Approximating Bayes in the 21st Century

TL;DR

This paper reviews the development and application of approximate Bayesian methods in the 21st century, highlighting their role in solving complex statistical problems that are intractable for exact methods.

Contribution

It provides a comprehensive overview of various approximate Bayesian techniques, clarifies their differences, and discusses their practical usefulness and combinations for empirical research.

Findings

Summarizes key approximate Bayesian methods and their applications.

Highlights the advantages of approximate methods over exact solutions.

Provides guidance on choosing and combining techniques in practice.

Abstract

The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain Monte Carlo: for instance, models with unavailable likelihoods, high-dimensional models, and models featuring large data sets. These approximate methods are the subject of this review. The aim is to help new researchers in particular -- and more generally those interested in adopting a Bayesian approach to empirical work -- distinguish between different approximate techniques; understand the sense in which they are approximate; appreciate when and why particular methods are useful; and see the ways in which they can can be combined.