{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(Bayes_factor)=\n", "# Bayes Factors and Marginal Likelihood\n", ":::{post} Jan 10, 2023\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 v5.26.1\n" ] } ], "source": [ "import arviz.preview as az\n", "import numpy as np\n", "import preliz as pz\n", "import pymc as pm\n", "import xarray as xr\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-variat\")" ] }, { "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": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for a, b in priors:\n", " pz.Beta(a, b).plot_pdf(figsize=(8, 3))" ] }, { "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" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c9470f3afeb84452b4c7d428aa7a8b85", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/osvaldo/proyectos/00_BM/arviz-devs/arviz/arviz/data/base.py:272: 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"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3037d85e6a5f480c9fba56fa6f7acf6d",
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
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     "metadata": {},
     "output_type": "display_data"
    },
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       "
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      ],
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     "metadata": {},
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/osvaldo/proyectos/00_BM/arviz-devs/arviz/arviz/data/base.py:272: 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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       "
meansdeti89_lbeti89_ub
a0.50.050.420.58
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       "
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      ],
      "text/plain": [
       "   mean    sd  eti89_lb  eti89_ub\n",
       "a   0.5  0.05      0.42      0.58"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idatas[0], var_names=\"a\", kind=\"stats\", round_to=2)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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meansdeti89_lbeti89_ub
a0.50.040.440.56
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       "
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      ],
      "text/plain": [
       "   mean    sd  eti89_lb  eti89_ub\n",
       "a   0.5  0.04      0.44      0.56"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idatas[1], var_names=\"a\", kind=\"stats\", round_to=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",
     "text": [
      "Sampling: [yl]\n"
     ]
    },
    {
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       "model_id": "b95dd6809c864731ad13adf5e2ba75f0",
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       "Output()"
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
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      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [yl]\n"
     ]
    },
    {
     "data": {
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       "model_id": "90c2d8849b1b403f8718f4a48521bf96",
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       "Output()"
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
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     "metadata": {},
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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": [
       "
"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "models = {\n",
    "    \"model_0\": xr.Dataset({\"yl\": ppc_0[\"yl\"].mean(\"yl_dim_0\")}),\n",
    "    \"model_1\": xr.Dataset({\"yl\": ppc_1[\"yl\"].mean(\"yl_dim_0\")}),\n",
    "}\n",
    "az.plot_dist(\n",
    "    models,\n",
    "    visuals={\n",
    "        \"dist\": False,\n",
    "        \"point_estimate_text\": False,\n",
    "    },\n",
    ");"
   ]
  },
  {
   "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": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [a]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f6b46a00ef994da692ea510a6432e08e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": []
     },
     "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 2 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": [
       "
"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_bf(idata_uni, var_names=\"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": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [a]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "32c9c1ca6402436ea07c8dc21b37189f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": []
     },
     "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 2 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": [
       "
"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_bf(idata_conc, var_names=\"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\n",
    "* Re-executed by Reshama Shaikh with PyMC v5 in Jan, 2023\n",
    "* Updated by Osvaldo Martin in Dec, 2025"
   ]
  },
  {
   "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: Wed Dec 03 2025\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.13.5\n",
      "IPython version      : 9.3.0\n",
      "\n",
      "pytensor: 2.35.1\n",
      "\n",
      "xarray    : 2025.6.1\n",
      "arviz     : 0.23.0.dev0\n",
      "numpy     : 2.2.6\n",
      "matplotlib: 3.10.3\n",
      "pymc      : 5.26.1\n",
      "preliz    : 0.21.0\n",
      "\n",
      "Watermark: 2.5.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p pytensor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md\n",
    ":::"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pymc",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}