The Gibbs Sampler with Particle Efficient Importance Sampling for State-Space Models

Abstract: We consider Particle Gibbs (PG) as a tool for Bayesian analysis of non-linear non-Gaussian state-space models. PG is a Monte Carlo (MC) approximation of the standard Gibbs procedure which uses sequential MC (SMC) importance sampling inside the Gibbs procedure to update the latent and potentially high-dimensional state trajectories. We propose to combine PG with a generic and easily implementable SMC approach known as Particle Efficient Importance Sampling (PEIS). By using SMC importance sampling densities which are approximately fully globally adapted to the targeted density of the states, PEIS can substantially improve the mixing and the efficiency of the PG draws from the posterior of the states and the parameters relative to existing PG implementations. The efficiency gains achieved by PEIS are illustrated in PG applications to a univariate stochastic volatility model for asset returns, a non-Gaussian nonlinear local-level model for interest rates, and a multivariate stochastic volatility model for the realized covariance matrix of asset returns.