  Recently, Andrieu, Doucet and Holenstein (2010) introduced a general
framework for using particle filters (PFs) to construct proposal kernels for
Markov chain Monte Carlo (MCMC) methods. This framework, termed Particle Markov
chain Monte Carlo (PMCMC), was shown to provide powerful methods for joint
Bayesian state and parameter inference in nonlinear/non-Gaussian state-space
models. However, the mixing of the resulting MCMC kernels can be quite
sensitive, both to the number of particles used in the underlying PF and to the
number of observations in the data. In the discussion following (Andrieu et
al., 2010), Whiteley suggested a modified version of one of the PMCMC samplers,
namely the particle Gibbs (PG) sampler, and argued that this should improve its
mixing. In this paper we explore the consequences of this modification and show
that it leads to a method which is much more robust to a low number of
particles as well as a large number of observations. Furthermore, we discuss
how the modified PG sampler can be used as a basis for alternatives to all
three PMCMC samplers derived in (Andrieu et al., 2010). We evaluate these
methods on several challenging inference problems in a simulation study. One of
these is the identification of an epidemiological model for predicting
influenza epidemics, based on search engine query data.
