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Kernel approximate Bayesian computation in population genetic inferences

Author

Listed:
  • Nakagome Shigeki

    (Department of Mathematical Analysis and Statistical Inference, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan)

  • Fukumizu Kenji

    (Department of Mathematical Analysis and Statistical Inference, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan)

  • Mano Shuhei

    (Department of Mathematical Analysis and Statistical Inference, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan Japan Science and Technology Agency, 4-1-8, Honcho, Kawaguchi-shi, Saitama 332-0012, Japan)

Abstract

Approximate Bayesian computation (ABC) is a likelihood-free approach for Bayesian inferences based on a rejection algorithm method that applies a tolerance of dissimilarity between summary statistics from observed and simulated data. Although several improvements to the algorithm have been proposed, none of these improvements avoid the following two sources of approximation: 1) lack of sufficient statistics: sampling is not from the true posterior density given data but from an approximate posterior density given summary statistics; and 2) non-zero tolerance: sampling from the posterior density given summary statistics is achieved only in the limit of zero tolerance. The first source of approximation can be improved by adding a summary statistic, but an increase in the number of summary statistics could introduce additional variance caused by the low acceptance rate. Consequently, many researchers have attempted to develop techniques to choose informative summary statistics. The present study evaluated the utility of a kernel-based ABC method [Fukumizu, K., L. Song and A. Gretton (2010): “Kernel Bayes’ rule: Bayesian inference with positive definite kernels,” arXiv, 1009.5736 and Fukumizu, K., L. Song and A. Gretton (2011): “Kernel Bayes’ rule. Advances in Neural Information Processing Systems 24.” In: J. Shawe-Taylor and R. S. Zemel and P. Bartlett and F. Pereira and K. Q. Weinberger, (Eds.), pp. 1549–1557., NIPS 24: 1549–1557] for complex problems that demand many summary statistics. Specifically, kernel ABC was applied to population genetic inference. We demonstrate that, in contrast to conventional ABCs, kernel ABC can incorporate a large number of summary statistics while maintaining high performance of the inference.

Suggested Citation

  • Nakagome Shigeki & Fukumizu Kenji & Mano Shuhei, 2013. "Kernel approximate Bayesian computation in population genetic inferences," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(6), pages 667-678, December.
  • Handle: RePEc:bpj:sagmbi:v:12:y:2013:i:6:p:667-678:n:2
    DOI: 10.1515/sagmb-2012-0050
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    References listed on IDEAS

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    1. C. C. Drovandi & A. N. Pettitt, 2011. "Estimation of Parameters for Macroparasite Population Evolution Using Approximate Bayesian Computation," Biometrics, The International Biometric Society, vol. 67(1), pages 225-233, March.
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    4. Nunes Matthew A & Balding David J, 2010. "On Optimal Selection of Summary Statistics for Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-16, September.
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