Posterior contraction rates of computational methods for Bayesian data assimilation
Numerical Analysis
2025-06-18 v1 Numerical Analysis
Probability
Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2506.14685,
title = {Posterior contraction rates of computational methods for Bayesian data assimilation},
author = {Erik Burman and Mingfei Lu},
journal= {arXiv preprint arXiv:2506.14685},
year = {2025}
}