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Pré-Publication, Document De Travail Année : 2021

Constrained Optimal Smoothing and Bayesian Estimation

Résumé

In this paper, we extend the correspondence between Bayesian estima- tion and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) by adding convex constraints to the problem. Through a sequence of approxi- mating Hilbertian subspaces and a discretized model, we prove that the Max- imum a posteriori (MAP) of the posterior distribution is exactly the optimal constrained smoothing function in the RKHS. This paper can be read as a generalization of the paper [15], where it is proved that the optimal smooth- ing solution is the mean of the posterior distribution. Synthetic and real data studies confirm the correspondence established in this paper.
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Dates et versions

hal-03282857 , version 1 (09-07-2021)
hal-03282857 , version 2 (10-04-2023)

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Citer

Laurence Grammont, Hassan Maatouk, Xavier Bay. Constrained Optimal Smoothing and Bayesian Estimation. 2021. ⟨hal-03282857v1⟩
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