CIRM - Videos & books Library - Bayesian data assimilation and filtering

Multi angle

Auteurs : Schillings, Claudia (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : We consider the inverse problem of recovering an unknown parameter from a finite set of indirect measurements. We start with reviewing the formulation of the Bayesian approach to inverse problems. In this approach the data and the unknown parameter are modelled as random variables; the distribution of the data is given and the unknown is assumed to be drawn from a given prior distribution. The solution, called the posterior distribution, is the probability distribution of the unknown given the data, obtained through the Bayes rule. We will talk about the conditions under which this formulation leads to well-posedness of the inverse problem at the level of probability distributions. We then discuss the connection of the Bayesian approach to inverse problems with the variational regularization. This will also help us to study the properties of the modes of the posterior distribution as point estimators for the unknown parameter. We will also briefly talk about the Markov chain Monte Carlo methods in this context.

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http://smai.emath.fr/cemracs/cemracs21/data/presentation-speakers/schillings2.pdf

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2021-07-21-Schillings_2.mp4

Informations sur la Rencontre

Nom de la rencontre : CEMRACS 2021: Data Assimilation and Model Reduction in High Dimensional Problems / CEMRACS 2021: Assimilation de données et réduction de modèle pour des problêmes en grande dimension
Organisateurs de la rencontre : Ehrlacher, Virginie ; Lombardi, Damiano ; Mula Hernandez, Olga ; Nobile, Fabio ; Taddei, Tommaso
Dates : 19/07/2021 - 23/07/2021
Année de la rencontre : 2021
URL Congrès : https://conferences.cirm-math.fr/2412.html

Données de citation

DOI : 10.24350/CIRM.V.19788703
Citer cette vidéo: Schillings, Claudia (2021). Bayesian data assimilation and filtering - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19788703
URI : http://dx.doi.org/10.24350/CIRM.V.19788703

Voir aussi

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[Virtualconference] Statistical theory for deep neural networks - lecture 1 / Auteur de la Conférence Schmidt-Hieber, Johannes.
[Multi angle] Approximation and learning with tree tensor networks - lecture 2 / Auteur de la Conférence Nouy, Anthony.
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[Virtualconference] Bayesian methods for inverse problems - lecture 2 / Auteur de la Conférence Dashti, Masoumeh.
[Multi angle] Theory of approximation of high-dimensional functions - lecture 2 / Auteur de la Conférence Cohen, Albert.

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