Approximating the Likelihood in ABC

Authored by: Christopher C. Drovandi , Clara Grazian , Kerrie Mengersen , Christian Robert

Handbook of Approximate Bayesian Computation

Print publication date:  August  2018
Online publication date:  August  2018

Print ISBN: 9781439881507
eBook ISBN: 9781315117195
Adobe ISBN:

10.1201/9781315117195-12

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Abstract

Approximate Bayesian computation (ABC) is now a mature algorithm for likelihood-free estimation. It has been successfully applied to a wide range of real-world problems for which more standard analytic tools were unsuitable due to the absence or complexity of the associated likelihood. It has also paved the way for a range of algorithmic extensions that take advantage of appealing ideas embedded in other approaches. Despite the usefulness of ABC, the method does have a number of drawbacks. The approach is simulation intensive, requires tuning of the tolerance threshold, discrepancy function and weighting function, and suffers from a curse of dimensionality of the summary statistic. The latter issue stems from the fact that ABC uses a non-parametric estimate of the likelihood function of a summary statistic (Blum, 2010).

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