lectures/Week-05.2-Bayesian-Model-Selection.ipynb

{
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   "cell_type": "markdown",
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     "slide_type": "slide"
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   "source": [
    "### Astrostatistics, University of Washington\n",
    "\n",
    "\n",
    "# Week 5.2: Bayesian Model Selection\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Model Selection\n",
    "\n",
    "We've fit a straight line to our data; but **what if we have a competing model?**\n",
    "\n",
    "For example, how do we know that we should fit a straight line to our data and not, perhaps, \n",
    "a parabola, or y=sin(x), etc? \n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "## Let's use Jake's excellent example from\n",
    "## http://jakevdp.github.io/blog/2015/08/07/frequentism-and-bayesianism-5-model-selection/\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set() # set default plot styles\n",
    "from scipy import stats\n",
    "from scipy import optimize\n",
    "\n",
    "# this function computes polynomial models given some data x\n",
    "# and parameters theta\n",
    "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))\n",
    "\n",
    "# compute the data log-likelihood given a model\n",
    "def logL(theta, data, model=polynomial_fit):\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))\n",
    "\n",
    "# a direct optimization approach is used to get best model \n",
    "# parameters (which minimize -logL)\n",
    "def best_theta(degree, data, model=polynomial_fit):\n",
    "    theta_0 = (degree + 1) * [0]\n",
    "    neg_logL = lambda theta: -logL(theta, data, model)\n",
    "    return optimize.fmin_bfgs(neg_logL, theta_0, disp=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CHI2:\n",
      "   best linear model: 11.324128378349815\n",
      "best quadratic model: 9.462835218566871\n",
      "    best cubic model: 8.99360837038816\n",
      "CHI2 per degree of freedom:\n",
      "   best linear model: 0.6291182432416564\n",
      "best quadratic model: 0.5566373657980512\n",
      "    best cubic model: 0.56210052314926\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate (x,y, sigma_y) \"data\" \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\n",
    "Ndata = x.size\n",
    "\n",
    "# get best-fit parameters for linear, quadratic and cubic models\n",
    "theta1 = best_theta(1, data=data)\n",
    "theta2 = best_theta(2, data=data)\n",
    "theta3 = best_theta(3, data=data)\n",
    "# generate best fit lines on a fine grid \n",
    "xfit = np.linspace(-0.1, 1.1, 1000)\n",
    "yfit1 = polynomial_fit(theta1, xfit)\n",
    "yfit2 = polynomial_fit(theta2, xfit)\n",
    "yfit3 = polynomial_fit(theta3, xfit)\n",
    "# and compute chi2 per degree of freedom: sum{[(y-yfit)/sigma_y]^2} \n",
    "chi21 = np.sum(((y-polynomial_fit(theta1, x))/sigma_y)**2) \n",
    "chi22 = np.sum(((y-polynomial_fit(theta2, x))/sigma_y)**2) \n",
    "chi23 = np.sum(((y-polynomial_fit(theta3, x))/sigma_y)**2) \n",
    "# the number of fitted parameters is 2, 3, 4\n",
    "chi2dof1 = chi21/(Ndata - 2)\n",
    "chi2dof2 = chi22/(Ndata - 3)\n",
    "chi2dof3 = chi23/(Ndata - 4)\n",
    "\n",
    "print(\"CHI2:\")\n",
    "print('   best linear model:', chi21)\n",
    "print('best quadratic model:', chi22)\n",
    "print('    best cubic model:', chi23)\n",
    "print(\"CHI2 per degree of freedom:\")\n",
    "print('   best linear model:', chi2dof1)\n",
    "print('best quadratic model:', chi2dof2)\n",
    "print('    best cubic model:', chi2dof3)\n",
    "\n",
    "# plot \n",
    "fig, ax = plt.subplots(figsize=(16, 8))\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.plot(xfit, polynomial_fit(theta3, xfit), label='best cubic model')\n",
    "ax.legend(loc='best', fontsize=14)\n",
    "ax.set(xlabel='x', ylabel='y', title='data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "$\\chi^2$ per degree of freedom was computed as \n",
    "\n",
    "$$ \\chi^2_{dof}  = \\frac{1}{N-k} \\sum_i^N \\left( \\frac{y - y_{fit}}{\\sigma_y} \\right)^2, $$\n",
    "\n",
    "where $N$ is the number of data points and $k$ is the number of free model parameters (2, 3, and 4).\n",
    "\n",
    "For large values of $(N-k)$ (larger than about 10), the distribution of \n",
    "$\\chi^2$ per degre of freedom is approximately Gaussian centered on $\\mu=1$ and the width of\n",
    "$\\sigma=\\sqrt{2/(N-k)}$  (here, $\\sigma = 0.33, 0.34, 0.35$). \n",
    "\n",
    "The values of $\\chi^2$ per degre of freedom for the three models are: \n",
    "\n",
    "   best linear model: 0.629 \n",
    "\n",
    "best quadratic model: 0.557\n",
    "\n",
    "best cubic model: 0.562 \n",
    "\n",
    " \n",
    "**Which model should we adopt?**\n",
    "\n",
    "Obviously, the cubic model has the lowest $\\chi^2$ (\"fits the best\"), but \n",
    "it has 4 free parameters while the linear model has only 2 free parameters.\n",
    "\n",
    "**How do we trade improvement in $\\chi^2$ with increasing model\n",
    "complexity?**\n",
    "\n",
    "**Occam’s razor:** select the simplest model that is in fair agreement with the data. This sounds reasonable, but can we understand why?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bayesian Model Comparison: Odds Ratio\n",
    "\n",
    "That leads us to a discussion of model comparison (see textbook $\\S$5.4 and $\\S$5.7.1-3). To determine which model is better we compute the ratio of the posterior probabilities or the **odds ratio** for two models as\n",
    "\n",
    "$$O_{21} \\equiv \\frac{p(M_2|D,I)}{p(M_1|D,I)}.$$\n",
    "\n",
    "This is the ratio of probabilities that models $M_2$ and $M_1$ are correct, given the observed data $D$ and prior information $I$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bayesian Model Comparison: Bayes Factor\n",
    "\n",
    "As the posterior probability that the model $M$ is correct given data $D$ is\n",
    "\n",
    "$$p(M\\,|\\,D,I) = \\frac{p(D\\,|\\,M,I)p(M\\,|\\,I)}{p(D\\,|\\,I)},$$\n",
    "\n",
    "we can write:\n",
    "\n",
    "$$O_{21} = \\frac{p(D\\,|\\,M_2,I)\\,p(M_2\\,|\\,I)}{p(D\\,|\\,M_1,I)\\,p(M_1\\,|\\,I)} \\equiv B_{21} \\, \\frac{p(M_2\\,|\\,I)}{p(M_1\\,|\\,I)},$$\n",
    "\n",
    "where $B_{21}$ is called the **Bayes factor**. Note how $p(D|I)$ cancels out, since it's the same for both models.\n",
    "\n",
    "The Bayes factor compares how well the models fit the data: it is a ratio of data likelihoods averaged over \n",
    "all allowed values of the model parameters; if two models fit the data equally well, the \"winner\" is decided based on priors. For example, consider a noisy image of a source which is equally likely to be a star or a galaxy. \n",
    "The posterior probability that the source is a star will greatly depend on whether we are looking \n",
    "at the Galactic plane or not!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "How do we evaluate $p(D\\,|\\,M,I)$?\n",
    "\n",
    "We start with conditional probability:\n",
    "\n",
    "$$ p(\\theta, D, M, I) = p(\\theta \\,|\\, D, M, I) \\,p(D, M, I) = p(D \\,|\\, \\theta, M, I) \\,p( \\theta, M, I) $$\n",
    "\n",
    "... and more conditional probability:\n",
    "\n",
    "$$ p(\\theta \\,|\\, D, M, I) \\,p(D \\,|\\, M, I) \\,p(M, I) = p(D \\,|\\, \\theta, M, I) p( \\theta \\,|\\, M, I) \\,p(M, I) $$\n",
    "\n",
    "cancel out $p(M, I)$ and then integrate (a.k.a \"marginalize\") over the model parameter space $\\theta$:\n",
    "\n",
    "$$ p(D \\,|\\, M, I) \\int p(\\theta \\,|\\, D, M, I)\\,d\\theta = \\int p(D \\,|\\, \\theta, M, I)\\,p( \\theta \\,|\\, M, I)\\,d\\theta $$\n",
    "\n",
    "and once we notice that that the integral to the left sums up to 1, we're left with:\n",
    "\n",
    "$$ p(D\\,|\\,M, I) = \\int p(D\\,|\\,M, \\theta, I) \\, p(\\theta\\,|\\,M, I) \\, d\\theta, $$\n",
    "\n",
    "(note we could have started with the Bayes theorem, saving us $\\sim$one line of math; I personally find starting with conditional probability less confusing and error-prone)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Evidence\n",
    "\n",
    "The expression we've obtained:\n",
    "\n",
    "$$ E(M) \\equiv p(D\\,|\\,M, I) = \\int p(D\\,|\\,M, \\theta, I) \\, p(\\theta\\,|\\,M, I) \\, d\\theta, $$\n",
    "\n",
    "is called **the marginal likelihood for model $M$** and it quantifies the probability that the \n",
    "data $D$ would be observed if the model $M$ were the correct model. It's the denominator when writing out the Bayes theorem for a given model and prior information:\n",
    "\n",
    "$$ p(\\theta \\,|\\, D, M, I) = \\frac{p(D \\,|\\, \\theta, M, I) \\, p( \\theta \\,|\\, M, I)}{p(D \\,|\\, M, I)} $$\n",
    "\n",
    "In the physics literature, the marginal likelihood $E(M)$ is often called **evidence** (despite the fact that to \n",
    "scientists, evidence and data mean essentially the same thing). \n",
    "Since the evidence $E(M)$ involves integration of the data likelihood $p(D|M,\\theta,I)$, it is also \n",
    "called **the global likelihood for model M**. It's a weighted average \n",
    "of the likelihood function, with the prior for model parameters acting as the weighting function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example\n",
    "\n",
    "The following plot shows the likelihood $p(D|M, \\theta, I)$ for a sample drawn from Gaussian distribution (i.e., $\\theta$ represents the pair of parameters $\\{\\mu, \\sigma\\}$). \n",
    "\n",
    "![BayesSlide1](figures/Lgauss.jpg)\n",
    "\n",
    "The evidence for model $M={\\rm Gauss}$ is found by **integrating** (summing up) this image over $\\mu$ and $\\sigma$.\n",
    "\n",
    "If we think that the sample might have been drawn from some other distribution, we can produce an analogous\n",
    "$p(D|M, \\theta, I)$, say for $M={\\rm Cauchy}$ ([here is an example](http://www.astroml.org/book_figures/chapter5/fig_likelihood_cauchy.html)),\n",
    "integrate it, and compute the Bayes factor, and the models odds\n",
    "ratio (with models assigned equal prior probabilities unless there is a reason that one model is more \n",
    "likely than another, e.g. recall the star/galaxy case) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## How do we interpret the values of the odds ratio in practice?\n",
    "\n",
    "Jeffreys proposed a five-step scale for interpreting the odds ratio, where $O_{21} > 10$ represents “strong” evidence in favor of $M_2$ ($M_2$ is ten times more probable than $M_1$), and $O_{21} > 100$ is “decisive” evidence ($M_2$ is one hundred times more probable than $M_1$). When $O_{21} < 3$, the evidence is “not worth more than a bare mention.”\n",
    "\n",
    "But note:\n",
    "  * These are just **definitions of conventions**, i.e., a way to give a quantitative meaning to qualitative phrases.\n",
    "  * The odds ratio **compares** the models, it doesn't tell us about the *absolute* goodness of fit: model A can be 100x better than model B, but still be pretty lousy.\n",
    "  \n",
    "The thresholds ultimately depend on what action you plan to take given the evidence.\n",
    "\n",
    "If the competing models are \"the plane will survive given this design\" and \"the plane will crash given this design\", you'll probably want to set a very high threshold on the odds ratio (see: Administration, Federal Aviation; CC: The Boeing Company)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Sidenote: Bayesian Hypothesis Testing\n",
    "\n",
    "In *hypothesis testing* we are essentially comparing a model, $M_1$, to its complement. That is $p(M_1) + p(M_2) = 1$.  \n",
    "\n",
    "If we take $M_1$ to be the \"null\" (default) hypothesis (which is generally that, for example, a correlation does *not* exist), then we are asking whether or not the data reject the null hypothesis.\n",
    "\n",
    "In classical hypothesis testing we can ask whether or not a single model provides a good description of the data.  \n",
    "\n",
    "** In Bayesian hypothesis testing, we must have an alternative comparison model! **"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayesian Model Comparison: Example\n",
    "\n",
    "Let's draw increasingly larger sample from a Cauchy distribution and perform Bayesian Model Comparison for Cauchy and Gaussian models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results for first 10 points:\n",
      "  L(M = Cauchy) = 1.18e-12 +/- 5.39e-16\n",
      "  L(M = Gauss)  = 8.09e-13 +/- 7.45e-16\n",
      "  O_{CG} = 1.45 +/- 0.00134\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.stats import cauchy, norm\n",
    "from scipy import integrate\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=14, usetex=False)\n",
    "\n",
    "\n",
    "def logL_cauchy(xi, gamma, mu,\n",
    "                mu_min=-10, mu_max=10, sigma_min=0.01, sigma_max=100):\n",
    "    \"\"\"Equation 5.74: cauchy likelihood\"\"\"\n",
    "    xi = np.asarray(xi)\n",
    "    n = xi.size\n",
    "    shape = np.broadcast(gamma, mu).shape\n",
    "\n",
    "    xi = xi.reshape(xi.shape + tuple([1 for s in shape]))\n",
    "\n",
    "    prior_normalization = - (np.log(mu_max - mu_min)\n",
    "                             + np.log(np.log(sigma_max / sigma_min)))\n",
    "\n",
    "    return (prior_normalization\n",
    "            - n * np.log(np.pi)\n",
    "            + (n - 1) * np.log(gamma)\n",
    "            - np.sum(np.log(gamma ** 2 + (xi - mu) ** 2), 0))\n",
    "\n",
    "\n",
    "def logL_gaussian(xi, sigma, mu,\n",
    "                  mu_min=-10, mu_max=10, sigma_min=0.01, sigma_max=100):\n",
    "    \"\"\"Equation 5.57: gaussian likelihood\"\"\"\n",
    "    xi = np.asarray(xi)\n",
    "    n = xi.size\n",
    "    shape = np.broadcast(sigma, mu).shape\n",
    "\n",
    "    xi = xi.reshape(xi.shape + tuple([1 for s in shape]))\n",
    "\n",
    "    prior_normalization = - (np.log(mu_max - mu_min)\n",
    "                             + np.log(np.log(sigma_max / sigma_min)))\n",
    "\n",
    "    return (prior_normalization\n",
    "            - 0.5 * n * np.log(2 * np.pi)\n",
    "            - (n + 1) * np.log(sigma)\n",
    "            - np.sum(0.5 * ((xi - mu) / sigma) ** 2, 0))\n",
    "\n",
    "\n",
    "def calculate_odds_ratio(xi, epsrel=1E-8, epsabs=1E-15):\n",
    "    \"\"\"\n",
    "    Compute the odds ratio by perfoming a double integral\n",
    "    over the likelihood space.\n",
    "    \"\"\"\n",
    "    gauss_Ifunc = lambda mu, sigma: np.exp(logL_gaussian(xi, mu, sigma))\n",
    "    cauchy_Ifunc = lambda mu, gamma: np.exp(logL_cauchy(xi, mu, gamma))\n",
    "\n",
    "    I_gauss, err_gauss = integrate.dblquad(gauss_Ifunc, -np.inf, np.inf,\n",
    "                                           lambda x: 0, lambda x: np.inf,\n",
    "                                           epsabs=epsabs, epsrel=epsrel)\n",
    "    I_cauchy, err_cauchy = integrate.dblquad(cauchy_Ifunc, -np.inf, np.inf,\n",
    "                                             lambda x: 0, lambda x: np.inf,\n",
    "                                             epsabs=epsabs, epsrel=epsrel)\n",
    "\n",
    "    if I_gauss == 0:\n",
    "        O_CG = np.inf\n",
    "        err_O_CG = np.inf\n",
    "    else:\n",
    "        O_CG = I_cauchy / I_gauss\n",
    "        err_O_CG = O_CG * np.sqrt((err_gauss / I_gauss) ** 2)\n",
    "\n",
    "    return (I_gauss, err_gauss), (I_cauchy, err_cauchy), (O_CG, err_O_CG)\n",
    "\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Draw points from a Cauchy distribution\n",
    "np.random.seed(44)\n",
    "mu = 0\n",
    "gamma = 2\n",
    "xi = cauchy(mu, gamma).rvs(100)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# compute the odds ratio for the first 10 points\n",
    "((I_gauss, err_gauss),\n",
    " (I_cauchy, err_cauchy),\n",
    " (O_CG, err_O_CG)) = calculate_odds_ratio(xi[:10])\n",
    "\n",
    "print (\"Results for first 10 points:\")\n",
    "print (\"  L(M = Cauchy) = %.2e +/- %.2e\" % (I_cauchy, err_cauchy))\n",
    "print (\"  L(M = Gauss)  = %.2e +/- %.2e\" % (I_gauss, err_gauss))\n",
    "print (\"  O_{CG} = %.3g +/- %.3g\" % (O_CG, err_O_CG))\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# calculate the results as a function of number of points\n",
    "Nrange = np.arange(10, 101, 2)\n",
    "Odds = np.zeros(Nrange.shape)\n",
    "for i, N in enumerate(Nrange):\n",
    "    res = calculate_odds_ratio(xi[:N])\n",
    "    Odds[i] = res[2][0]\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# plot the results\n",
    "fig = plt.figure(figsize=(16, 10))\n",
    "fig.subplots_adjust(hspace=0.1)\n",
    "\n",
    "ax1 = fig.add_subplot(211, yscale='log')\n",
    "ax1.plot(Nrange, Odds, '-k')\n",
    "ax1.set_ylabel(r'$O_{CG}$ for $N$ points')\n",
    "ax1.set_xlim(0, 100)\n",
    "ax1.set_ylim(1, Odds.max()*1.1)\n",
    "ax1.xaxis.set_major_formatter(plt.NullFormatter())\n",
    "ax1.yaxis.set_major_locator(plt.LogLocator(base=10000.0))\n",
    "\n",
    "ax2 = fig.add_subplot(212)\n",
    "ax2.scatter(np.arange(1, len(xi) + 1), xi, lw=0, s=16, c='k')\n",
    "ax2.set_xlim(0, 100)\n",
    "ax2.set_ylim(xi.min()*1.1, xi.max()*1.1)\n",
    "ax2.set_xlabel('Sample Size $N$')\n",
    "ax2.set_ylabel('Sample Value')\n",
    "\n",
    "plt.show() \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The odds ratio for the first 10 points is very close to unity ($O_{CG} = 1.45$) and \n",
    "is therefore inconclusive.\n",
    " \n",
    "Why do we get an inconclusive odds ratio? With only 10 points, the probability of \n",
    "drawing at least one point far away from the mean, which would strongly argue against \n",
    "the Gaussian model, is fairly small. As the number of data values is increased, the \n",
    "ability to discriminate between the models increases, too. As the above figure shows,\n",
    "when we increase the size of the observed sample, the odds ratio quickly favors the \n",
    "Cauchy over the Gaussian model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Practical (Computational) Problems\n",
    "\n",
    "Going back to our polynomial example, we could use the same method and \n",
    "integrate (marginalize) the posterior over model parameter space $\\theta$.\n",
    "\n",
    "However, the data likelihood in that example can become cumbersome to track\n",
    "(for the cubic fit, it's a 4-dimensional space to integrate!) and it's much\n",
    "easier to compare the fits using numerical methods such as Markov Chain\n",
    "Monte Carlo (MCMC).\n",
    "\n",
    "We'll introduce MCMC next week (and apply it to this example, too). \n",
    "\n",
    "Meanwhile, let's introduce an approximate method for model comparison."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Approximate Bayesian Model Comparison\n",
    "\n",
    "### Bayesian Information Criterion\n",
    "A common scoring system is the **Bayesian information criterion (BIC)**. It can \n",
    "be derived from the model odds ratio by assuming that the data likelihood is \n",
    "Gaussian (see $\\S$5.4.2 in textbook for details). The BIC is easier to compute \n",
    "than the model odds ratio because it only depends on the maximum value of the data \n",
    "likelihood, $L_0(M)$. For $N$ data points and a model \n",
    "with $k$ parameters:\n",
    "\n",
    "$${\\rm BIC} \\equiv -2 \\ln [L_0(M)] + k \\ln N$$ \n",
    "\n",
    "Interpretation: the 1st term is equal to model's $\\chi^2$ (if the model was Gaussian); the 2nd term penalizes complex models relative to simple ones.\n",
    "\n",
    "### Aikake Information Criterion\n",
    "\n",
    "Another well-known scoring system is the **Aikake information criterion (AIC)**,  computed as\n",
    "\n",
    "$${\\rm AIC} \\equiv -2 \\ln [L_0(M)] + 2k + \\frac{2k(k+1)}{N-k-1}.$$\n",
    "\n",
    "This comes from information theory considerations -- if you think of modeling as \"lossy compression\", which model loses less data? We won't discuss it in great detail here, but see the textbook if you're curious.\n",
    "\n",
    "When two models are compared, their BIC (or AIC) are compared analogously to the \n",
    "odds ratio, that is, the model with the smaller value wins. If the models are \n",
    "equally successful in describing the data (i.e., they have the same value of $L_0(M)$), \n",
    "then the model with fewer free parameters wins. Note: sometimes BIC and AIC are defined using the ***opposite*** sign, in which case the model with the largest value wins!\n",
    "\n",
    "***Both the BIC and AIC are approximations and might not be valid if the underlying \n",
    "assumptions are not met***. Furthermore, unlike the odds ratio, both of them penalize \n",
    "unconstrained parameters. In general, it is better to compute the odds ratio when \n",
    "computationally feasible. "
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    "Let's us BIC to choose the best polynomial from the earlier line fitting example. \n",
    "Starting with\n",
    "\n",
    "$${\\rm BIC} = \\chi^2 + k \\ln N,$$ \n",
    "\n",
    "with $N=20$ we have:\n",
    "\n",
    "<pre>\n",
    "     model     chi2    k   k*ln(N)   BIC       \n",
    "    linear    11.32    2    5.99    17.31   \n",
    "  quadratic    9.46    3    8.99    18.45   \n",
    "     cubic     8.99    4   11.98    20.97  \n",
    "</pre>\n",
    "\n",
    "Therefore, the improvement in $\\chi^2$ for the quadratic model, relative \n",
    "to the linear model, **is not large enough to justify another free model\n",
    "parameter.** "
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    "### Cross-validation\n",
    "\n",
    "Another useful method for model selection is the **cross-validation method**.\n",
    "Its disadvantage is that it may be computationally intensive for complex\n",
    "problems, but its great advantage is that it is conceptually simple and\n",
    "easy to implement (for details see textbook, Section 8.11.1). The basic idea of \n",
    "the cross-validation method is to set aside a fraction of the sample when\n",
    "obtaining the best-fit parameters and then compute the goodness-of-fit \n",
    "(e.g. $\\chi^2$, but any metric can be implemented) with this unused subsample. \n",
    "The \"leave-one-out\" implementation repeats model fitting $N$ times, using\n",
    "$N-1$ data points. Each time the missing point is used to compute the \n",
    "goodness-of-fit, and the $N$ values are averaged. \n",
    "\n",
    "When the model is too simple, it will have high bias (under-fitting)\n",
    "and when the model is too complex, the variance will be high (over-fitting).\n",
    "\n",
    "\n",
    "![BayesSlide1](figures/fig8-13.jpg)"
   ]
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    "This concludes our introduction to Bayesian inference and model comparison!\n",
    "\n",
    "We now know how to:\n",
    "* Interpret probability as quantified knowledge (degree of belief)\n",
    "* Select priors\n",
    "* Update our knowledge given new data\n",
    "* Compare and select models\n",
    "\n",
    "We've also noticed a problem: Bayesian inference doesn't result in just \"best fit\" values, but full probability density functions, and sometime highly dimensional ones. This results in computational challenges, which we'll tackle next with Markov Chain Monte Carlo."
   ]
  }
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