Likelihood-free estimation of model evidence

X Didelot, RG Everitt, AM Johansen, DJ Lawson

Research output: Contribution to journalArticle (Academic Journal)peer-review

59 Citations (Scopus)

Abstract

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of \likelihood-free" methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in e±ciency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of di®erent demographic models based upon genetic data from the Y chromosome.
Translated title of the contributionLikelihood-free estimation of model evidence
Original languageEnglish
Pages (from-to)49 - 76
Number of pages28
JournalBayesian Analysis
Volume6
Issue number1
DOIs
Publication statusPublished - Jan 2011

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