Computational Statistics

, Volume 28, Issue 6, pp 2777–2796 | Cite as

Adaptive approximate Bayesian computation for complex models

  • Maxime Lenormand
  • Franck Jabot
  • Guillaume Deffuant
Original Paper


We propose a new approximate Bayesian computation (ABC) algorithm that aims at minimizing the number of model runs for reaching a given quality of the posterior approximation. This algorithm automatically determines its sequence of tolerance levels and makes use of an easily interpretable stopping criterion. Moreover, it avoids the problem of particle duplication found when using a MCMC kernel. When applied to a toy example and to a complex social model, our algorithm is 2–8 times faster than the three main sequential ABC algorithms currently available.


ABC Population Monte Carlo Sequential Monte Carlo 



This publication has been funded by the Prototypical policy impacts on multifunctional activities in rural municipalities collaborative project, European Union 7th Framework Programme (ENV 2007-1), contract no. 212345. The work of the first author has been funded by the Auvergne region.


  1. Beaumont MA (2010) Approximate Bayesian computation in evolution and ecology. Annu Rev Ecol Evol Syst 41(1):379–406Google Scholar
  2. Beaumont MA, Cornuet J, Marin J, Robert CP (2009) Adaptive approximate Bayesian computation. Biometrika 96(4):983–990Google Scholar
  3. Beaumont MA, Zhang W, Balding DJ (2002) Approximate Bayesian computation in population genetics. Genetics 162(4):2025–2035Google Scholar
  4. Blum MGB, François O (2010) Non-linear regression models for approximate Bayesian computation. Stat Comput 20(1):63–73MathSciNetCrossRefGoogle Scholar
  5. Carnell R (2009) lhs: Latin hypercube samples. R package version 0.5Google Scholar
  6. Del Moral P, Doucet A, Jasra A (2006) Sequential Monte Carlo samplers. J R Stat Soc Ser B Stat Methodol 68(3):411–436MathSciNetCrossRefzbMATHGoogle Scholar
  7. Del Moral P, Doucet A, Jasra A (2012) An adaptive sequential Monte Carlo method for approximate Bayesian computation. Stat Comput 22(5):1009–1020MathSciNetCrossRefzbMATHGoogle Scholar
  8. Drovandi CC, Pettitt AN (2011) Estimation of parameters for macroparasite population evolution using approximate Bayesian computation. Biometrics 67(1):225–233MathSciNetCrossRefzbMATHGoogle Scholar
  9. Fearnhead P, Prangle D (2011) Constructing summary statistics for approximate Bayesian computation: semi-automatic ABC. Technical report 1004.1112. arXiv.orgGoogle Scholar
  10. Filippi S, Barnes C, Stumpf MPH (2012) On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo. arXiv:1106.6280v4Google Scholar
  11. Glynn P, Whitt W (1992) The asymptotic effciency of simulation estimators. Oper Res 40(3):505–520MathSciNetCrossRefzbMATHGoogle Scholar
  12. Huet S, Deffuant G (2011) Common framework for the microsimulation model in prima project. Technical report, Cemagref LISCGoogle Scholar
  13. Jabot F, Faure T, Dumoulin N (2013) EasyABC: performing efficient approximate Bayesian computation sampling schemes using R. Methods Ecol Evol (in press). doi: 10.1111/2041-210X.12050
  14. Joyce P, Marjoram P (2008) Approximately sufficient statistics and Bayesian computation. Stat Appl Genet Mol Biol 7(1):1–18Google Scholar
  15. Marjoram P, Molitor J, Plagnol V, Tavaré S (2003) Markov chain Monte Carlo without likelihoods. Proc Natl Acad Sci USA 100(26):15324–15328CrossRefGoogle Scholar
  16. R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0Google Scholar
  17. Sisson SA, Fan Y, Tanaka MM (2007) Sequential Monte Carlo without likelihoods. Proc Natl Acad Sci USA 104(6):1760–1765MathSciNetCrossRefzbMATHGoogle Scholar
  18. Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MPH (2009) Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface 6:187CrossRefGoogle Scholar
  19. Wegmann D, Leuenberger C, Excoffier L (2009) Efficient approximate Bayesian computation coupled with Markov chain Monte Carlo without likelihood. Genetics 182(4):1207–1218CrossRefGoogle Scholar
  20. Wegmann D, Leuenberger C, Neuenschwander S, Excoffier L (2010) Abctoolbox: a versatile toolkit for approximate Bayesian computations. BMC Bioinformatics 11(1):116CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Maxime Lenormand
    • 1
  • Franck Jabot
    • 1
  • Guillaume Deffuant
    • 1
  1. 1.IRSTEALISCAubiereFrance

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