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Switching state-space models (SSSM) are a very popular class of time seriesmodels that have found many applications in statistics, econometrics andadvanced signal processing. Bayesian inference for these models typicallyrelies on Markov chain Monte Carlo (MCMC) techniques. However, evensophisticated MCMC methods dedicated to SSSM can prove quite inefficient asthey update potentially strongly correlated discrete-valued latent variablesone-at-a-time (Carter and Kohn, 1996; Gerlach et al., 2000; Giordani and Kohn,2008). Particle Markov chain Monte Carlo (PMCMC) methods are a recentlydeveloped class of MCMC algorithms which use particle filters to buildefficient proposal distributions in high-dimensions (Andrieu et al., 2010). Theexisting PMCMC methods of Andrieu et al. (2010) are applicable to SSSM, but arerestricted to employing standard particle filtering techniques. Yet, in thecontext of discrete-valued latent variables, specialised particle techniqueshave been developed which can outperform by up to an order of magnitudestandard methods (Fearnhead, 1998; Fearnhead and Clifford, 2003; Fearnhead,2004). In this paper we develop a novel class of PMCMC methods relying on thesevery efficient particle algorithms. We establish the theoretical validy of thisnew generic methodology referred to as discrete PMCMC and demonstrate it on avariety of examples including a multiple change-points model for well-log dataand a model for U.S./U.K. exchange rate data. Discrete PMCMC algorithms areshown to outperform experimentally state-of-the-art MCMC techniques for a fixedcomputational complexity. Additionally they can be easily parallelized (Lee etal., 2010) which allows further substantial gains.

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