Efficient Bayesian Inference for Switching State-Space Models using Discrete Particle Markov Chain Monte Carlo Methods

Abstract

Switching state-space models (SSSM) are a very 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 inefficient as they update potentially strongly correlated discrete-valued latent variables one-at-a-time (Carter and Kohn, 1996; Gerlach et al., 2000; Giordani and Kohn, 2008). Particle Markov chain Monte Carlo (PMCMC) methods are a recently developed class of MCMC algorithms which use particle filters to build efficient proposal distributions in high-dimensions (Andrieu et al., 2010). The existing PMCMC methods of Andrieu et al. (2010) are applicable to SSSM, but are restricted to employing standard particle filtering techniques. Yet, in the context of discrete-valued latent variables, specialised particle techniques have been developed which can outperform by up to an order of magnitude standard methods (Fearnhead, 1998; Fearnhead and Clifford, 2003; Fearnhead, 2004). In this paper we develop a novel class of PMCMC methods relying on these very efficient particle algorithms. We establish the theoretical validy of this new generic methodology referred to as discrete PMCMC and demonstrate it 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. Discrete PMCMC algorithms are shown to outperform experimentally state-of-the-art MCMC techniques for a fixed computational complexity. Additionally they can be easily parallelized (Lee et al., 2010) which allows further substantial gains.