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Likelihood-Free Algorithms

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Book cover Likelihood-Free Methods for Cognitive Science

Part of the book series: Computational Approaches to Cognition and Perception ((CACP))

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Abstract

In this chapter, we will present several algorithms, which differ in how they approximate the likelihood function and generate proposals for the posterior distribution, for performing likelihood-free inference. Four classes of algorithms—rejection-based, kernel-based, general methods, and hierarchical—will be discussed in great detail. We will provide a brief overview of the origins of each class as well as discussing the advantages and disadvantages of each. Finally, we will close the discussion by offering guidance on how to choose the appropriate class of algorithms for use in a given situation.

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Notes

  1. 1.

    The notation Model(θ) describes the distribution of a random variable X, whereas the notation Model(y|θ) denotes the probability density at the location y, conditional on the parameters θ, as in Eq. (1.2).

  2. 2.

    For the curious reader, the file GibbsABC.R contains code to sample from the posterior using traditional Gibbs sampling, as well as the Gibbs ABC algorithm so that accuracy of the algorithm can be assessed. Within this code, the parameters of the conditional distribution are specified.

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Authors and Affiliations

  1. Department of Psychology, The Ohio State University, Columbus, OH, USA

    James J. Palestro, Per B. Sederberg, Trisha Van Zandt & Brandon M. Turner

  2. University of Melbourne, Parkville, VIC, Australia

    Adam F. Osth

Authors
  1. James J. Palestro
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  2. Per B. Sederberg
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  3. Adam F. Osth
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  4. Trisha Van Zandt
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  5. Brandon M. Turner
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Palestro, J.J., Sederberg, P.B., Osth, A.F., Zandt, T.V., Turner, B.M. (2018). Likelihood-Free Algorithms. In: Likelihood-Free Methods for Cognitive Science. Computational Approaches to Cognition and Perception. Springer, Cham. https://doi.org/10.1007/978-3-319-72425-6_2

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