  Particle Markov Chain Monte Carlo methods are used to carry out inference in
non-linear and non-Gaussian state space models, where the posterior density of
the states is approximated using particles. Current approaches usually perform
Bayesian inference using either a particle Marginal Metropolis-Hastings (PMMH)
algorithm or a particle Gibbs (PG) sampler. This paper shows how the two ways
of generating variables mentioned above can be combined in a flexible manner to
give sampling schemes that converge to a desired target distribution. The
advantage of our approach is that the sampling scheme can be tailored to obtain
good results for different applications. For example, when some parameters and
the states are highly correlated, such parameters can be generated using PMMH,
while all other parameters are generated using PG because it is easier to
obtain good proposals for the parameters within the PG framework. We derive
some convergence properties of our sampling scheme and also investigate its
performance empirically by applying it to univariate and multivariate
stochastic volatility models and comparing it to other PMCMC methods proposed
in the literature.
