Equivalent between constrained optimal smoothing and Bayesian estimation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Nonparametric Statistics Année : 2024

Equivalent between 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.
Fichier principal
Vignette du fichier
AS-Maatouk-2023.pdf (603.91 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

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

Identifiants

Citer

Laurence Grammont, Hassan Maatouk, Xavier Bay. Equivalent between constrained optimal smoothing and Bayesian estimation. Journal of Nonparametric Statistics, inPress. ⟨hal-03282857v2⟩
156 Consultations
69 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More