Posterior contraction rates of computational methods for Bayesian data assimilation

Erik Burman; Mingfei Lu

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arXiv · 2506.14685

Posterior contraction rates of computational methods for Bayesian data assimilation

Erik Burman·Mingfei Lu

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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 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.

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Erik Burman, Mingfei Lu. 2025-06-17. Posterior contraction rates of computational methods for Bayesian data assimilation. https://arxiv.org/abs/2506.14685

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