Title: Flexible density tempering approaches for state space models with an application to factor stochastic volatility models
Authors: David Gunawan - University of Wollongong (Australia) [presenting]
Robert Kohn - University of New South Wales (Australia)
Christopher K Carter - UNSW (Australia)
Minh-Ngoc Tran - University of Sydney (Australia)
Abstract: A tempering or annealing approach to Bayesian inference for time series state space models is proposed. In such models the likelihood is often analytically and computationally intractable. Their approach generalizes the annealed importance sampling (AIS) approac when the likelihood can be computed analytically. A critical component of the annealing or density tempering method is the Markov move component that is implemented at every stage of the annealing process. The Markov move component effectively runs a small number of Markov chain Monte Carlo iterations for each combination of parameters and latent variables so that they are better approximations to that level of the tempered target density. Previously a pseudo marginal Metropolis-Hastings (PMMH) approach with the likelihood estimated unbiasedly in the Markov move component has been used. One of the drawbacks of this approach, however, is that it is difficult to obtain good proposals when the parameter space is high dimensional, such as for a high dimensional factor stochastic volatility models. We propose using instead more flexible Markov move steps that are based on particle Gibbs and Hamiltonian Monte Carlo and demonstrate the proposed methods using a high dimensional stochastic volatility factor model. An estimate of the marginal likelihood is obtained as a byproduct of the estimation procedure.