DOI: 10.1007/S11336-013-9381-X HIERARCHICAL APPROXIMATE BAYESIAN COMPUTATION

Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior dis-tribution 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 ac-commodate. 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 tech-niques 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. Key words: approximate Bayesian computation, hierarchical Bayesian estimation, signal detection the-ory, dynamic signal detection