ABSTRACT
Approximate Bayesian computation (ABC) is now a mature algorithm for likelihood-free estimation. This chapter reviews two alternative methods of approximating the intractable likelihood function for the model of interest, both of which aim to improve computational efficiency relative to ABC. It applies BSL to dynamic ecological models and compares it with an alternative Bayesian method for state space models. The chapter provides a more thorough review of synthetic likelihood (SL) both in the classical and Bayesian frameworks. It considers uses an empirical likelihood (EL) within a Bayesian framework. The chapter describes a more sophisticated algorithm based on adaptive multiple importance sampling. The synthetic likelihood approach has a strong connection with indirect inference, which is a classical method for obtaining point estimates of parameters of models with intractable likelihoods. ABC is a popular computational method of choice not only when there is no likelihood, but also when the likelihood is available, but difficult or impossible to evaluate.
