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A Scheme for Adaptive Selection of Population Sizes in Approximate Bayesian Computation - Sequential Monte Carlo

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Computational Methods in Systems Biology (CMSB 2017)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 10545))

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Abstract

Parameter inference and model selection in systems biology often requires likelihood-free methods, such as Approximate Bayesian Computation (ABC). In recent years, this approach has frequently been combined with a Sequential Monte Carlo (ABC-SMC) scheme. In this scheme, the approximation of the posterior distribution through a population of particles is iteratively improved by a sequential sampling strategy. However, it has been difficult to give general guidelines on how to choose the size of these populations. In this manuscript, we propose a method to adaptively and automatically select these population sizes. The method exploits the cross-validated approximation error of a kernel density estimate of the particles in the current population to select the number of particles for the subsequent population.

We found the proposed method to be robust to the initially chosen population size and to the number of posterior modes. We demonstrated that the method is applicable to parameter inference as well as to model selection. The study of a computationally demanding multiscale model confirmed the method’s scalability. In conclusion, the proposed method is applicable to a wide range of parameter and model selection tasks. The method makes the influence of the population size on the approximation error explicit simplifying the application of ABC-SMC schemes.

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Notes

  1. 1.

    A population is a sequence of pairs. Pairs \((w,\theta )\) can occur multiple times in a population. The curly braces \(\{\}\) denote a finite sequence (not a set).

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Authors and Affiliations

  1. Department of Connectomics, Max Planck Institute for Brain Research, 60438, Frankfurt, Germany

    Emmanuel Klinger

  2. Helmholtz Zentrum München - German Research Center for Environmental Health, Institute of Computational Biology, 85764, Neuherberg, Germany

    Emmanuel Klinger & Jan Hasenauer

  3. Center for Mathematics, Chair of Mathematical Modeling of Biological Systems, Technische Universität München, 85748, Garching, Germany

    Emmanuel Klinger & Jan Hasenauer

Authors
  1. Emmanuel Klinger
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  2. Jan Hasenauer
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Correspondence to Jan Hasenauer .

Editor information

Editors and Affiliations

  1. Inria & École normale supérieure, Paris, France

    Jérôme Feret

  2. Technische Universität Darmstadt, Darmstadt, Germany

    Heinz Koeppl

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Klinger, E., Hasenauer, J. (2017). A Scheme for Adaptive Selection of Population Sizes in Approximate Bayesian Computation - Sequential Monte Carlo. In: Feret, J., Koeppl, H. (eds) Computational Methods in Systems Biology. CMSB 2017. Lecture Notes in Computer Science(), vol 10545. Springer, Cham. https://doi.org/10.1007/978-3-319-67471-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-67471-1_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67470-4

  • Online ISBN: 978-3-319-67471-1

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