  Approximate Bayesian computation (ABC) have become a essential tool for the
analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated
the use of ABC for Bayesian model choice in the specific case of Gibbs random
fields, relying on a inter-model sufficiency property to show that the
approximation was legitimate. Having implemented ABC-based model choice in a
wide range of phylogenetic models in the DIY-ABC software (Cornuet et al.,
2008), we now present theoretical background as to why a generic use of ABC for
model choice is ungrounded, since it depends on an unknown amount of
information loss induced by the use of insufficient summary statistics. The
approximation error of the posterior probabilities of the models under
comparison may thus be unrelated with the computational effort spent in running
an ABC algorithm. We then conclude that additional empirical verifications of
the performances of the ABC procedure as those available in DIYABC are
necessary to conduct model choice.
