通过专用于数据同化的蒙特卡洛过程进行后验不确定性估计
Posterior Uncertainty Estimation via a Monte Carlo Procedure Specialized for Data Assimilation
AI总结：
本文形式化了Chevallier等人提出的用于大规模数据同化的蒙特卡洛后验方差近似算法，证明其收敛性，并扩展了考虑采样不确定性的贝叶斯可信区间，通过模拟实验验证了其有效性。
摘要：
通过数据同化的贝叶斯视角，模型参数的不确定性传统上通过后验协方差矩阵来量化。然而，在现代涉及高维且计算成本高昂的正向模型的环境中，后验协方差的知识必须放宽为确定性或随机近似。在碳通量反演文献中，Chevallier等人提出了一种随机方法，能够近似模型参数线性泛函的后验方差，特别适用于大规模地球系统数据同化任务。本文将该算法形式化并阐明其性质。我们提供了算法的正式陈述，证明了其为何收敛到所需的后验方差量，并提供了额外的不确定性量化，使得蒙特卡洛采样不确定性能够纳入该方法的贝叶斯可信区间。该方法通过玩具模拟和现实的碳通量反演观测系统模拟实验进行了演示。
英文摘要：
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, Chevallier et al. proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well-suited for large-scale Earth-system data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment.
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