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

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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.