Irreducible Markov Chain Monte Carlo Schemes for Partially Observed Diffusions

Abstract

This paper presents a Markov chain Monte Carlo algorithm suitable for a class of partially observed non-linear diffusions. This class is of high practical interest; it includes for instance stochastic volatility models. We use data augmentation, treating the unobserved paths as missing data. However, unless these paths are transformed, the algorithm becomes reducible. We circumvent the problem by introducing appropriate reparametrisations of the likelihood that can be used to construct irreducible data augmentation schemes.