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| HAL : hal-00721164, version 1 |
| arXiv : 1207.6461 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (27-07-2012) | v2 (03-06-2013) |
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| New Insights into Approximate Bayesian Computation |
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| Gérard Biau 1, 2, 3, 4Frédéric Cérou 5 |
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| (26/07/2012) |
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| Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever suitable likelihoods are not available. In the present paper, we analyze the procedure from the point of view of k-nearest neighbor theory and explore the statistical properties of its outputs. We discuss in particular some asymptotic features of the genuine conditional density estimate associated with ABC, which is a new interesting hybrid between a k-nearest neighbor and a kernel method. |
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| 1 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot |
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| 2 : | Laboratoire de Statistique Théorique et Appliquée (LSTA) |
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Université Pierre et Marie Curie (UPMC) - Paris VI |
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| 3 : | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris |
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| 4 : | CLASSIC (INRIA Paris - Rocquencourt) |
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Ecole normale supérieure de Paris - ENS Paris – INRIA |
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| 5 : | ASPI (INRIA - IRISA) |
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INRIA – Université de Rennes 1 – Université de Rennes II - Haute Bretagne |
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| Processus stochastique |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| Approximate Bayesian Computation – Nonparametric estimation – Conditional density estimation – Nearest neighbor methods – Mathematical statistics |
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| hal-00721164, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00721164 | |
| oai:hal.archives-ouvertes.fr:hal-00721164 | |
| Contributeur : Gérard Biau | |
| Soumis le : Jeudi 26 Juillet 2012, 16:58:13 | |
| Dernière modification le : Lundi 10 Septembre 2012, 09:44:25 | |
