Abstract

Delayed-acceptance is a technique for reducing computational effort for Bayesian models with expensive likelihoods. Using delayed-acceptance kernels in MCMC can reduce the number of expensive likelihoods evaluations required to approximate a posterior expectation to a given accuracy. It uses a surrogate, or approximate, likelihood to avoid evaluation of the expensive likelihood when possible. Importantly, delayed-acceptance kernels preserve the intended targeted distribution of the Markov chain, when viewed as an extension of a Metropolis-Hastings kernel. Within the sequential Monte Carlo (SMC) framework, we utilise the history of the sampler to adaptively tune the surrogate likelihood to yield better approximations of the expensive likelihood, and use a surrogate first annealing schedule to further increase computational efficiency. Moreover, we propose a framework for optimising computation time whilst avoiding particles degeneracy, which encapsulates existing strategies in the literature. Overall, we develop a novel algorithm for computationally efficient SMC with expensive likelihood functions. The method is applied to static Bayesian models, which we demonstrate on toy and real examples.