The Gibbs sampler with particle efficient importance sampling for state-space models*

Abstract We consider Particle Gibbs (PG) for Bayesian analysis of non-linear non-Gaussian state-space models. As a Monte Carlo (MC) approximation of the Gibbs procedure, PG uses sequential MC (SMC) importance sampling inside the Gibbs to update the latent states. We propose to combine PG with the Particle Efficient Importance Sampling (PEIS). By using SMC sampling densities which are approximately globally fully adapted to the targeted density of the states, PEIS can substantially improve the simulation efficiency of the PG relative to existing PG implementations. The efficiency gains are illustrated in PG applications to a non-linear local-level model and stochastic volatility models.