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Hierarchical Approximate Bayesian Computation

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  • Brandon Turner

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  • Trisha Zandt

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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. Copyright The Psychometric Society 2014

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    File URL: http://hdl.handle.net/10.1007/s11336-013-9381-x
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    Bibliographic Info

    Article provided by Springer in its journal Psychometrika.

    Volume (Year): 79 (2014)
    Issue (Month): 2 (April)
    Pages: 185-209

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    Handle: RePEc:spr:psycho:v:79:y:2014:i:2:p:185-209

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    Related research

    Keywords: approximate Bayesian computation; hierarchical Bayesian estimation; signal detection theory; dynamic signal detection;

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    1. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, 06.
    2. Jeffrey Rouder & Dongchu Sun & Paul Speckman & Jun Lu & Duo Zhou, 2003. "A hierarchical bayesian statistical framework for response time distributions," Psychometrika, Springer, vol. 68(4), pages 589-606, December.
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