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Centre de Recherche en Économie et Statistique |  |
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Centre de Recherche en Économie et Statistique | |
| HAL : hal-00567239, version 1 |
| arXiv : 1101.5091 |
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| Why approximate Bayesian computational (ABC) methods cannot handle model choice problems |
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| Christian P. Robert 1, 2, 3Jean-michel MARIN 4 |
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| (27/01/2011) |
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| 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 large, can guarantee a proper approximation of the posterior probabilities of the models under comparison. |
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| 1 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 2 : | Centre de Recherche en Économie et Statistique (CREST) |
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INSEE – École Nationale de la Statistique et de l'Administration Économique |
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| 3 : | Institut Universitaire de France (IUF) |
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Ministère de l'Enseignement Supérieur et de la Recherche Scientifique |
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| 4 : | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
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CNRS : UMR5149 – Université Montpellier II - Sciences et techniques |
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| 5 : | Department of Statistics, Harvard University |
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Harvard university (Cambridge, USA) |
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| Domaine | : | Statistiques/Calcul Statistiques/Applications |
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| ABC – model choice – Bayes factor – sufficiency |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1101.5091 |
| hal-00567239, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00567239 | |
| oai:hal.archives-ouvertes.fr:hal-00567239 | |
| Contributeur : Christian Robert | |
| Soumis le : Samedi 19 Février 2011, 08:43:36 | |
| Dernière modification le : Samedi 19 Février 2011, 08:43:36 | |
