Posterior Contraction Rates of Computational Methods for Bayesian Data Assimilation
Authors:
- 29 October 2026
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM/ASA Journal on Uncertainty Quantification
- Vol. 14 (4) , 1530-1562
Abstract
In this paper, we analyze posterior consistency of a Bayesian data assimilation problem under discretization. We prove convergence rates for the discrete posterior to the ground truth solution under both conforming discretization and finite element discretization (usually nonconforming). The analysis is based on the coupling of asymptotics between the number of samples and the dimension of discrete spaces. In the finite element discretization, tailor-made discrete priors, instead of the discretization of continuous priors, are used to generate posterior contraction.Keywords
Funding Information
- Engineering and Physical Sciences Research Council (EP/T033126/1)
- Engineering and Physical Sciences Research Council (EP/V050400/1)
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