Abstract

Co-authors: Christophe Andrieu (University of Bristol), Arnaud Doucet (University of Oxford)

We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in Andrieu et al. (2010) and presents several practical advantages over standard approaches. The ratio is estimated using a unique source of randomness instead of estimating separately the two likelihood terms involved. Beyond the benefits in terms of variance reduction one may expect in general from this type of approach, an important point here is that the variance of this estimator decreases as the distance between the likelihood parameters decreases. We show how this can be exploited in the context of Monte Carlo Markov chain (MCMC) algorithms, leading to the development of a new class of exact-approximate MCMC methods to perform Bayesian static parameter inference in state-space models. We show through simulations that, in contrast to the Particle Mar ginal Metropolis–Hastings (PMMH) algorithm of Andrieu et al. (2010), the computational effort required by this novel MCMC scheme scales favourably for large data sets.