Open Access
March 2011 Likelihood-free estimation of model evidence
Xavier Didelot, Richard G. Everitt, Adam M. Johansen, Daniel J. Lawson
Bayesian Anal. 6(1): 49-76 (March 2011). DOI: 10.1214/11-BA602


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 efficiency 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 different demographic models based upon genetic data from the Y chromosome.


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Xavier Didelot. Richard G. Everitt. Adam M. Johansen. Daniel J. Lawson. "Likelihood-free estimation of model evidence." Bayesian Anal. 6 (1) 49 - 76, March 2011.


Published: March 2011
First available in Project Euclid: 13 June 2012

zbMATH: 1330.62118
MathSciNet: MR2781808
Digital Object Identifier: 10.1214/11-BA602

Primary: 62F15
Secondary: 62P10 , 65C05 , 68W20

Rights: Copyright © 2011 International Society for Bayesian Analysis

Vol.6 • No. 1 • March 2011
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