examples/diagnostics_and_criticism/Bayes_factor.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayes Factors and Marginal Likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.11.0\n"
     ]
    }
   ],
   "source": [
    "import arviz as az\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.special import betaln\n",
    "from scipy.stats import beta\n",
    "\n",
    "print(f\"Running on PyMC3 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)."
   ]
  },
  {
   "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",
    "$$BF =  \\frac{p(y \\mid M_0)}{p(y \\mid M_1)}$$\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 some authors have proposed tables with levels of *support* or *strength*, 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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\n",
      "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=fr\"$\\alpha$ = {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 2 chains in 2 jobs\n",
      "Stage:   0 Beta: 0.107\n",
      "Stage:   1 Beta: 0.891\n",
      "Stage:   2 Beta: 1.000\n",
      "Stage:   0 Beta: 0.101\n",
      "Stage:   1 Beta: 0.824\n",
      "Stage:   2 Beta: 1.000\n",
      "Initializing SMC sampler...\n",
      "Sampling 2 chains in 2 jobs\n",
      "Stage:   0 Beta: 1.000\n",
      "Stage:   0 Beta: 1.000\n"
     ]
    }
   ],
   "source": [
    "models = []\n",
    "traces = []\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",
    "        trace = pm.sample_smc(1000, random_seed=42)\n",
    "        models.append(model)\n",
    "        traces.append(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5., 5.])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BF_smc = np.exp(traces[1].report.log_marginal_likelihood - traces[0].report.log_marginal_likelihood)\n",
    "np.round(BF_smc)"
   ]
  },
  {
   "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",
    "We obtain an array with two values, one per SMC run. As with other samplers PyMC3 attempts to run the sampler more than one time. Having independent samples may help diagnose the performace of the sampler.\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 a metropolis kernel as implemented in PyMC3) 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 requiere a larger number of `draws`. Additionally, a larger number of `n_steps` may help, specially if after stage 1 we notice that SMC uses a number of steps that are close to `n_steps`, i.e. SMC is having trouble to automatically reduce this number.\n",
    "\n",
    "You can check the number of steps per stage by doing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([2, 2, 2], [2, 2, 2])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traces[0].report.nsteps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayes factors and inference\n",
    "\n",
    "In this example 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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/CloudChaoszero/opt/anaconda3/envs/pymc3-dev-py38/lib/python3.8/site-packages/arviz/data/io_pymc3.py:88: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n",
      "  warnings.warn(\n"
     ]
    },
    {
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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>0.05</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.58</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean    sd  hdi_3%  hdi_97%\n",
       "a   0.5  0.05     0.4     0.58"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(traces[0], var_names=\"a\", kind=\"stats\").round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/CloudChaoszero/opt/anaconda3/envs/pymc3-dev-py38/lib/python3.8/site-packages/arviz/data/io_pymc3.py:88: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n",
      "  warnings.warn(\n"
     ]
    },
    {
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       "</style>\n",
       "<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>0.42</td>\n",
       "      <td>0.57</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean    sd  hdi_3%  hdi_97%\n",
       "a   0.5  0.04    0.42     0.57"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(traces[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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MultiTrace: 2 chains, 1000 iterations, 2 variables>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traces[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/CloudChaoszero/Documents/Projects-Dev/pymc3/pymc3/sampling.py:1687: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample\n",
      "  warnings.warn(\n"
     ]
    },
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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, ax = plt.subplots(figsize=(9, 6))\n",
    "ppc_0 = pm.sample_posterior_predictive(traces[0], 100, models[0], size=(len(y), 20))\n",
    "ppc_1 = pm.sample_posterior_predictive(traces[1], 100, models[1], size=(len(y), 20))\n",
    "for m_0, m_1 in zip(ppc_0[\"yl\"].T, ppc_1[\"yl\"].T):\n",
    "    az.plot_kde(np.mean(m_0, 0), ax=ax, plot_kwargs={\"color\": \"C0\"})\n",
    "    az.plot_kde(np.mean(m_1, 0), ax=ax, plot_kwargs={\"color\": \"C1\"})\n",
    "ax.plot([], label=\"model_0\")\n",
    "ax.plot([], label=\"model_1\")\n",
    "ax.legend()\n",
    "ax.set_xlabel(\"$\\\\theta$\")\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 factors. 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 WAIC, LOO or cross-validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sun Feb 07 2021\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.8.6\n",
      "IPython version      : 7.20.0\n",
      "\n",
      "matplotlib: None\n",
      "numpy     : 1.20.0\n",
      "pymc3     : 3.11.0\n",
      "arviz     : 0.11.0\n",
      "\n",
      "Watermark: 2.1.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python PyMC3 (Dev)",
   "language": "python",
   "name": "pymc3-dev-py38"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}