Consistency of Bayesian Inference for a Subdiffusion Equation
Journal
SIAM/ASA Journal on Uncertainty Quantification
Journal Volume
13
Journal Issue
3
Start Page
1116
End Page
1144
ISSN
2166-2525
Date Issued
2025-08-18
Author(s)
Kow, Pu-Zhao
Abstract
In this work, we consider the inverse problem of determining an unknown potential in a subdiffusion equation from its solution using a nonparametric Bayesian approach. Our aim is to establish the consistency of the posterior distribution with Gaussian priors. To do so, we need some key estimates of the forward problem. For the forward problem, we have to overcome the fact that the solution of the subdiffusion equation is less regular than that of the classical heat equation. The main ingredient is the maximum principle for the subdiffusion equation. We show that the posterior contracts to the ground truth at a polynomial rate.
SDGs
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Type
journal article