Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Tina Toni, David Welch, Natalja Strelkowa, Andreas Ipsen, Michael P.H Stumpf

Abstract

Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.

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Footnotes

  • Present address: Department of Statistics, Pennsylvania State University, University Park, PA 16802, USA.

  • For a more general version of the algorithm, suitable especially for application to stochastic models, see appendix A.

  • In the stochastic framework, we again suggest using the general form of the algorithm with Bt>1; see appendix A.

  • See also http://web.maths.unsw.edu.au/scott/papers/paper_smcabc_optimal.pdf.

  • This, including the experiment below, was suggested by Beaumont (2008b).

    • Received April 30, 2008.
    • Accepted June 12, 2008.
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