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Hierarchical Approximate Bayesian Computation

Published online by Cambridge University Press:  01 January 2025

Brandon M. Turner  and
Trisha Van Zandt
Brandon M. Turner*
Affiliation:
Stanford University
Trisha Van Zandt
Affiliation:
The Ohio State University
*
Requests for reprints should be sent to Brandon M. Turner, Stanford University, Stanford, USA. E-mail: turner.826@gmail.com
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Abstract

Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper, we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function.

Keywords

approximate Bayesian computationhierarchical Bayesian estimationsignal detection theorydynamic signal detection

Information

Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 2 , April 2014 , pp. 185 - 209
Copyright
Copyright © 2013 The Psychometric Society

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