Ensemble MCMC: Accelerating Pseudo-Marginal MCMC for State Space Models using the Ensemble Kalman Filter

Abstract

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 are 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 extended ensemble MCMC (eMCMC) methods 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.