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Why approximate Bayesian computational (ABC) methods cannot handle model choice problems.

Thu, 01/27/2011 - 16:01 — SomNambul
Authors: Christian Robert, Natesh S. Pillai, Jean-Michel Marin
Subjects: Computation
link: http://arxiv.org/abs/1101.5091
Abstract

Approximate Bayesian computation (ABC), also known as likelihood-free
methods, have become a favourite tool for the analysis of complex stochastic
models, primarily in population genetics but also in financial analyses. We
advocated in Grelaud et al. (2009) the use of ABC for Bayesian model choice in
the specific case of Gibbs random fields (GRF), relying on a sufficiency
property mainly enjoyed by GRFs to show that the approach was legitimate.
Despite having previously suggested the use of ABC for model choice in a wider
range of models in the DIY ABC software (Cornuet et al., 2008), we present
theoretical evidence that the general use of ABC for model choice is fraught
with danger in the sense that no amount of computation, however larger, can
guarantee a proper approximation of the posterior probabilities of the models
under comparison.

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