Posterior contraction rates of computational methods for Bayesian data assimilation

Fuente: arXiv
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Main Authors: Burman, Erik, Lu, Mingfei
Format: Preprint
Published: 2025
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author Burman, Erik
Lu, Mingfei
author_facet Burman, Erik
Lu, Mingfei
contents In this paper, we analyze posterior consistency of a Bayesian data assimilation problem under discretization. We prove convergence rates for the discrete posterior to ground truth solution under both conforming discretization and finite element discretization (usually non-conforming). 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 an optimal convergence rate.
format Preprint
id arxiv_https___arxiv_org_abs_2506_14685
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Posterior contraction rates of computational methods for Bayesian data assimilation
Burman, Erik
Lu, Mingfei
Numerical Analysis
Probability
Statistics Theory
65N21, 62F15, 35R30, 65N30, 65C60, 35R25
In this paper, we analyze posterior consistency of a Bayesian data assimilation problem under discretization. We prove convergence rates for the discrete posterior to ground truth solution under both conforming discretization and finite element discretization (usually non-conforming). 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 an optimal convergence rate.
title Posterior contraction rates of computational methods for Bayesian data assimilation
topic Numerical Analysis
Probability
Statistics Theory
65N21, 62F15, 35R30, 65N30, 65C60, 35R25
url https://arxiv.org/abs/2506.14685