Efficient Particle MCMC for State Space Models through Emulation of Expensive Likelihoods

Recently proposed particle MCMC methods provide a flexible way of performing Bayesian inference for parameters in (nonlinear) state space models. Each iteration of the scheme re-quires an estimate of marginal likelihood calculated from the output of a sequential Monte Carlo scheme (also known as a particle filter). Consequently, the method can be extremely computationally intensive. We therefore aim to negate the expensive likelihood calculation through use of a fast approximation, or ‘emulator’. We propose a simple adaptive emulation procedure and find that it performs well in several scenarios. We illustrate the method by considering two applications, namely, inference for parameters governing a nonlinear multi-variate diffusion process and inference for a nonlinear state space model of pupal densities of the pine looper moth (Bupalis pineria)