Constrained Optimal Smoothing and Bayesian Estimation
Numerical Analysis
2021-07-13 v1 Numerical Analysis
Abstract
In this paper, we extend the correspondence between Bayesian estimation and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) adding a convexe constraints on the solution. Through a sequence of approximating Hilbertian spaces and a discretized model, we prove that the Maximum 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 [7] of Kimeldorf-Wahba where it is proved that the optimal smoothing solution is the mean of the posterior distribution.
Cite
@article{arxiv.2107.05275,
title = {Constrained Optimal Smoothing and Bayesian Estimation},
author = {X Bay and Laurence Grammont},
journal= {arXiv preprint arXiv:2107.05275},
year = {2021}
}