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arXiv · 2107.05275

Constrained Optimal Smoothing and Bayesian Estimation

X Bay·Laurence Grammont
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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.

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X Bay, Laurence Grammont. 2021-07-12. Constrained Optimal Smoothing and Bayesian Estimation. https://arxiv.org/abs/2107.05275

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