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From robust tests to robust Bayes-like posterior distribution
Multi angle
Authors : Baraud, Yannick (Author of the conference)
CIRM (Publisher )
62F15 - Bayesian inference
62F35 - Robustness and adaptive procedures
62G05 - Nonparametric estimation
62G35 - Robustness
CIRM (Publisher )
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Abstract :
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.
Keywords : robust statistics; bayesian posterior; robust estimation; density estimation.
MSC Codes : Keywords : 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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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 14/01/2025 Conference Date : 16/12/2024 Subseries : Research talks arXiv category : Statistics Theory Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:30:56 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-16_baraud.mp4 
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Information on the Event
Event Title : New challenges in high-dimensional statistics / Statistique mathématiqueEvent Organizers : Klopp, Olga ; Pouet, Christophe ; Rakhlin, Alexander Dates : 16/12/2024 - 20/12/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3055.html
Citation Data
DOI : 10.24350/CIRM.V.20279103Cite this video as: 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 |
See Also
- [Multi angle] Statistical learning in biological neural networks / Author of the conference Schmidt-Hieber, Johannes.
- [Multi angle] Are adaptive robust confidence intervals possible? / Author of the conference Gao, Chao.
- [Multi angle] Attention layers provably solve single-location regression / Author of the conference Boyer, Claire.
- [Multi angle] An introduction to conformal prediction and distribution-free inference / Author of the conference Barber, Rina Foygel.
Bibliography
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- 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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