English
From robust tests to robust Bayes-like posterior distribution
Multi angle
Auteurs : Baraud, Yannick (Auteur de la conférence)
CIRM (Editeur )
62F15 - Bayesian inference
62F35 - Robustness and adaptive procedures
62G05 - Nonparametric estimation
62G35 - Robustness
CIRM (Editeur )
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Résumé :
We address the problem of estimating the distribution of presumed i.i.d. observations within the framework of Bayesian statistics. We propose a new posterior distribution that shares some similarities with the classical Bayesian one. In particular, when the statistical model is exact, we show that this new posterior distribution concentrates its mass around the target distribution, just as the classical Bayes posterior would do. However, unlike the Bayes posterior, we prove that these concentration properties remain stable when the equidistribution assumption is violated or when the data are i.i.d. with a distribution that does not belong to our model but only lies close enough to it. The results we obtain are non-asymptotic and involve explicit numerical constants.
Mots-Clés : robust statistics; bayesian posterior; robust estimation; density estimation.
Codes MSC : Mots-Clés : robust statistics; bayesian posterior; robust estimation; density estimation.
62F15 - Bayesian inference
62F35 - Robustness and adaptive procedures
62G05 - Nonparametric estimation
62G35 - Robustness
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Informations sur la Vidéo
Réalisateur : Récanzone, LucaLangue : Anglais Date de Publication : 14/01/2025 Date de Captation : 16/12/2024 Sous Collection : Research talks Catégorie arXiv : Statistics Theory Domaine(s) : Probabilités & Statistiques Format : MP4 (.mp4) - HD Durée : 00:30:56 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-16_baraud.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : New challenges in high-dimensional statistics / Statistique mathématiqueOrganisateurs de la Rencontre : Klopp, Olga ; Pouet, Christophe ; Rakhlin, Alexander Dates : 16/12/2024 - 20/12/2024 Année de la rencontre : 2024 URL de la Rencontre : https://conferences.cirm-math.fr/3055.html
Données de citation
DOI : 10.24350/CIRM.V.20279103Citer cette vidéo: Baraud, Yannick (2024). From robust tests to robust Bayes-like posterior distribution. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20279103 URI : http://dx.doi.org/10.24350/CIRM.V.20279103 |
Voir Aussi
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Bibliographie
- AUDIBERT, Jean-Yves et CATONI, Olivier. Linear regression through PAC-Bayesian truncation. arXiv preprint arXiv:1010.0072, 2010.² - https://doi.org/10.48550/arXiv.1010.0072
- BARAUD, Yannick. Tests and estimation strategies associated to some loss functions. Probability Theory and Related Fields, 2021, vol. 180, no 3, p. 799-846. - https://doi.org/10.1007/s00440-021-01065-1
- BARAUD, Yannick. From robust tests to Bayes-like posterior distributions. Probability Theory and Related Fields, 2024, vol. 188, no 1, p. 159-234. - https://doi.org/10.1007/s00440-023-01222-8
- BIRGÉ, Lucien. About the non-asymptotic behaviour of Bayes estimators. Journal of statistical planning and inference, 2015, vol. 166, p. 67-77. - https://doi.org/10.1016/j.jspi.2014.07.009
- GHOSAL, Subhashis, GHOSH, Jayanta K., et VAN DER VAART, Aad W. Convergence rates of posterior distributions. Annals of Statistics, 2000, p. 500-531. - https://www.jstor.org/stable/2674039
- LE CAM, L. On local and global properties in the theory of asymptotic normality of experiments. Stochastic processes and related topics, 1975, vol. 1, p. 13-54. -
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