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Bayesian posterior distributions can be numerically intractable, even by the means of Markov Chain Monte Carlo methods. Bayesian variational methods can then be used to compute directly (and fast) a deterministic approximation of these posterior distributions. In this course, I describe the principles of the variational methods and their application in Bayesian inference, review main theoretical results and discuss their use on examples.

62F15 ; 62H12 ; 49J40

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