  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.
