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Approximate Bayesian Computation: A Survey on Recent Results

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 163)

Abstract

Approximate Bayesian Computation (ABC) methods have become a “mainstream” statistical technique in the past decade, following the realisation by statisticians that they are a special type of non-parametric inference. In this survey of ABC methods, we focus on the recent literature, building on the previous survey of Marin et al. Stat Comput 21(2):279–291, 2011, [39]. Given the importance of model choice in the applications of ABC, and the associated difficulties in its implementation, we also give emphasis to this aspect of ABC techniques.

Keywords

  • Approximate Bayesian computation
  • Likelihood-free methods
  • Bayesian model choice
  • Sufficiency
  • Monte Carlo methods
  • Summary statistics

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Notes

  1. 1.

    As detailed below, the distance may depend solely on an insufficient statistic \(S(\varvec{x})\) and hence not be a distance from a formal perspective, while introduction a second level of approximation to the ABC scheme.

  2. 2.

    Or, more accurately, posterior-to-prior.

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Acknowledgments

The author is most grateful to an anonymous referee for her or his help with the syntax and grammar of this survey. He also thanks the organisers of MCqMC 2014 in Leuven for their kind invitation.

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Robert, C.P. (2016). Approximate Bayesian Computation: A Survey on Recent Results. In: Cools, R., Nuyens, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-319-33507-0_7

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