Particle MCMC and the correlated particle hybrid sampler for state space models
Publication Name
Journal of Econometrics
Abstract
Particle Markov Chain Monte Carlo (PMCMC) is a powerful approach to Bayesian computation for general state space models. Our article enables PMCMC to handle a larger number of observations and parameters compared to previous approaches by generating the parameters that are highly correlated with the states in a pseudo-marginal step(s) with the states ‘integrated out’; the rest of the parameters are generated conditional on the states. We make the pseudo-marginal step much more efficient than previous approaches by positively correlating the numerator and denominator in the Metropolis–Hastings acceptance probability 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 which expresses the target density in terms of the 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 this 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. An online supplement to the article and computer code are available online.
Open Access Status
This publication is not available as open access
Article Number
105731
Funding Number
CE140100049