{ "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 v5.28.0+58.gf58491a3\n" ] } ], "source": [ "import arviz 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 scipy.special import betaln\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": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/osvaldo/anaconda3/envs/arviz_1/lib/python3.14/site-packages/pytensor/link/numba/dispatch/basic.py:215: UserWarning: Numba will use object mode to run XlogY0's perform method. Set `pytensor.config.compiler_verbose = True` to see more details.\n", " warnings.warn(\n" ] }, { "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": "db82150adace4378b07a64dedf7536ef", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
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      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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": "d41f0045c66b432a997528f833c90c91",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
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      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": {
      "text/html": [
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       "  \n",
       "
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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "
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       "  \n",
       "
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"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a3e89138c0bb487bac73dd59b1f0929a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "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": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "86570cc4f3de4faea27013d7ac00483e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "
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      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": [
    {
     "data": {
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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`)."
   ]
  },
  {
   "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": "844ea9072dd44405bca5fd35bc1685ee",
       "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 13 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[\"prior\"] = pm.sample_prior_predictive(8000).prior"
   ]
  },
  {
   "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": "f8db5c2baa684760b31626d74a6d3c45",
       "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 14 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[\"prior\"] = pm.sample_prior_predictive(8000).prior"
   ]
  },
  {
   "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\n",
    "* Updated by Osvaldo Martin in Apr, 2026"
   ]
  },
  {
   "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: Sat, 25 Apr 2026\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.14.4\n",
      "IPython version      : 9.12.0\n",
      "\n",
      "pytensor: 2.38.0+133.g80cc113b5\n",
      "\n",
      "arviz : 1.1.0\n",
      "numpy : 2.4.4\n",
      "preliz: 0.24.0\n",
      "pymc  : 5.28.0+58.gf58491a3\n",
      "xarray: 2026.4.0\n",
      "\n",
      "Watermark: 2.6.0\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": "arviz_1",
   "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": "3.14.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}