  Delayed-acceptance is a technique for reducing computational effort for
Bayesian models with expensive likelihoods. Using a delayed-acceptance kernel
for Markov chain Monte Carlo can reduce the number of expensive likelihoods
evaluations required to approximate a posterior expectation. Delayed-acceptance
uses a surrogate, or approximate, likelihood to avoid evaluation of the
expensive likelihood when possible. Within the sequential Monte Carlo
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 particle 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, code for which is available at
https://github.com/bonStats/smcdar.
