ABC and Indirect Inference

This chapter will appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). Indirect inference (II) is a classical likelihood-free approach that pre-dates the main developments of ABC and relies on simulation from a parametric model of interest to determine point estimates of the parameters. It is not surprising then that some likelihood-free Bayesian approaches have harnessed the II literature. This chapter provides an introduction to II and details the connections between ABC and II. A particular focus is placed on the use of an auxiliary model with a tractable likelihood function, an approach commonly adopted in the II literature, to facilitate likelihood-free Bayesian inferences.