Likelihood-free estimation of model evidence

Didelot, X., Everitt, R. G., Johansen, A. M. and Lawson, D. J. (2011) Likelihood-free estimation of model evidence. Bayesian Analysis, 6 (1). pp. 49-76. ISSN 1931-6690 doi: 10.1214/11-BA602

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/29114
Identification Number/DOI	10.1214/11-BA602
Refereed	Yes
Divisions	No Reading authors. Back catalogue items Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics > Applied Statistics
Publisher	International Society for Bayesian Analysis
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