  Particle MCMC is a class of algorithms that can be used to analyse
state-space models. They use MCMC moves to update the parameters of the models,
and particle filters to propose values for the path of the state-space model.
Currently the default is to use random walk Metropolis to update the parameter
values. We show that it is possible to use information from the output of the
particle filter to obtain better proposal distributions for the parameters. In
particular it is possible to obtain estimates of the gradient of the log
posterior from each run of the particle filter, and use these estimates within
a Langevin-type proposal. We propose using the recent computationally efficient
approach of Nemeth et al. (2013) for obtaining such estimates. We show
empirically that for a variety of state-space models this proposal is more
efficient than the standard random walk Metropolis proposal in terms of:
reducing autocorrelation of the posterior samples, reducing the burn-in time of
the MCMC sampler and increasing the squared jump distance between posterior
samples.
