  Particle Markov chain Monte Carlo (pMCMC) is now a popular method for
performing Bayesian statistical inference on challenging state space models
(SSMs) with unknown static parameters. It uses a particle filter (PF) at each
iteration of an MCMC algorithm to unbiasedly estimate the likelihood for a
given static parameter value. However, pMCMC can be computationally intensive
when a large number of particles in the PF is required, such as when the data
is highly informative, the model is misspecified and/or the time series is
long. In this paper we exploit the ensemble Kalman filter (EnKF) developed in
the data assimilation literature to speed up pMCMC. We replace the unbiased PF
likelihood with the biased EnKF likelihood estimate within MCMC to sample over
the space of the static parameter. On a wide class of different non-linear SSM
models, we demonstrate that our new ensemble MCMC (eMCMC) method can
significantly reduce the computational cost whilst maintaining reasonable
accuracy. We also propose several extensions of the vanilla eMCMC algorithm to
further improve computational efficiency. Computer code to implement our
methods on all the examples can be downloaded from
https://github.com/cdrovandi/Ensemble-MCMC.
