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Bayesian network modeling of correlated random variables drawn from a Gaussian random field

机译：从高斯随机场得出的相关随机变量的贝叶斯网络建模

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摘要

In many civil engineering applications, it is necessary to model vectors of random variables drawn from a random field. Furthermore, it is often of interest to update the random field model in light of available or assumed observations on the random field or related variables. The Bayesian network (BN) methodology is a powerful tool for such updating purposes. However, there is a limiting characteristic of the BN that poses a challenge when modeling random variables drawn from a random field: due to the full correlation structure of the random variables, the BN becomes densely connected and inference can quickly become computationally intractable with increasing number of random variables. In this paper, we develop approximation methods to achieve computationally tractable BN models of correlated random variables drawn from a Gaussian random field. Using several generic and systematic spatial configuration models, numerical investigations are performed to compare the relative effectiveness of the proposed approximation methods. Finally, the effects of the random field approximation on estimated reliabilities of example spatially distributed systems are investigated. The paper concludes with a set of recommendations for BN modeling of random variables drawn from a random field.
机译：在许多土木工程应用中，必须对从随机字段中提取的随机变量的向量进行建模。此外，经常有兴趣根据对随机场或相关变量的可用或假定观察来更新随机场模型。贝叶斯网络（BN）方法是用于此类更新目的的强大工具。但是，BN的一个局限性在对从随机字段中提取的随机变量进行建模时提出了挑战：由于随机变量的完全相关结构，BN变得紧密相连，并且随着数量的增加，推理可能很快变得难以计算随机变量。在本文中，我们开发了一种近似方法来实现从高斯随机场得出的相关随机变量的可计算的可计算BN模型。使用几个通用和系统的空间配置模型，进行了数值研究，以比较所提出的近似方法的相对有效性。最后，研究了随机场近似对示例空间分布系统的估计可靠性的影响。本文以针对从随机字段中抽取的随机变量进行BN建模的一组建议作为结尾。

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