| Resumo: |
Approximate Bayesian computation (ABC), also known as likelihood-free methods, have become a standard tool for the analysis of complex models, primarily in population genetics but also for complex financial models. The development of new ABC methodology is undergoing a rapid increase in the past years, as shown by multiple publications, conferences and even software. While one valid interpretation of ABC based estimation is connected with nonparametrics, the setting is quite different for model choice issues. We examined in Grelaud et al. (2009, Bayesian Analysis) the use of ABC for Bayesian model choice in the specific of Gaussian random fields (GRF), relying on a sufficient property only 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, Bioinformatics, 24:2713-2719), we present in Robert et al. (http://arxiv.org/abs/1102.4432) theoretical evidence that the general use of ABC for model choice is fraught with danger in the sense that no amount of computation, however large, can guarantee a proper approximation of the posterior probabilities of the models under comparison. This work shows as a corollary that GRFs are the most natural exception to this lack of convergence.
|
