E cient Bayesian Inference for Switching State-Space Models using Particle Markov Chain Monte Carlo Methods

Switching state-space models (SSSM) are a popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov chain Monte Carlo (MCMC) techniques. However, even sophisticated MCMC methods dedicated to SSSM can prove quite ine cient as they update potentially strongly correlated variables one-at-a-time. Particle Markov chain Monte Carlo (PMCMC) methods are a recently developed class of MCMC algorithms which use particle lters to build e cient proposal distributions in high-dimensions [1]. The existing PMCMC methods of [1] are applicable to SSSM, but are restricted to employing standard particle ltering techniques. Yet, in the context of SSSM, much more e cient particle techniques have been developed [22, 23, 24]. In this paper, we extend the PMCMC framework to enable the use of these e cient particle methods within MCMC. We demonstrate the resulting generic methodology on a variety of examples including a multiple change-points model for well-log data and a model for U.S./U.K. exchange rate data. These new PMCMC algorithms are shown to outperform experimentally state-of-the-art MCMC techniques for a xed computational complexity. Additionally they can be easily parallelized [39] which allows further substantial gains.