Méthodes bayésiennes variationnelles : concepts et applications en neuroimagerie
[Variational Bayesian methods : concepts and neuroimage applications]
Journal de la société française de statistique, Volume 151 (2010) no. 2, pp. 107-131.

Bayesian posterior distributions can be numerically intractable, even by the means of Markov Chains Monte Carlo methods. Bayesian variational methods can then be used to compute directly (and fast) a deterministic approximation of these posterior distributions. This paper describes the principle of variational methods and their applications in the Bayesian inference, surveys the main theoretical results and details two examples in the neuroimage field.

En estimation bayésienne, les lois a posteriori sont rarement accessibles, même par des méthodes de Monte-Carlo par Chaîne de Markov. Les méthodes bayésiennes variationnelles permettent de calculer directement (et rapidement) une approximation déterministe des lois a posteriori. Cet article décrit le principe des méthodes variationnelles et leur application à l’inférence bayésienne, fait le point sur les principaux résultats théoriques et présente deux exemples d’utilisation en neuroimagerie.

Mot clés : Méthodes variationnelles, analyse bayésienne, approximation en champ moyen, approximation de Laplace, algorithme EM, données IRMf
Keywords: Variational methods, Bayesian analysis, mean field approximation, Laplace approximation, EM algorithm, IRMf data
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     title = {M\'ethodes bay\'esiennes variationnelles~: concepts et applications en neuroimagerie},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
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Keribin, Christine. Méthodes bayésiennes variationnelles : concepts et applications en neuroimagerie. Journal de la société française de statistique, Volume 151 (2010) no. 2, pp. 107-131. http://www.numdam.org/item/JSFS_2010__151_2_107_0/

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