Theoretical and Methodological Aspects of Markov Chain Monte Carlo Computations with Noisy Likelihoods

Authored by: Christophe Andrieu , Anthony Lee , Matti Vihola

Handbook of Approximate Bayesian Computation

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

Print ISBN: 9781439881507
eBook ISBN: 9781315117195
Adobe ISBN:

10.1201/9781315117195-9

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Abstract

Approximate Bayesian computation (ABC) [1,2] is a popular method for Bayesian inference involving an intractable, or expensive to evaluate, likelihood function, but where simulation from the model is easy. The method consists of defining an alternative likelihood function, which is also in general intractable, but naturally lends itself to pseudo-marginal computations [3], hence, making the approach of practical interest. The aim of this chapter is to show the connections of ABC Markov chain Monte Carlo with pseudo-marginal algorithms, review their existing theoretical results, and discuss how these can inform practice and hopefully lead to fruitful methodological developments.

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