贝叶斯数据同化计算方法的后验收缩率
Posterior contraction rates of computational methods for Bayesian data assimilation
AI总结：
该研究分析离散化下贝叶斯数据同化问题的后验一致性，证明两类离散化下离散后验的收敛速率，提出用定制离散先验实现有限元离散化的最优收敛速率。
摘要：
本文分析了离散化下贝叶斯数据同化问题的后验一致性。我们证明了在协调离散化和通常非协调的有限元离散化两种情形下，离散后验向真实解收敛的速率。该分析基于样本数量与离散空间维度之间的渐近耦合。在有限元离散化中，我们采用定制的离散先验而非连续先验的离散化形式，以获得最优收敛速率。
英文摘要：
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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