The Correlated Particle Hybrid Sampler for State Space Models

TL;DR

This paper introduces a novel correlated particle MCMC method that enhances efficiency in Bayesian inference for complex state space models by correlating components in the pseudo-marginal step, combining two existing approaches.

Contribution

It proposes a new hybrid particle MCMC algorithm that improves efficiency by correlating the numerator and denominator in the acceptance ratio, and unifies particle Gibbs with correlated pseudo-marginal methods.

Findings

Significantly improved efficiency over existing PMCMC methods.

Effective in models with many parameters and latent states.

Empirical validation on stochastic volatility models.

Abstract

Particle Markov Chain Monte Carlo (PMCMC) is a general computational approach to Bayesian inference for general state space models. Our article scales up PMCMC in terms of the number of observations and parameters by generating the parameters that are highly correlated with the states \lq integrated out\rq{} in a pseudo marginal step; the rest of the parameters are generated conditional on the states. The novel contribution of our article is to make the pseudo-marginal step much more efficient by positively correlating the numerator and denominator in the Metropolis-Hastings acceptance probability. This is done in a novel way by expressing the target density of the PMCMC in terms of the basic uniform or normal random numbers used in the sequential Monte Carlo algorithm instead of the standard way in terms of state particles. We also show that the new sampler combines and generalizes two separate particle MCMC approaches: particle Gibbs and the correlated pseudo marginal Metropolis-Hastings. We investigate the performance of the hybrid sampler empirically by applying it to univariate and multivariate stochastic volatility models having both a large number of parameters and a large number of latent states and show that it is much more efficient than competing PMCMC methods.