Bayesian model comparison and asymptotics for state-space models

Abstract

This thesis studies the implementation and properties of a novel criterion for model comparison, with a keen interest in the task of selecting Bayesian state-space models. This criterion, based on the Hyvärinen score and termed the H-factor, was recently advocated in the decision theoretic literature as an appealing alternative to the ubiquitous Bayes factor, particularly in settings where the presence of vague prior distributions renders the latter unreliable. The practical use of H-factors requires them to be numerically estimated, which we propose to consistently achieve by using sequential Monte Carlo methods. The uncertainty of the model choice, resulting from this estimation, is quantified by using new advances in unbiased Markov chain Monte Carlo methods to construct confidence intervals for the exact H factors. Proving theoretical guarantees for this new criterion in large samples will bring us to the realm of Bayesian asymptotics. It will require us to look into the consistency and asymptotic Normality of posterior distributions, à la Bernstein-von Mises, in general and possibly misspecified state-space models.