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Approximate Bayesian computation (ABC), also known as likelihood-freemethods, have become a favourite tool for the analysis of complex stochasticmodels, primarily in population genetics but also in financial analyses. Weadvocated in Grelaud et al. (2009) the use of ABC for Bayesian model choice inthe specific case of Gibbs random fields (GRF), relying on a sufficiencyproperty mainly enjoyed by GRFs to show that the approach was legitimate.Despite having previously suggested the use of ABC for model choice in a widerrange of models in the DIY ABC software (Cornuet et al., 2008), we presenttheoretical evidence that the general use of ABC for model choice is fraughtwith danger in the sense that no amount of computation, however large, canguarantee a proper approximation of the posterior probabilities of the modelsunder comparison.

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