{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Bayes_factor)=\n",
    "# Bayes Factors and Marginal Likelihood\n",
    ":::{post} Jun 1, 2022\n",
    ":tags: Bayes Factors, model comparison \n",
    ":category: beginner, explanation\n",
    ":author: Osvaldo Martin\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC v4.3.0\n"
     ]
    }
   ],
   "source": [
    "import arviz as az\n",
    "import numpy as np\n",
    "import pymc as pm\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.ticker import FormatStrFormatter\n",
    "from scipy.special import betaln\n",
    "from scipy.stats import beta\n",
    "\n",
    "print(f\"Running on PyMC v{pm.__version__}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"Bayesian way\" to compare models is to compute the _marginal likelihood_ of each model $p(y \\mid M_k)$, _i.e._ the probability of the observed data $y$ given the $M_k$ model. This quantity, the marginal likelihood, is just the normalizing constant of Bayes' theorem. We can see this if we write Bayes' theorem and make explicit the fact that all inferences are model-dependant. \n",
    "\n",
    "$$p (\\theta \\mid y, M_k ) = \\frac{p(y \\mid \\theta, M_k) p(\\theta \\mid M_k)}{p( y \\mid M_k)}$$\n",
    "\n",
    "where:\n",
    "\n",
    "* $y$ is the data\n",
    "* $\\theta$ the parameters\n",
    "* $M_k$ one model out of K competing models\n",
    "\n",
    "\n",
    "Usually when doing inference we do not need to compute this normalizing constant, so in practice we often compute the posterior up to a constant factor, that is:\n",
    "\n",
    "$$p (\\theta \\mid y, M_k ) \\propto p(y \\mid \\theta, M_k) p(\\theta \\mid M_k)$$\n",
    "\n",
    "However, for model comparison and model averaging the marginal likelihood is an important quantity. Although, it's not the only way to perform these tasks, you can read about model averaging and model selection using alternative methods [here](model_comparison.ipynb), [there](model_averaging.ipynb) and [elsewhere](GLM-model-selection.ipynb). Actually, these alternative methods are most often than not a better choice compared with using the marginal likelihood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian model selection\n",
    "\n",
    "If our main objective is to choose only one model, the _best_ one, from a set of models we can just choose the one with the largest $p(y \\mid M_k)$. This is totally fine if **all models** are assumed to have the same _a priori_ probability. Otherwise, we have to take into account that not all models are equally likely _a priori_ and compute:\n",
    "\n",
    "$$p(M_k \\mid y) \\propto p(y \\mid M_k) p(M_k)$$\n",
    "\n",
    "Sometimes the main objective is not to just keep a single model but instead to compare models to determine which ones are more likely and by how much. This can be achieved using Bayes factors:\n",
    "\n",
    "$$BF_{01} =  \\frac{p(y \\mid M_0)}{p(y \\mid M_1)}$$\n",
    "\n",
    "that is, the ratio between the marginal likelihood of two models. The larger the BF the _better_ the model in the numerator ($M_0$ in this example). To ease the interpretation of BFs  Harold Jeffreys proposed a scale for interpretation of Bayes Factors with levels of *support* or *strength*. This is just a way to put numbers into words. \n",
    "\n",
    "* 1-3: anecdotal\n",
    "* 3-10: moderate\n",
    "* 10-30: strong\n",
    "* 30-100: very strong\n",
    "* $>$ 100: extreme\n",
    "\n",
    "Notice that if you get numbers below 1 then the support is for the model in the denominator, tables for those cases are also available. Of course, you can also just take the inverse of the values in the above table or take the inverse of the BF value and you will be OK.\n",
    "\n",
    "It is very important to remember that these rules are just conventions, simple guides at best. Results should always be put into context of our problems and should be accompanied with enough details so others could evaluate by themselves if they agree with our conclusions. The evidence necessary to make a claim is not the same in particle physics, or a court, or to evacuate a town to prevent hundreds of deaths."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian model averaging\n",
    "\n",
    "Instead of choosing one single model from a set of candidate models, model averaging is about getting one meta-model by averaging the candidate models. The Bayesian version of this weights each model by its marginal posterior probability.\n",
    "\n",
    "$$p(\\theta \\mid y) = \\sum_{k=1}^K p(\\theta \\mid y, M_k) \\; p(M_k \\mid y)$$\n",
    "\n",
    "This is the optimal way to average models if the prior is _correct_ and the _correct_ model is one of the $M_k$ models in our set. Otherwise, _bayesian model averaging_ will asymptotically select the one single model in the set of compared models that is closest in [Kullback-Leibler divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence).\n",
    "\n",
    "Check this [example](model_averaging.ipynb) as an alternative way to perform model averaging."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Some remarks\n",
    "\n",
    "Now we will briefly discuss some key facts about the _marginal likelihood_\n",
    "\n",
    "* The good\n",
    "    * **Occam Razor included**: Models with more parameters have a larger penalization than models with fewer parameters. The intuitive reason is that the larger the number of parameters the more _spread_ the _prior_ with respect to the likelihood.\n",
    "\n",
    "\n",
    "* The bad\n",
    "    * Computing the marginal likelihood is, generally, a hard task because it’s an integral of a highly variable function over a high dimensional parameter space. In general this integral needs to be solved numerically using more or less sophisticated methods.\n",
    "    \n",
    "$$p(y \\mid M_k) = \\int_{\\theta_k} p(y \\mid \\theta_k, M_k) \\; p(\\theta_k | M_k) \\; d\\theta_k$$\n",
    "\n",
    "* The ugly\n",
    "    * The marginal likelihood depends **sensitively** on the specified prior for the parameters in each model $p(\\theta_k \\mid M_k)$.\n",
    "\n",
    "Notice that *the good* and *the ugly* are related. Using the marginal likelihood to compare models is a good idea because a penalization for complex models is already included (thus preventing us from overfitting) and, at the same time, a change in the prior will affect the computations of the marginal likelihood. At first this sounds a little bit silly; we already know that priors affect computations (otherwise we could simply avoid them), but the point here is the word **sensitively**. We are talking about changes in the prior that will keep inference of $\\theta$ more or less the same, but could have a big impact in the value of the marginal likelihood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing Bayes factors\n",
    "\n",
    "The marginal likelihood is generally not available in closed-form except for some restricted models. For this reason many methods have been devised to compute the marginal likelihood and the derived Bayes factors, some of these methods are so simple and [naive](https://radfordneal.wordpress.com/2008/08/17/the-harmonic-mean-of-the-likelihood-worst-monte-carlo-method-ever/) that works very bad in practice. Most of the useful methods have been originally proposed in the field of Statistical Mechanics. This connection is explained because the marginal likelihood is analogous to a central quantity in statistical physics known as the _partition function_ which in turn is closely related to another very important quantity the _free-energy_. Many of the connections between Statistical Mechanics and Bayesian inference are summarized [here](https://arxiv.org/abs/1706.01428)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using a hierarchical model\n",
    "\n",
    "Computation of Bayes factors can be framed as a hierarchical model, where the high-level parameter is an index assigned to each model and sampled from a categorical distribution. In other words, we perform inference for two (or more) competing models at the same time and we use a discrete _dummy_ variable that _jumps_ between models. How much time we spend sampling each model is proportional to $p(M_k \\mid y)$.\n",
    "\n",
    "Some common problems when computing Bayes factors this way is that if one model is better than the other, by definition, we will spend more time sampling from it than from the other model. And this could lead to inaccuracies because we will be undersampling the less likely model. Another problem is that the values of the parameters get updated even when the parameters are not used to fit that model. That is, when model 0 is chosen, parameters in model 1 are updated but since they are not used to explain the data, they only get restricted by the prior. If the prior is too vague, it is possible that when we choose model 1, the parameter values are too far away from the previous accepted values and hence the step is rejected. Therefore we end up having a problem with sampling.\n",
    "\n",
    "In case we find these problems, we can try to improve sampling by implementing two modifications to our model:\n",
    "\n",
    "* Ideally, we can get a better sampling of both models if they are visited equally, so we can adjust the prior for each model in such a way to favour the less favourable model and disfavour the most favourable one. This will not affect the computation of the Bayes factor because we have to include the priors in the computation.\n",
    "\n",
    "* Use pseudo priors, as suggested by Kruschke and others. The idea is simple: if the problem is that the parameters drift away unrestricted, when the model they belong to is not selected, then one solution is to try to restrict them artificially, but only when not used! You can find an example of using pseudo priors in a model used by Kruschke in his book and [ported](https://github.com/aloctavodia/Doing_bayesian_data_analysis) to Python/PyMC3.\n",
    "\n",
    "If you want to learn more about this approach to the computation of the marginal likelihood see [Chapter 12 of Doing Bayesian Data Analysis](http://www.sciencedirect.com/science/book/9780124058880). This chapter also discuss how to use Bayes Factors as a Bayesian alternative to classical hypothesis testing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analytically\n",
    "\n",
    "For some models, like the beta-binomial model (AKA the _coin-flipping_ model) we can compute the marginal likelihood analytically. If we write this model as:\n",
    "\n",
    "$$\\theta \\sim Beta(\\alpha, \\beta)$$\n",
    "$$y \\sim Bin(n=1, p=\\theta)$$\n",
    "\n",
    "the _marginal likelihood_ will be:\n",
    "\n",
    "$$p(y) = \\binom {n}{h}  \\frac{B(\\alpha + h,\\ \\beta + n - h)} {B(\\alpha, \\beta)}$$\n",
    "\n",
    "where:\n",
    "\n",
    "* $B$ is the [beta function](https://en.wikipedia.org/wiki/Beta_function) not to get confused with the $Beta$ distribution\n",
    "* $n$ is the number of trials\n",
    "* $h$ is the number of success\n",
    "\n",
    "Since we only care about the relative value of the _marginal likelihood_ under two different models (for the same data), we can omit the binomial coefficient $\\binom {n}{h}$, thus we can write:\n",
    "\n",
    "$$p(y) \\propto \\frac{B(\\alpha + h,\\ \\beta + n - h)} {B(\\alpha, \\beta)}$$\n",
    "\n",
    "This expression has been coded in the following cell, but with a twist. We will be using the `betaln` function instead of the `beta` function, this is done to prevent underflow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def beta_binom(prior, y):\n",
    "    \"\"\"\n",
    "    Compute the marginal likelihood, analytically, for a beta-binomial model.\n",
    "\n",
    "    prior : tuple\n",
    "        tuple of alpha and beta parameter for the prior (beta distribution)\n",
    "    y : array\n",
    "        array with \"1\" and \"0\" corresponding to the success and fails respectively\n",
    "    \"\"\"\n",
    "    alpha, beta = prior\n",
    "    h = np.sum(y)\n",
    "    n = len(y)\n",
    "    p_y = np.exp(betaln(alpha + h, beta + n - h) - betaln(alpha, beta))\n",
    "    return p_y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our data for this example consist on 100 \"flips of a coin\" and the same number of observed \"heads\" and \"tails\". We will compare two models one with a uniform prior and one with a _more concentrated_ prior around $\\theta = 0.5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.repeat([1, 0], [50, 50])  # 50 \"heads\" and 50 \"tails\"\n",
    "priors = ((1, 1), (30, 30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for a, b in priors:\n",
    "    distri = beta(a, b)\n",
    "    x = np.linspace(0, 1, 300)\n",
    "    x_pdf = distri.pdf(x)\n",
    "    plt.plot(x, x_pdf, label=rf\"$\\alpha$ = {a:d}, $\\beta$ = {b:d}\")\n",
    "    plt.yticks([])\n",
    "    plt.xlabel(\"$\\\\theta$\")\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell returns the Bayes factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "BF = beta_binom(priors[1], y) / beta_binom(priors[0], y)\n",
    "print(round(BF))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the model with the more concentrated prior $\\text{beta}(30, 30)$ has $\\approx 5$ times more support than the model with the more extended prior $\\text{beta}(1, 1)$. Besides the exact numerical value this should not be surprising since the prior for the most favoured model is concentrated around $\\theta = 0.5$ and the data $y$ has equal number of head and tails, consintent with a value of $\\theta$ around 0.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sequential Monte Carlo\n",
    "\n",
    "The [Sequential Monte Carlo](SMC2_gaussians.ipynb) sampler is a method that basically progresses by a series of successive *annealed* sequences from the prior to the posterior. A nice by-product of this process is that we get an estimation of the marginal likelihood. Actually for numerical reasons the returned value is the log marginal likelihood (this helps to avoid underflow)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing SMC sampler...\n",
      "Sampling 4 chains in 4 jobs\n"
     ]
    },
    {
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       "      100.00% [100/100 00:00&lt;?  Stage: 2 Beta: 1.000]\n",
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     "text": [
      "   "
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [a]\n"
     ]
    },
    {
     "name": "stdout",
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     "text": [
      " "
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    {
     "name": "stderr",
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     "text": [
      "Sampling: [a]\n",
      "Sampling: [a]\n",
      "Sampling: [a]\n",
      "/home/osvaldo/proyectos/00_BM/arviz/arviz/data/base.py:221: UserWarning: More chains (4) than draws (3). Passed array should have shape (chains, draws, *shape)\n",
      "  warnings.warn(\n",
      "Initializing SMC sampler...\n",
      "Sampling 4 chains in 4 jobs\n"
     ]
    },
    {
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      "text/html": [
       "\n",
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     "text": [
      "    "
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [a]\n",
      "Sampling: [a]\n",
      "Sampling: [a]\n",
      "Sampling: [a]\n",
      "/home/osvaldo/proyectos/00_BM/arviz/arviz/data/base.py:221: UserWarning: More chains (4) than draws (1). Passed array should have shape (chains, draws, *shape)\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "models = []\n",
    "idatas = []\n",
    "for alpha, beta in priors:\n",
    "    with pm.Model() as model:\n",
    "        a = pm.Beta(\"a\", alpha, beta)\n",
    "        yl = pm.Bernoulli(\"yl\", a, observed=y)\n",
    "        idata = pm.sample_smc(random_seed=42)\n",
    "        models.append(model)\n",
    "        idatas.append(idata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BF_smc = np.exp(\n",
    "    idatas[1].sample_stats[\"log_marginal_likelihood\"].mean()\n",
    "    - idatas[0].sample_stats[\"log_marginal_likelihood\"].mean()\n",
    ")\n",
    "np.round(BF_smc).item()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see from the previous cell, SMC gives essentially the same answer as the analytical calculation! \n",
    "\n",
    "Note: In the cell above we compute a difference (instead of a division) because we are on the log-scale, for the same reason we take the exponential before returning the result. Finally, the reason we compute the mean, is because we get one value log marginal likelihood value per chain. \n",
    "\n",
    "The advantage of using SMC to compute the (log) marginal likelihood is that we can use it for a wider range of models as a closed-form expression is no longer needed. The cost we pay for this flexibility is a more expensive computation. Notice that SMC (with an independent Metropolis kernel as implemented in PyMC) is not as efficient or robust as gradient-based samplers like NUTS. As the dimensionality of the problem increases a more accurate estimation of the posterior and the _marginal likelihood_ will require a larger number of `draws`, rank-plots can be of help to diagnose sampling problems with SMC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayes factors and inference\n",
    "\n",
    "So far we have used Bayes factors to judge which model seems to be better at explaining the data, and we get that one of the models is $\\approx 5$ _better_ than the other. \n",
    "\n",
    "But what about the posterior we get from these models? How different they are?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.59</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   mean    sd  hdi_3%  hdi_97%\n",
       "a   0.5  0.05    0.41     0.59"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idatas[0], var_names=\"a\", kind=\"stats\").round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.43</td>\n",
       "      <td>0.57</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   mean    sd  hdi_3%  hdi_97%\n",
       "a   0.5  0.04    0.43     0.57"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idatas[1], var_names=\"a\", kind=\"stats\").round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may argue that the results are pretty similar, we have the same mean value for $\\theta$, and a slightly wider posterior for `model_0`, as expected since this model has a wider prior. We can also check the posterior predictive distribution to see how similar they are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
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   "source": [
    "ppc_0 = pm.sample_posterior_predictive(idatas[0], model=models[0]).posterior_predictive\n",
    "ppc_1 = pm.sample_posterior_predictive(idatas[1], model=models[1]).posterior_predictive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, ax = plt.subplots(figsize=(9, 6))\n",
    "\n",
    "bins = np.linspace(0.2, 0.8, 8)\n",
    "ax = az.plot_dist(\n",
    "    ppc_0[\"yl\"].mean(\"yl_dim_2\"),\n",
    "    label=\"model_0\",\n",
    "    kind=\"hist\",\n",
    "    hist_kwargs={\"alpha\": 0.5, \"bins\": bins},\n",
    ")\n",
    "ax = az.plot_dist(\n",
    "    ppc_1[\"yl\"].mean(\"yl_dim_2\"),\n",
    "    label=\"model_1\",\n",
    "    color=\"C1\",\n",
    "    kind=\"hist\",\n",
    "    hist_kwargs={\"alpha\": 0.5, \"bins\": bins},\n",
    "    ax=ax,\n",
    ")\n",
    "ax.legend()\n",
    "ax.set_xlabel(\"$\\\\theta$\")\n",
    "ax.xaxis.set_major_formatter(FormatStrFormatter(\"%0.1f\"))\n",
    "ax.set_yticks([]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example the observed data $y$ is more consistent with `model_1` (because the prior is concentrated around the correct value of $\\theta$) than `model_0` (which assigns equal probability to every possible value of $\\theta$), and this difference is captured by the Bayes factor. We could say Bayes factors are measuring which model, as a whole, is better, including details of the prior that may be irrelevant for parameter inference. In fact in this example we can also see that it is possible to have two different models, with different Bayes factors, but nevertheless get very similar predictions. The reason is that the data is informative enough to reduce the effect of the prior up to the point of inducing a very similar posterior. As predictions are computed from the posterior we also get very similar predictions. In most scenarios when comparing models what we really care is the predictive accuracy of the models, if two models have similar predictive accuracy we consider both models as similar. To estimate the predictive accuracy we can use tools like PSIS-LOO-CV (`az.loo`), WAIC (`az.waic`), or cross-validation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Savage-Dickey Density Ratio\n",
    "\n",
    "For the previous examples we have compared two beta-binomial models, but sometimes what we want to do is to compare a null hypothesis H_0 (or null model) against an alternative one H_1. For example, to answer the question _is this coin biased?_, we could compare the value $\\theta = 0.5$ (representing no bias) against the result from a model were we let $\\theta$ to vary. For this kind of comparison the null-model is nested within the alternative, meaning the null is a particular value of the model we are building. In those cases computing the Bayes Factor is very easy and it does not require any special method, because the math works out conveniently so we just need to compare the prior and posterior evaluated at the null-value (for example $\\theta = 0.5$), under the alternative model. We can see that is true from the following expression:\n",
    "\n",
    "\n",
    "$$\n",
    "BF_{01} = \\frac{p(y \\mid H_0)}{p(y \\mid H_1)} \\frac{p(\\theta=0.5 \\mid y, H_1)}{p(\\theta=0.5 \\mid H_1)}\n",
    "$$\n",
    "\n",
    "Which only [holds](https://statproofbook.github.io/P/bf-sddr) when H_0 is a particular case of H_1.\n",
    "\n",
    "Let's do it with PyMC and ArviZ. We need just need to get posterior and prior samples for a model. Let's try with beta-binomial model with uniform prior we previously saw."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [a]\n"
     ]
    },
    {
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       "\n",
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       "      <progress value='12000' class='' max='12000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [12000/12000 00:02&lt;00:00 Sampling 4 chains, 0 divergences]\n",
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     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 3 seconds.\n",
      "Sampling: [a, yl]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_uni:\n",
    "    a = pm.Beta(\"a\", 1, 1)\n",
    "    yl = pm.Bernoulli(\"yl\", a, observed=y)\n",
    "    idata_uni = pm.sample(2000, random_seed=42)\n",
    "    idata_uni.extend(pm.sample_prior_predictive(8000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now we call ArviZ's `az.plot_bf` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_bf(idata_uni, var_name=\"a\", ref_val=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows one KDE for the prior (blue) and one for the posterior (orange). The two black dots show we evaluate both distribution as 0.5. We can see that the Bayes factor in favor of the null BF_01 is $\\approx 8$, which we can interpret as a _moderate evidence_ in favor of the null (see the Jeffreys' scale we discussed before).\n",
    "\n",
    "As we already discussed Bayes factors are measuring which model, as a whole, is better at explaining the data. And this includes the prior, even if the prior has a relatively low impact on the posterior computation. We can also see this effect of the prior when comparing a second model against the null.\n",
    "\n",
    "If instead our model would be a beta-binomial with prior beta(30, 30), the BF_01 would be lower (_anecdotal_ on the Jeffreys' scale). This is because under this model the value of $\\theta=0.5$ is much more likely a priori than for a uniform prior, and hence the posterior and prior will me much more similar. Namely there is not too much surprise about seeing the posterior concentrated around 0.5 after collecting data.\n",
    "\n",
    "Let's compute it to see for ourselves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [a]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "      <progress value='12000' class='' max='12000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [12000/12000 00:02&lt;00:00 Sampling 4 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 3 seconds.\n",
      "Sampling: [a, yl]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_conc:\n",
    "    a = pm.Beta(\"a\", 30, 30)\n",
    "    yl = pm.Bernoulli(\"yl\", a, observed=y)\n",
    "    idata_conc = pm.sample(2000, random_seed=42)\n",
    "    idata_conc.extend(pm.sample_prior_predictive(8000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_bf(idata_conc, var_name=\"a\", ref_val=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Authored by Osvaldo Martin in September, 2017 ([pymc#2563](https://github.com/pymc-devs/pymc/pull/2563))\n",
    "* Updated by Osvaldo Martin in August, 2018 ([pymc#3124](https://github.com/pymc-devs/pymc/pull/3124))\n",
    "* Updated by Osvaldo Martin in May, 2022 ([pymc-examples#342](https://github.com/pymc-devs/pymc-examples/pull/342))\n",
    "* Updated by Osvaldo Martin in Nov, 2022"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    ":::{bibliography}\n",
    ":filter: docname in docnames\n",
    "\n",
    "Dickey1970\n",
    "Wagenmakers2010\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sun Nov 13 2022\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.9.0\n",
      "IPython version      : 8.4.0\n",
      "\n",
      "arviz     : 0.13.0\n",
      "matplotlib: 3.6.2\n",
      "numpy     : 1.22.3\n",
      "pymc      : 4.3.0\n",
      "\n",
      "Watermark: 2.3.1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md\n",
    ":::"
   ]
  }
 ],
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