Efficient estimation of likelihood ratios in state-space models–application to scalable exact approximations of MCMCs

We present a new class of exact-approximate Markov chain Monte Carlo methods for static parameter estimation in hidden Markov models. Like the particle marginal Metropolis-Hastings (PMMH) algorithm, the proposed algorithms target the joint posterior distribution of the latent states while they ‘mimic’ the marginal Metropolis-Hastings algorithm for the static parameter. In contrast to PMMH, these algorithms estimate the acceptance ratio directly without having to use of the same estimate in its denominator, which is a well-known cause for stickiness in pseudo-marginal type algorithms.