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

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 particle filter (PF) at each iteration of an MCMC algorithm to unbiasedly estimate the likelihood given parameter value. However, pMCMC can be computationally intensive when large number particles in PF required, such as data are highly informative, model misspecified and/or time series long. In this paper we exploit ensemble Kalman (EnKF) developed assimilation literature speed up pMCMC. We replace unbiased biased EnKF within sample over parameter. On wide class different non-linear SSM models, demonstrate that our extended (eMCMC) methods significantly reduce computational cost whilst maintaining reasonable accuracy. also propose several extensions vanilla eMCMC further improve efficiency. Computer code implement all examples downloaded from https://github.com/cdrovandi/Ensemble-MCMC.