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

## TL;DR

This paper introduces ensemble MCMC, a method that uses the ensemble Kalman filter to accelerate Bayesian inference in state space models, reducing computational costs while maintaining accuracy.

## Contribution

It replaces the particle filter with the ensemble Kalman filter within MCMC, providing a faster alternative for likelihood estimation in complex models.

## Key findings

- eMCMC significantly reduces computational time
- Maintains reasonable accuracy across various models
- Extensions further improve efficiency

## 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 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.