IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v99y2015icp31-42.html
   My bibliography  Save this article

AABC: Approximate approximate Bayesian computation for inference in population-genetic models

Author

Listed:
  • Buzbas, Erkan O.
  • Rosenberg, Noah A.

Abstract

Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric models when evaluating likelihoods is difficult. Central to the success of ABC methods, which have been used frequently in biology, is computationally inexpensive simulation of data sets from the parametric model of interest. However, when simulating data sets from a model is so computationally expensive that the posterior distribution of parameters cannot be adequately sampled by ABC, inference is not straightforward. We present “approximate approximate Bayesian computation†(AABC), a class of computationally fast inference methods that extends ABC to models in which simulating data is expensive. In AABC, we first simulate a number of data sets small enough to be computationally feasible to simulate from the parametric model. Conditional on these data sets, we use a statistical model that approximates the correct parametric model and enables efficient simulation of a large number of data sets. We show that under mild assumptions, the posterior distribution obtained by AABC converges to the posterior distribution obtained by ABC, as the number of data sets simulated from the parametric model and the sample size of the observed data set increase. We demonstrate the performance of AABC on a population-genetic model of natural selection, as well as on a model of the admixture history of hybrid populations. This latter example illustrates how, in population genetics, AABC is of particular utility in scenarios that rely on conceptually straightforward but potentially slow forward-in-time simulations.

Suggested Citation

  • Buzbas, Erkan O. & Rosenberg, Noah A., 2015. "AABC: Approximate approximate Bayesian computation for inference in population-genetic models," Theoretical Population Biology, Elsevier, vol. 99(C), pages 31-42.
  • Handle: RePEc:eee:thpobi:v:99:y:2015:i:c:p:31-42
    DOI: 10.1016/j.tpb.2014.09.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580914000744
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.tpb.2014.09.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/6334 is not listed on IDEAS
    2. 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.
    3. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    4. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    5. Siegmund Kimberly D. & Marjoram Paul & Shibata Darryl, 2008. "Modeling DNA Methylation in a Population of Cancer Cells," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-23, June.
    6. Bonassi Fernando V. & You Lingchong & West Mike, 2011. "Bayesian Learning from Marginal Data in Bionetwork Models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, October.
    7. Joyce Paul & Marjoram Paul, 2008. "Approximately Sufficient Statistics and Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-18, August.
    8. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cecilia Viscardi & Michele Boreale & Fabio Corradi, 2021. "Weighted approximate Bayesian computation via Sanov’s theorem," Computational Statistics, Springer, vol. 36(4), pages 2719-2753, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wilkinson Richard David, 2013. "Approximate Bayesian computation (ABC) gives exact results under the assumption of model error," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(2), pages 129-141, May.
    2. Baey, Charlotte & Smith, Henrik G. & Rundlöf, Maj & Olsson, Ola & Clough, Yann & Sahlin, Ullrika, 2023. "Calibration of a bumble bee foraging model using Approximate Bayesian Computation," Ecological Modelling, Elsevier, vol. 477(C).
    3. Mikael Sunnåker & Alberto Giovanni Busetto & Elina Numminen & Jukka Corander & Matthieu Foll & Christophe Dessimoz, 2013. "Approximate Bayesian Computation," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-10, January.
    4. Creel, Michael & Kristensen, Dennis, 2016. "On selection of statistics for approximate Bayesian computing (or the method of simulated moments)," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 99-114.
    5. Silk Daniel & Filippi Sarah & Stumpf Michael P. H., 2013. "Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(5), pages 603-618, October.
    6. Li, J. & Nott, D.J. & Fan, Y. & Sisson, S.A., 2017. "Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 77-89.
    7. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    8. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.
    9. Jonathan U Harrison & Ruth E Baker, 2020. "An automatic adaptive method to combine summary statistics in approximate Bayesian computation," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-21, August.
    10. Prangle Dennis & Fearnhead Paul & Cox Murray P. & Biggs Patrick J. & French Nigel P., 2014. "Semi-automatic selection of summary statistics for ABC model choice," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 67-82, February.
    11. Frazier, David T. & Maneesoonthorn, Worapree & Martin, Gael M. & McCabe, Brendan P.M., 2019. "Approximate Bayesian forecasting," International Journal of Forecasting, Elsevier, vol. 35(2), pages 521-539.
    12. Creel, Michael & Kristensen, Dennis, 2015. "ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 85-108.
    13. Soubeyrand Samuel & Carpentier Florence & Guiton François & Klein Etienne K., 2013. "Approximate Bayesian computation with functional statistics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 17-37, March.
    14. 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.
    15. Michael Stocks & Mathieu Siol & Martin Lascoux & Stéphane De Mita, 2014. "Amount of Information Needed for Model Choice in Approximate Bayesian Computation," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-13, June.
    16. Soubeyrand, Samuel & Haon-Lasportes, Emilie, 2015. "Weak convergence of posteriors conditional on maximum pseudo-likelihood estimates and implications in ABC," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 84-92.
    17. D.T. Frazier & G.M. Martin & C.P. Robert & J. Rousseau, 2016. "Asymptotic Properties of Approximate Bayesian Computation," Monash Econometrics and Business Statistics Working Papers 18/16, Monash University, Department of Econometrics and Business Statistics.
    18. Xing Ju Lee & Christopher C. Drovandi & Anthony N. Pettitt, 2015. "Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets," Biometrics, The International Biometric Society, vol. 71(1), pages 198-207, March.
    19. McKinley, Trevelyan J. & Ross, Joshua V. & Deardon, Rob & Cook, Alex R., 2014. "Simulation-based Bayesian inference for epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 434-447.
    20. Pierre-Olivier Goffard & Patrick Laub, 2021. "Approximate Bayesian Computations to fit and compare insurance loss models," Working Papers hal-02891046, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:99:y:2015:i:c:p:31-42. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.