Approximate Bayesian Computation

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Abstract

Many of the statistical models that could provide an accurate, interesting, and testable explanation for the structure of a data set turn out to have intractable likelihood functions. The method of approximate Bayesian computation (ABC) has become a popular approach for tackling such models. This review gives an overview of the method and the main issues and challenges that are the subject of current research.

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Most cited references 85

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Bayesian calibration of computer models

Marc C Kennedy, Anthony O'Hagan (2001)

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Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems.

Tina Toni, David Welch, Natalja Strelkowa … (2009)

Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.

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Sequential Monte Carlo without likelihoods.

S. Sisson, Y. Fan, Mark M. Tanaka (2007)

Recent new methods in Bayesian simulation have provided ways of evaluating posterior distributions in the presence of analytically or computationally intractable likelihood functions. Despite representing a substantial methodological advance, existing methods based on rejection sampling or Markov chain Monte Carlo can be highly inefficient and accordingly require far more iterations than may be practical to implement. Here we propose a sequential Monte Carlo sampler that convincingly overcomes these inefficiencies. We demonstrate its implementation through an epidemiological study of the transmission rate of tuberculosis.

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Author and article information

Journal

Title: Annual Review of Statistics and Its Application

Abbreviated Title: Annu. Rev. Stat. Appl.

Publisher: Annual Reviews

ISSN (Print): 2326-8298

ISSN (Electronic): 2326-831X

Publication date Created: March 07 2019

Publication date (Print): March 07 2019

Volume: 6

Issue: 1

Pages: 379-403

Affiliations

[1 ]School of Biological Sciences, University of Bristol, Bristol BS8 1TQ, United Kingdom;

Article

DOI: 10.1146/annurev-statistics-030718-105212

SO-VID: ae6f94e1-9da5-434b-add7-71a6e251b866

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Self URI (article page): https://www.annualreviews.org/doi/10.1146/annurev-statistics-030718-105212

Approximate Bayesian Computation

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Abstract

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Most cited references 85

Bayesian calibration of computer models

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems.

Sequential Monte Carlo without likelihoods.

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