjPtQ1Pkf4oEFZKQVprNohzdXt5zb6aTTq\nPBvMGosNjDXngmoBtErgjYwReKsKYx3CrWjrtXf8tj1WrQXGBuPBMFebJl4TzziHMQatFLujjINR\nTl56KroUkkhJNvoxs0XNbFHSy+LWsl3KoGYhfFDw4rIyOPDWLYsuiRVSCrSUlNYym1eQeYq896EK\nShGBqr0oLFkiEG3GsgxI1jrmRU0nidprXdW21ehzIZBGwjPwEA3lW5y5Rs0Nw6omYaNpCP5m47Pa\nZ1qvaU8wKO3u7nJwcNA+f/DgATs7OwC89dZbXL16tY30P//zP8/rr7/+oUHptdde47XXXjuz7dat\nW3zzm998zEe/xucFjYDo+92Nbw1TrHNnsqhISZx8/8+kiaYoaxCCapWxFgZZYy3D4u413ZzzA69a\nglLLPhTAyaRo6eDdVNFJIrLgzQRLNYM0rjg4zckry2ai6XU6/NIwZV4YlJKUlfd+6nZi7h3OyEvD\n/aMZo14YuM10+91H44WX/HGOw3HB0bjg5Wc3qa1jMq/Y6Cd0Us39O2MOxzkC+OIzmz57Mctjr2sv\nVVRWhkEo+9mQdTnnOJkWwfbD6/ztbXbaa11UNXnhNfAcymdw7mzG2bL5eHRbVdugYAGd9LM76bJe\n054gJfwb3/gG/+E//AcAfvCDH7C3t0enE2YoLl/mrbfeoix9+eH111/n2rVrT+rQ1njK8GF30Q+X\n9c77jHOOovTeRwCqZZXR9j5U6C95NlxD3fZZQR0UF2pjMNYP1Rpj28wkiT1bz1jL3cMZ41mJEP7Y\nnHPklQkZAVhEa93uB0ttm51UlWlJFINuQqxlUC1X7fH2shhrHbX1EkFSwv2jOXXt3WxnecV8UTGe\nF1hr6XejEARse+zgmYzOOcraMc+9F5P/bp/FJLGiNoa3bp+wf+zVKnBNL0iitTijjm6DtJMxhrxY\nXmvrPBmlKGuqyg/rRqo5r89mhrTGEk/sluKrX/0qL7/8Mr/+67+OUoo//dM/5S//8i/p9/u8+uqr\nfPvb3+Y3f/M30Vrz1a9+la997WtP6tDWWOOnRhEcZo0xqNSXtyQrVg6h/qRWhEd9hibBWcaFz4aE\noB2EBb+wb/SX1Ou3bp9yPCk5nZbsbOx4W/Sg2A0wCHI+RbUMRD7QERTM/Y3eld0uaVAMz86QAbyb\n7O39KYvCoCQYKzg4yemkEf2O4GRSttnW5iBlc5AF193lcSeRr1EqZSkry3hm6XdidCB21MaQRIo3\nD+ccTQqOJwW/9HOXz9Dx01iHeSwfZJuKaV7UvkdmLSoMMBelabPSOJJIJZGBlv9ZLd19GM5j36VZ\nwmI+/4SO6OPBE81zf+/3fu/M8xdffLF9/K1vfYtvfetbT/Jw1ljj8WKFHbYyObp8ubG9OO9Dq1tW\nPuNcoDyvzt6uPD5v+W1VvFcerw7zntdXW1pyLI9wlWLdDuGe+cKGmvDBx3Pmy5py3Lk9OnGmXPdB\nsOfs9LwM9/OEh9l3S9bdjc88424Vn93i6xprfIKII0lZW1Sw8bbWG/Up6ctPqwu/dSDDDI8xlrKs\ng6+QCMO7rawb4EtqDj/8em2vR6wlo4E37SsrPzvUUKir2hLHiiSSWAOH45x7x3MubnXJYoXoJ8xz\nr76ttaSXapQUFLXPrEQ4l5ef3eQn752QRAproagMz18eMplXHE9ykkiRpZrNUUasJXlZczQu6XUi\nitIwWcDOqEMnUQigtnA8yelnMdO88oPKSvLC1ZF31411GK6NfSa5cm3zsubwZEEca4a9mCzVlJW3\nTpdCUNaGorJoKby+4Oc7FrV4mH33eWPdNVgHpTXW+BngyQbLUkqjBm4d6NDrMSvZQCMsWlaGyvgy\nXzP8ugrBkoxRWi9geuNSnzjy/1QXRQmIM/NSUbCvsNLx4HiBMd7NVqYRWeKZbE0PKA5qEpVxWJYq\nClJKrl8cMM99WfHCVoZW3up9vu/daC/v9khijbWWvPQ6fpN51Yqubg8tWmviCFxlMQZOZ2UbbNNY\nopTkxqUhRek184Y91/aQwGdsp9OCvLIUVclmP/Hq63KpvJEXpmXnZUnEGp8vrIPSGms8Bmjtla0b\nIsLD5ScHzBaVnxsS0O8sZ4BWS1ard/1Zon0/xUJZGqQSdLOIojI0q7JWgiTWlJV3hd3bzKiM7+cI\n4e3VB92Ik2lBbRzjeUmkZJvVdZIo7N9/j8+IFOAZcULA1b0+eVmjpKSufdAadBPKyhBHXhboZJJz\n8+6UrVFKlkaepGE8tV5J6GTen6ksDQJBEsnAkhMUZc28NEigl3nViSypcNb37qSyrWJDEvnzKUpD\nFCwxPq89pKcV66C0xhqPAVII5IoOkT2nKdKQI6QQaOUzFsFKL2RlbW0Gd4UUOOuJEzKQALT0s0vg\nZX6k8GW9orIgREv7FkAc+3/ikVJUdR2Gdl2wg1/K+VTGU9Wl8B5I4BUYrAs25mEg10EgVIigWQcI\n4b+bs067ArCAjiRarTjx4rPBJmsrauuHd/2J+ywy1pS17xw1w7zNrJiUkixda0l/XrEOSmus8YSg\nle9DrZqmflA/36tme6wmA6uD56a2CC1DictnaUFF6QxRIdISWdK60tbG0UwYWesp3E2J0ISMr1Ej\nPyOeYJfPJQKLI9bSZ3Vl3fbHrHPelVdKnHFtRtNIPDVdpNVzbGSDmtJcAylpmYXNZ4y1rXJEs+8l\nWcO1MkSfpyxqlX33eWTdNVgHpTXW+BjQBIZVDHoxWararME9FDhW0SysUaSQ1hKFz5yMC4oglGoc\nTBc1nVQHQVav1RdHqjXJAz8T1e/GJJHAhWyrLE2rVPG3/3Cf01nF85eHbA4zxtMKYw15aYm0oJPG\nCCmwte+HAYx6cfA+cqSJZmcjY57XdLOIk0nB7QcTrIMLWx2MU0wXNYNORDeLSEyj4iC8qaF1RIrW\nr8oHVEkc+WCsVbCVbz5TVJ6kIWzbk9MKlBDtdQN//T9PY0sN++7zyrprsM6B11jjMcIPe9pH7tCb\n2BNp1d7Vf1RV66bJL4Roje/iSBHpMJAbVl67omsX64YV6IJtu6MILrP+M0vWYGPvniV6JWvxj5JI\nt8GgeV2KZVZT1rZ13222RdpLCJ09/+X5arUkLWi1so2lf9XDXlerx7uaNf20aFTbP4vY2t5jd+8y\n2zt7Levu85QJNlhnSmus8ZhQVqYNClki2nIa/PRlJCEEstHQW/loN9NkiWyFWJsSmTUFx7MS6yCL\nFVL77Gn/JMdYx8mkYJ7XSOGzFyk9EaGy8NyVDZ67PPJ26M4F1qBi0IlJQsByzou/ppHXBrQOFnlF\nUXnFh1irVvYniTU3Lg05mSwFYvvd6NxAncQaKX3vqNHQC18Y/oIMth/OOfIwdKwCnd7r44kV0sj5\n1w04I+e0Jkh8erEOSmus8Zhw3sDn2UHYRxfCD1ocW5Xyh7bJFXp0E5yMXVEjD1mVs7alpZsVynrT\nsFlNGB421YNldnLmPFaOpy2T2UfP3R+nf63JtD7oHD9oWHYZSJaPpWSp3n7ONTrv6z6b+dHTh3VQ\nWmONxwSthVdgELBqReecozaORVnTSfRKT8n3P4RzrfL1h8Fr5lWksR+CNWHmadCJqKqa0jTCpIbJ\nrKCqauJYk8R+yPT/b+/cY6y66j3+XWvvfV7zAIbHUOFWaa+laR0pqEHhJtgW0ZuSNiYSq6aNjamP\nJmhLiCLEWo1IjdHYwF+k0UQTg7YpCcZHjUhMmhCL2lIhppEa8XJ7h2GcNUSyNgAAG7FJREFUzsA8\nzmPvte4fa6999p5z5sEwc84+Z76fhHDOPnvv89srJ+s3v7V+v+8v45lGg0oBnguIQGCiFGB0rISl\nXUaMVimFrOcYBXBl6omKJR/dHVlopSMNvs68h9EJU4ckYJYRBUw79vGij2tjZXTkMyiWAniuKd4N\n/LCBotZQMtn2wqJtkoQw9VdBoCFgMhCNTclMiHpRUb17Jt/PfA1pDnRKhMwTjpRwsvW3aa+Om8nb\nlUEiPRoIU6RnOUOOjldCLTkfHaEatgDgeg56l3eYthsABocnMHS1BAAo5I1qQiEvsKTDqHdX/ABK\nm+64bw6OhRN9KdqzWtrlwnUcjE1UMPDWBACjyGDTw7OZajO+8aIPjbA9uhS4Nl7G/w6MAjARmOs4\nuDpWQVfBFLr6fgDpyDCTL+wJpVQ0Hn64TxXANGLUMM7YcWRCJ9CM+ezGLR4VtmojQJt9p7XfbFMW\nFDolQhpAV8FDsZjsXGsz9OwG/+SUZqCq8GDpLHhh+raT6MQaT4NWGljSlYV0JAS0KTatBMh5DgKl\n4fuBSU0Xxrnc3NuJ/n+Pm5qosLfSyLUyOgoZZDyJVcvyGLpaRLEcQIXPIgUiNQgBs3c1Ol7C8qU5\nLO3IwL2pC8NXS6bVutLwbDNBpVBWgBNoZDyJQAFSmI6xUptU8lzORSXMDrTPo8NrHWF6NQWBgu/r\nKPqTdSKuOFONdSuhlI+x0RH893+tb8usOwudEiELjBBGFsjrkInJ0G7K1+4zxS9O3st1JDrymei9\nrcWJF5aqwNTwLO3MRqnX8QijVDEyPa4n4DoSbj6DzkIFxbKJUNxQ8UEFCp7ropCTGJvwo3bj9l7V\nlhMOro2bpIYVEHBdB0s7nVDdAmHfKBldY/a/NLKhTJMM98kAQNqao0z1wW29lNYwSuBWJinaZJrZ\nwUw11q3E8hW9yOULbZt1Z2FKOCENYqomgdMyh935+B3r3T5euGr/2eVD05HWnGdUKXRiP8YkNYTH\nws+lEPDC1O5AVe9ZLfyt89y6+mx+7Br7XfHX9UZITLMEN1VaeTtP5O0EIyVCUka8/frkWqa4yCtQ\nnWjj13iuDOWMALNrk6Sz4KFY9uG5TrRMuKw7B3e8bKR/YARcXVeiVAlQKpu2554rkM+ZFuYIM+Yc\nab7vP/9jGQaGx+FIgYlyBa504Hmms60t5q34phmfIzRcz3i/8WIF48UA+awDz5VQYSLF8GgZriPQ\n21NIPE+1A6/Z05KitsWGlUxypY6aGZLWgZESISlEytriWhsBACbDDVrVvcZq6tnU6MnXxCV5LEIY\nsVfXMZJF+axpwR6ESQdR8awQUFobsdXo2rA5YWc2vKZaD2RF0G3hq7XJCtfauq5iqRKJvVoFct/X\nYbZfNS3djIEO7137HLaDLzCzhJNSuiaaIs2HkRIhLYCdwDWqeyxKG6mdyZv8pUoA31cQorqXE79m\nZKyIckUhn3XQ3ZGJjjtCQIvqPtV40UfZN8twHXmTyh4ECuVwTyqXERBCRtFWNuPCDarSP+WKCttm\nVCKh1nLZiMI6FYVC1kVHzsPYRAXFCjBa9LFySQ4d+TxKVoWioszzBGaZsJA3yuLxiNEqiAeBEaXV\nOpQdmib5Icp8bCEporeG/o1sfgJa39xsUxYUOiVCWoR6f9PX2yexkcRUQYCVGkrURoWFOyJ2vCrZ\nWpU6UrG2HObaZOKGG0uoiIsz2NdWIigp9aOjc2xhsOvIyM7oeaZQarDvzX6WeS3rRIOtjlI+VNDe\n6eAAl+8IaRmiFHD7T9QWhQJWWy5c3kLtNbmw1ii+HOb7flQ4q8JjAnapzdQWaW3qhmTovPxAhVp0\n4ZJZzAuV/QDlSlUSKEqkCO+XCW2w9jpGMQhjE5UwSSG2PBjOUkGgwyitthBWRwXI1XGZbmlOTPq/\nFVi+ohcrVva2nbOdDCMlQloAm9Zta2ym09TzXAnXSbZyiF+T6cwmjk2UzF/fQgWmg22go/0dT5ql\nrrKvIB3TByqXRbi8ZpboLE7WqEyMl3xceasIAFixxEE260UqD64r0eEJ5LJm2fDaeBmOY+wdmahg\nouRDStOryRH2GV2UKxVMlAKMlwL09uRqutUGSofK4tX9p+lUwm1333af4FsROiVCWogaLboZzotE\nSGMp2koFUaFtLF8BGdeBChfsMp5EqRwAsMkSGhOlAPmsaTKYDYVZLY4QYZ6fQMaVWNLhYbzkI+MZ\n5xGEe0JKa0jpRPtAuYyDsWIFoxM+fKWQjeqZFFzbLwlAIecmlg2T3X3Ns+k641Jd+jNj4CtzrudK\nOqSUQqdESJuitUZy58ZgfYlZfjOvjRxQMvqoVBQC2whQAzowrSoyORdOuOejwj2ebLYqO+Q6DpZ0\nSnR3ZE3vpkrYcTd0Zo400kGmzYWDq6NjuDpmim9vuqkQ2W5aclh3I7GkU0bLjvFEB6t6MTlyij8z\nYNLc7XG7xEnSB50SIW2KmaOT4qVTUbfIN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "columns = [r'$\\theta_{0}$'.format(i) for i in range(3)]\n", "df_2D = pd.DataFrame(trace_2D, columns=columns[:2])\n", "\n", "with sns.axes_style('ticks'):\n", " jointplot = sns.jointplot(r'$\\theta_0$', r'$\\theta_1$',\n", " data=df_2D, kind=\"hex\");" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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l4P1TxKnGdUygc/z8CpvGq+hMjzFSD4q+GXmJqlK6eDIKdLGma7FcjulEabxG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\nwl7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df_3D = pd.DataFrame(trace_3D, columns=columns[:3])\n", "\n", "# get the colormap from the joint plot above\n", "cmap = jointplot.ax_joint.collections[0].get_cmap()\n", "\n", "with sns.axes_style('ticks'):\n", " grid = sns.PairGrid(df_3D)\n", " grid.map_diag(plt.hist, bins=30, alpha=0.5)\n", " grid.map_offdiag(plt.hexbin, gridsize=50, linewidths=0, cmap=cmap)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These samples give us a good idea of what the posterior for each model looks like, but we still must integrate this posterior to find the Bayes factor.\n", "\n", "For these lower-dimensional models, we'll do direct numerical integration using tools from the ``scipy.integrate`` package to integrate the posterior and compute the odds ratio. \n", "The call signature of the multiple integration routines is a bit confusing – I suggest referring to the [scipy.integrate documentation](http://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html) to read about the inputs." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy import integrate\n", "\n", "def integrate_posterior_2D(log_posterior, xlim, ylim, data=data):\n", " func = lambda theta1, theta0: np.exp(log_posterior([theta0, theta1], data))\n", " return integrate.dblquad(func, xlim[0], xlim[1],\n", " lambda x: ylim[0], lambda x: ylim[1])\n", "\n", "def integrate_posterior_3D(log_posterior, xlim, ylim, zlim, data=data):\n", " func = lambda theta2, theta1, theta0: np.exp(log_posterior([theta0, theta1, theta2], data))\n", " return integrate.tplquad(func, xlim[0], xlim[1],\n", " lambda x: ylim[0], lambda x: ylim[1],\n", " lambda x, y: zlim[0], lambda x, y: zlim[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The tricky part of the integration is choosing the integration limits correctly; fortunately we can use the MCMC traces to find appropriate values.\n", "We'll use IPython's ``%time`` magic to record how long each takes:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 228 ms, sys: 3.96 ms, total: 232 ms\n", "Wall time: 226 ms\n", "('Z1 =', 46949483.80874676, '+/-', 0.0005413387407315895)\n" ] } ], "source": [ "xlim, ylim = zip(trace_2D.min(0), trace_2D.max(0))\n", "%time Z1, err_Z1 = integrate_posterior_2D(log_posterior, xlim, ylim)\n", "print(\"Z1 =\", Z1, \"+/-\", err_Z1)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 39 s, sys: 27 ms, total: 39.1 s\n", "Wall time: 39 s\n", "('Z2 =', 111087202.77356707, '+/-', 0.00990512464341009)\n" ] } ], "source": [ "xlim, ylim, zlim = zip(trace_3D.min(0), trace_3D.max(0))\n", "%time Z2, err_Z2 = integrate_posterior_3D(log_posterior, xlim, ylim, zlim)\n", "print(\"Z2 =\", Z2, \"+/-\", err_Z2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Bayes factor is simply the quotient of the two integrals:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('Bayes factor:', 2.36610062053273)\n" ] } ], "source": [ "print(\"Bayes factor:\", Z2 / Z1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Bayes factor favors the quadratic model, but only slightly (an odds of about 7 to 3).\n", "In fact, this value for the Bayes factor ranks as \"not worth a mere mention\" according to the scale proposed by [Kass & Raferty (1995)](https://www.andrew.cmu.edu/user/kk3n/simplicity/KassRaftery1995.pdf) an influential paper on the subject.\n", "\n", "$$log_{10}(B_{10})$$ | $$B_{10}$$ | $$Evidence\\,against\\,H_0$$\n", "---------------------|------------|---------------------------\n", "0 to 1/2 | 1 to 3.2 | Not worth more than a bare mention\n", "1/2 to 1 | 3.2 to 10 | Substantial\n", "1 to 2 | 10 to 100 | Strong\n", ">2 | > 100 | Decisive\n", "\n", "Notice that this interpretation is very similar to what we found with the frequentist approach above, which favors the quadratic model but has too large a $p$-value to support discarding the simpler linear model. Indeed, at the risk of causing die-hard Bayesians to cringe, you can argue roughly that the equivalent \"Bayesian $p$-value\" assosiated with this odds ratio is" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('Bayesian \"p-value\":', 0.29707965171930506)\n" ] } ], "source": [ "print('Bayesian \"p-value\":', Z1 / (Z1 + Z2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is, the posterior probability in favor of the linear model is about 30%, which is not low enough to support rejecting the simpler model.\n", "I put \"$p$-value\" here in quotes, because while a classical (frequentist) p-value reflects probability conditioned on the models, this Bayesian \"$p$-value\" reflects probability conditioned on the data, and so the detailed interpretation is very different." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Other Bayesian approaches\n", "\n", "While direct numerical integration of the posterior works for low-dimensional models, computing Bayes factors for higher-dimensional models requires either a more sophisticated method, or an approximation of the integral.\n", "For very high dimensional models, this is actually a very hard problem, and an area of active research.\n", "Here is an incomplete list of approaches you might turn to in this case:\n", "\n", "- [Nested Sampling](https://en.wikipedia.org/wiki/Nested_sampling_algorithm) is a sampling-based algorithm like MCMC, which is specially designed to compute Bayes factors.\n", "- [Reversible Jump MCMC](https://en.wikipedia.org/wiki/Reversible-jump_Markov_chain_Monte_Carlo) (also see *bridge sampling*) can be used to sample multiple models in the same MCMC chain, so that the Bayes factor can be estimated directly from the joint trace (see, e.g. [this paper](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.399.8889&rep=rep1&type=pdf))\n", "- **Posterior Predictive Checks** are an interesting means of assessing the fitness of sampled posteriors without having to explicitly compute the integral, by empirically comparing the [Posterior Predictive Distribution](https://en.wikipedia.org/wiki/Posterior_predictive_distribution) to the data. For a technical but relatively approachable introduction, I'd suggest this [1996 paper by Gelman](http://www.cs.princeton.edu/courses/archive/fall09/cos597A/papers/GelmanMengStern1996.pdf).\n", "- [the Bayesian Information Criterion (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion) quickly approximates the Bayes factor using rather strong assumptions about the form of the posterior. It is very similar in form to the Akaike Information Criterion (AIC), mentioned above.\n", "\n", "Again, I will not demonstrate any of these techniques here, but my hope is that this post has given you the background to understand them from other available references." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Note On the Example Data\n", "\n", "In case you were curious, both the frequentist and Bayesian approaches landed on the correct answer, in the sense that our data actually was drawn from a straight line.\n", "Here is the function I used to generate the data used in this post:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "\n", "def generate_data(N=20, rseed=1):\n", " rng = np.random.RandomState(rseed)\n", " x = rng.rand(N)\n", " sigma_y = 0.1 * np.ones(N)\n", " \n", " # linear model with noise\n", " y = x - 0.2 + sigma_y * rng.randn(N)\n", " return np.vstack([x, y, sigma_y]).round(2)\n", "\n", "data = generate_data()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you *really* want to get a feel for how these methods work and respond to different inputs, you might wish to [download the notebook](http://jakevdp.github.io/downloads/notebooks/FreqBayes5.ipynb), and re-run the analysis with different functional forms or random seeds.\n", "In particular, you might think about how the above plots might change if the data were actually drawn from a quadratic function.\n", "Do the actual results match your intuition?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Some Final Thoughts\n", "\n", "My hope is that the above examples give you a flavor of the essential aspects of model selection within the frequentist and Bayesian paradigms.\n", "To summarize, I want to offer a few observations:\n", "\n", "**Model comparison is mainly an exercise in preventing over-fitting.**\n", "Though the value of the maximum likelihood may seem, at first glance, to be a useful metric for comparing models, when the models differ in degrees of freedom this intuition is misleading.\n", "The frequentist approach addresses this by devising and computing some statistic which implicitly or explicitly accounts for model complexity.\n", "The Bayesian approach addresses this by integrating over the model parameter space, which in effect acts to automatically penalize overly-complex models.\n", "\n", "Frequentist and Bayesian model selection approaches have complementary strengths and weaknesses:\n", "\n", "**Frequentist model selection** generally relies on the selection of specifically-constructed statistics which apply to the particular data and models being used.\n", "Because any particular statistic is only applicable in a narrow set of cases, an effective frequentist statistician must have a depth and breadth of knowledge about the properties of common statistical distributions, as well as a well-honed intuition about when to choose one statistic over another.\n", "This breadth of required knowledge is, in my mind, one of the weaknesses of the frequentist approach.\n", "In particular, it all but invites misuse: because so many people who deal with data on a daily basis do not have an advanced degree in classical statistics, it is common to see statistics like the $\\chi^2$ applied without due consideration of the assumptions required by the statistic.\n", "On the other hand, the frequentist approach does have the advantage that once the correct frequentist statistic is found, the results can often be computed very efficiently.\n", "\n", "**Bayesian model selection** takes a much more uniform approach: regardless of the data or model being used, the same posterior odds ratio approach is applicable.\n", "Thus, in some senses, the Bayesian approach is conceptually much easier than the frequentist approach, which is perhaps why it appeals to so many scientists.\n", "The disadvantage, of course, is computational complexity: integrating the posterior, especially for very high-dimensional models, can be very computationally expensive, and this computational expense makes it tempting to take shortcuts which might bias the results.\n", "\n", "I hope you found this discussion helpful, and thanks for reading!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "This post was written entirely in the IPython notebook. You can [download](http://jakevdp.github.io/downloads/notebooks/FreqBayes5.ipynb) this notebook, or see a static view on [nbviewer](http://nbviewer.ipython.org/url/jakevdp.github.io/downloads/notebooks/FreqBayes5.ipynb).\n", "" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }