An Approximate Likelihood Perspective on ABC Methods

TL;DR

This paper reviews and unifies Approximate Bayesian Computational (ABC) methods from an approximate likelihood perspective, clarifying their relationships, classifications, and potential for future research in Bayesian inference with intractable likelihoods.

Contribution

It provides a comprehensive review and a unifying framework for ABC methods based on approximate likelihood theory, aiding understanding and application.

Findings

Classifies ABC methods within a unifying theoretical framework

Clarifies relationships and distinctions among different ABC approaches

Suggests directions for future research in ABC methodology

Abstract

We are living in the big data era, as current technologies and networks allow for the easy and routine collection of data sets in different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive for describing the complexity of these datasets. These models often exhibit a likelihood function which is intractable due to the large sample size, high number of parameters, or functional complexity. Approximate Bayesian Computational (ABC) methods provides likelihood-free methods for performing statistical inferences with Bayesian models defined by intractable likelihood functions. The vastity of the literature on ABC methods created a need to review and relate all ABC approaches so that scientists can more readily understand and apply them for their own work. This article provides a unifying review, general representation, and classification of all ABC methods from the view of approximate likelihood theory. This clarifies how ABC methods can be characterized, related, combined, improved, and applied for future research. Possible future research in ABC is then suggested.