ABC and Indirect Inference

TL;DR

This chapter explores the relationship between Approximate Bayesian Computation (ABC) and Indirect Inference (II), highlighting how auxiliary models with tractable likelihoods can enhance likelihood-free Bayesian inference methods.

Contribution

It provides an introduction to II, details its connection with ABC, and emphasizes the use of auxiliary models to improve likelihood-free Bayesian inference.

Findings

Clarifies the link between ABC and II methods.

Highlights the use of auxiliary models with tractable likelihoods.

Provides insights into likelihood-free Bayesian inference techniques.

Abstract

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.