Matteo Ruggiero

Duality-based Inference in Bayesian dynamic models

After recalling the notion of duality for Markov processes and the probability structures it may give rise to, we will first overview some recent results on Bayesian inference based on duality. Casting the Bayesian dynamic problem in a hidden Markov model framework, where the hidden signal is the temporally evolving parameter, we provide sets of conditions for both exact and approximate filtering/smoothing in finite-dimensional settings. These conditions are shown to yield, for some dynamic extensions of classical Bayesian models, relaxed notions of conjugacy that can be exploited through recursive algorithms. We will then discuss the implications of these results for nonparametric problems and from a predictive viewpoint, and the performance of these algorithms in comparison with particle filters.