Statistics Surveys

An approximate likelihood perspective on ABC methods

George Karabatsos and Fabrizio Leisen

Full-text: Open access

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.

Article information

Source
Statist. Surv., Volume 12 (2018), 66-104.

Dates
Received: February 2018
First available in Project Euclid: 9 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ssu/1528509818

Digital Object Identifier
doi:10.1214/18-SS120

Mathematical Reviews number (MathSciNet)
MR3812816

Zentralblatt MATH identifier
1391.60003

Subjects
Primary: 60-08: Computational methods (not classified at a more specific level) [See also 65C50] 62F15: Bayesian inference
Secondary: 62G05: Estimation

Keywords
Approximate Bayesian computation approximate likelihood empirical likelihood bootstrap likelihood

Rights
Creative Commons Attribution 4.0 International License.

Citation

Karabatsos, George; Leisen, Fabrizio. An approximate likelihood perspective on ABC methods. Statist. Surv. 12 (2018), 66--104. doi:10.1214/18-SS120. https://projecteuclid.org/euclid.ssu/1528509818


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