  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.
