Easily computed Marginal Likelihoods from MCMC
vendredi 25 novembre 2022, 9h30 - 10h30
A key quantity in Bayesian model selection is the marginal likelihood (also known as the integrated likelihood, the evidence, or the normalizing constant). But estimation for Bayesian models is often done using Markov chain Monte Carlo (MCMC), and estimating the marginal likelihood from MCMC output is hard. We seek a method that is accurate, generic and simple, uses just the likelihoods and priors of sampled parameter values, and doesn’t need additional simulations. Most extant methods don’t fit these requirements. We propose a method that does, and illustrate its performance for a multivariate Gaussian model, a Bayesian regression model, and a Gaussian mixture model. This is joint work with Marie Perrot-Dockès, Pierre Latouche and Sarah Ouadah.