  Particle MCMC involves using a particle filter within an MCMC algorithm. For
inference of a model which involves an unobserved stochastic process, the
standard implementation uses the particle filter to propose new values for the
stochastic process, and MCMC moves to propose new values for the parameters. We
show how particle MCMC can be generalised beyond this. Our key idea is to
introduce new latent variables. We then use the MCMC moves to update the latent
variables, and the particle filter to propose new values for the parameters and
stochastic process given the latent variables. A generic way of defining these
latent variables is to model them as pseudo-observations of the parameters or
of the stochastic process. By choosing the amount of information these latent
variables have about the parameters and the stochastic process we can often
improve the mixing of the particle MCMC algorithm by trading off the Monte
Carlo error of the particle filter and the mixing of the MCMC moves. We show
that using pseudo-observations within particle MCMC can improve its efficiency
in certain scenarios: dealing with initialisation problems of the particle
filter; speeding up the mixing of particle Gibbs when there is strong
dependence between the parameters and the stochastic process; and enabling
further MCMC steps to be used within the particle filter.
