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Hierarchical Approximate Bayesian Computation

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  • Brandon Turner
  • Trisha Zandt

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

Suggested Citation

  • Brandon Turner & Trisha Zandt, 2014. "Hierarchical Approximate Bayesian Computation," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 185-209, April.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:2:p:185-209
    DOI: 10.1007/s11336-013-9381-x
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    References listed on IDEAS

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    1. Jeffrey Rouder & Dongchu Sun & Paul Speckman & Jun Lu & Duo Zhou, 2003. "A hierarchical bayesian statistical framework for response time distributions," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 589-606, December.
    2. 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, June.
    3. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    4. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
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    Cited by:

    1. Inhan Kang & Dylan Molenaar & Roger Ratcliff, 2023. "A Modeling Framework to Examine Psychological Processes Underlying Ordinal Responses and Response Times of Psychometric Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 940-974, September.
    2. Hazra, Indranil & Pandey, Mahesh D. & Manzana, Noldainerick, 2020. "Approximate Bayesian computation (ABC) method for estimating parameters of the gamma process using noisy data," Reliability Engineering and System Safety, Elsevier, vol. 198(C).

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