ABSTRACT
This chapter begins with a tutorial and a summary of the main developments of Indirect inference (II). It focuses on approximate Bayesian methods that harness such an auxiliary model. The chapter describes the parametric Bayesian indirect likelihood approach to approximate Bayesian inference using ideas from II. It discusses some possible future directions for utilising or building upon the current Bayesian II literature. The chapter provides a description of the indirect inference method and also detailed links between various likelihood-free Bayesian methods and indirect inference. It considers an extension of the reverse sampler of Forneron and Ng using regression adjustment, a Markov chain Monte Carlo (MCMC) implementation of the lazy approximate Bayesian computation (ABC) approach of Prangle and developed an ABC approach for spatial extremes models using the parameter estimate of a composite likelihood as the summary statistic. The chapter considers two case studies involving real data to demonstrate how ideas from indirect inference can enhance ABC inferences.
