Efficiently Combining Pseudo Marginal and Particle Gibbs Sampling

• Activity Number: 400 - Recent Advances in Bayesian Computation and Modeling of High-Dimensional Multivariate Data
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): David Gunawan* and Christopher Carter and Robert Kohn
• Companies: University of New South Wales and University of New South Wales and Univ of New South Wales
• Keywords: Correlated Pseudo marginal Metropolis-Hastings; Particle Gibbs sampler; Factor Stochastic Volatility Model

Abstract

Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Deligiannidis et al. (2017) introduce the correlated pseudo marginal sampler and show that it can be much more efficient than the standard pseudo marginal approach. Mendes et al (2018) propose a particle MCMC sampler that generates parameters that are highly correlated with the states using a pseudo marginal method that integrates out the states, while all other parameters are generated using particle Gibbs. Our article shows how to combine these two approaches to particle MCMC to obtain a flexible sampler with a superior performance to each of these two approaches. We illustrate the new sampler using a multivariate factor stochastic volatility model with leverage.