ANOVA-based transformed probabilistic collocation method for Bayesian data-worth analysis

Bayesian theory provides a coherent framework in quantifying the data worth of measurements and estimating unknown parameters. Nevertheless, one common problem in Bayesian methods is the considerably high computational cost since a large number of model evaluations is required in the likelihood evaluation. To address this issue, a new surrogate modeling method, i.e., ANOVA (analysis of variance)-based transformed probabilistic collocation method (ATPCM), is developed in this work. To cope with the strong nonlinearity, the model responses are transformed to the arrival times, which are then approximated with a set of low-order ANOVA components. The validity of the proposed method is demonstrated by synthetic numerical cases involving water and heat transport in the vadose zone. It is shown that, the ATPCM is more efficient than the existing surrogate modeling methods (e.g., PCM, ANOVA-based PCM and TPCM). At a very low computational cost, the ATPCM-based Bayesian data-worth analysis provides a quantitative metric in comparing different monitoring plans, and helps to improve the parameter estimation. Although the flow and heat transport in vadose zone is considered in this work, the proposed method can be equally applied in any other hydrologic problems.