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2018 An approximate likelihood perspective on ABC methods
George Karabatsos, Fabrizio Leisen
Statist. Surv. 12: 66-104 (2018). DOI: 10.1214/18-SS120

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 outlined.

Citation

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George Karabatsos. Fabrizio Leisen. "An approximate likelihood perspective on ABC methods." Statist. Surv. 12 66 - 104, 2018. https://doi.org/10.1214/18-SS120

Information

Received: 1 February 2018; Published: 2018
First available in Project Euclid: 9 June 2018

zbMATH: 1391.60003
MathSciNet: MR3812816
Digital Object Identifier: 10.1214/18-SS120

Subjects:
Primary: 60-08 , 62F15
Secondary: 62G05

Keywords: Approximate Bayesian Computation , approximate likelihood , Bootstrap likelihood , empirical likelihood

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