Bayesian Analysis

Adapting the ABC Distance Function

Dennis Prangle

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Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are close enough to the observations. There has been much progress on deciding which summary statistics of the data should be used to judge closeness, but less work on how to weight them. Typically weights are chosen at the start of the algorithm which normalise the summary statistics to vary on similar scales. However these may not be appropriate in iterative ABC algorithms, where the distribution from which the parameters are proposed is updated. This can substantially alter the resulting distribution of summary statistics, so that different weights are needed for normalisation. This paper presents two iterative ABC algorithms which adaptively update their weights and demonstrates improved results on test applications.

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Bayesian Anal., Volume 12, Number 1 (2017), 289-309.

First available in Project Euclid: 14 April 2016

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likelihood-free inference population Monte Carlo quantile distributions Lotka–Volterra

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Prangle, Dennis. Adapting the ABC Distance Function. Bayesian Anal. 12 (2017), no. 1, 289--309. doi:10.1214/16-BA1002.

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  • Barnes, C. P., Filippi, S., and Stumpf, M. P. H. (2012). “Contribution to the discussion of Fearnhead and Prangle (2012).” Journal of the Royal Statistical Society: Series B, 74: 453.
  • Beaumont, M. A. (2010). “Approximate Bayesian computation in evolution and ecology.” Annual Review of Ecology, Evolution and Systematics, 41: 379–406.
  • Beaumont, M. A., Cornuet, J.-M., Marin, J.-M., and Robert, C. P. (2009). “Adaptive approximate Bayesian computation.” Biometrika, 2025–2035.
  • Beaumont, M. A., Zhang, W., and Balding, D. J. (2002). “Approximate Bayesian Computation in Population Genetics.” Genetics, 162: 2025–2035.
  • Bezanson, J., Karpinski, S., Shah, V. B., and Edelman, A. (2012). “Julia: A fast dynamic language for technical computing.” arXiv:1209.5145.
  • Biau, G., Cérou, F., and Guyader, A. (2015). “New insights into Approximate Bayesian Computation.” Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques, 51(1): 376–403.
  • Blum, M. G. B., Nunes, M. A., Prangle, D., and Sisson, S. A. (2013). “A comparative review of dimension reduction methods in approximate Bayesian computation.” Statistical Science, 28: 189–208.
  • Bonassi, F. V. and West, M. (2015). “Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation.” Bayesian Analysis, 10(1): 171–187.
  • Cappé, O., Guillin, A., Marin, J.-M., and Robert, C. P. (2004). “Population Monte Carlo.” Journal of Computational and Graphical Statistics, 13(4).
  • Csilléry, K., Blum, M. G. B., Gaggiotti, O., and François, O. (2010). “Approximate Bayesian Computation in practice.” Trends in Ecology & Evolution, 25: 410–418.
  • Csilléry, K., François, O., and Blum, M. G. B. (2012). “abc: an R package for approximate Bayesian computation (ABC).” Methods in Ecology and Evolution, 3: 475–479.
  • Del Moral, P., Doucet, A., and Jasra, A. (2012). “An adaptive sequential Monte Carlo method for approximate Bayesian computation.” Statistics and Computing, 22(5): 1009–1020.
  • Drovandi, C. C. and Pettitt, A. N. (2011a). “Estimation of parameters for macroparasite population evolution using approximate Bayesian computation.” Biometrics, 67(1): 225–233.
  • Drovandi, C. C. and Pettitt, A. N. (2011b). “Likelihood-free Bayesian estimation of multivariate quantile distributions.” Computational Statistics & Data Analysis, 55(9): 2541–2556.
  • Fasiolo, M. and Wood, S. N. (2015). “Approximate methods for dynamic ecological models.” arXiv:1511.02644.
  • Fearnhead, P. and Prangle, D. (2012). “Constructing Summary Statistics for Approximate Bayesian Computation: Semi-automatic ABC.” Journal of the Royal Statistical Society, Series B, 74: 419–474.
  • Lenormand, M., Jabot, F., and Deffuant, G. (2013). “Adaptive approximate Bayesian computation for complex models.” Computational Statistics, 28(6): 2777–2796.
  • Marin, J.-M., Pudlo, P., Robert, C. P., and Ryder, R. J. (2012). “Approximate Bayesian computational methods.” Statistics and Computing, 22(6): 1167–1180.
  • McKinley, T., Cook, A. R., and Deardon, R. (2009). “Inference in epidemic models without likelihoods.” The International Journal of Biostatistics, 5(1).
  • Owen, J., Wilkinson, D. J., and Gillespie, C. S. (2015). “Likelihood free inference for Markov processes: a comparison.” Statistical applications in genetics and molecular biology, 14(2): 189–209.
  • Prangle, D. (2016). “Adapting the ABC distance function: Supplementary Material.” Bayesian Analysis.
  • Rayner, G. D. and MacGillivray, H. L. (2002). “Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions.” Statistics and Computing, 12(1): 57–75.
  • Sedki, M., Pudlo, P., Marin, J.-M., Robert, C. P., and Cornuet, J.-M. (2012). “Efficient learning in ABC algorithms.” arXiv:1210.1388.
  • Silk, D., Filippi, S., and Stumpf, M. P. H. (2013). “Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems.” Statistical Applications in Genetics and Molecular Biology, 12(5): 603–618.
  • Sisson, S. A., Fan, Y., and Tanaka, M. M. (2009). “Correction: Sequential Monte Carlo without likelihoods.” Proceedings of the National Academy of Sciences, 106(39): 16889–16890.
  • Toni, T., Welch, D., Strelkowa, N., Ipsen, A., and Stumpf, M. (2009). “Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems.” Journal of The Royal Society Interface, 6(31): 187–202.

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