Fundamentals and Recent Developments in Approximate Bayesian Computation.

Jarno Lintusaari,Samuel Kaski,Ritabrata Dutta,Jukka Corander,Michael U Gutmann

doi:10.1093/sysbio/syw077

Abstract

Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.]

Highlights

Many recent models in biology describe nature to a high degree of accuracy but are not amenable to analytical treatment
Gutmann and Corander (2016) proposed a framework called Bayesian optimization for likelihood-free inference (BOLFI) for performing approximate Bayesian computation (ABC) which overcomes this obstacle by learning a probabilistic model about the stochastic relation between the parameter values and the distance (Fig. 11)
ABC has become synonymous for approximate Bayesian inference for simulator-based models

Summary

Introduction

Many recent models in biology describe nature to a high degree of accuracy but are not amenable to analytical treatment. ABC algorithms sample from the posterior distribution of the parameters by finding values that yield simulated data sufficiently resembling the observed data.

Results

Conclusion