An efficient pseudo marginal method for state space models

Abstract

Pseudo Marginal Metropolis-Hastings (PMMH) is a general approach to carry out Bayesian inference when the likelihood is intractable but can be estimated unbiasedly. Our article develops an efficient PMMH method for estimating the parameters of complex and high-dimensional state space models and has the following features. First, it runs multiple particle filters in parallel and uses their averaged unbiased likelihood estimate. Second, it combines block and correlated PMMH sampling. The first two features enable our sampler to scale up better to longer time series and higher dimensional state vectors than previous approaches. Third, the article develops an efficient auxiliary disturbance particle filter, which is necessary when the bootstrap filter is inefficient, but the state transition density cannot be expressed in closed form. Fourth, it uses delayed acceptance to make the make the sampler more efficient. The performance of the sampler is investigated empirically by applying it to Dynamic Stochastic General Equilibrium models with relatively high state dimensions and with intractable state transition densities. Although our focus is on applying the method to state space models, the approach will be useful in a wide range of applications such as large panel data models and stochastic differential equation models with mixed effects.