Screening the Discrepancy Function of a Computer Model

Traditionally, screening refers to the problem of detecting influential (active) inputs in the computer model. We develop methodology that applies to screening, but the main focus is on detecting active inputs not in the computer model itself but rather on the discrepancy function that is introduced to account for model inadequacy when linking the computer model with field observations. We contend this is an important problem as it informs the modeler which are the inputs that are potentially being mishandled in the model, but also along which directions it may be less recommendable to use the model for prediction. The methodology is Bayesian and is inspired by the continuous spike-and-slab prior popularized by the literature on Bayesian variable selection. In our approach, and in contrast with previous proposals, a single MCMC sample from the full model allows us to compute the posterior probabilities of all the competing models, resulting in a methodology that is computationally very fast. The approach hinges on the ability to obtain posterior inclusion probabilities of the inputs, which are easy to interpret quantities, as the basis for selecting active inputs. For that reason, we name the methodology PIPS—posterior inclusion probability screening.

传统意义上，筛选（screening）指的是在计算机模型中识别具有影响力（或称活跃）输入项的问题。本文提出的方法可适用于该筛选任务，但核心研究目标并非识别计算机模型自身的活跃输入项，而是针对将计算机模型与现场观测数据结合时，为弥补模型缺陷而引入的偏差函数（discrepancy function）中的活跃输入项。我们认为该问题具备重要研究价值：它既能帮助建模者定位模型中可能处理不当的输入项，也能指明在哪些方向上使用该模型进行预测的可靠性较低。该方法基于贝叶斯框架，其灵感源自贝叶斯变量选择领域文献中广为推广的连续型尖峰-平板先验（continuous spike-and-slab prior）。与既往研究方案不同，本文方法仅需从全模型中获取一次马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）样本，即可计算所有候选模型的后验概率，从而实现极高的计算效率。该方法的核心在于获取输入项的后验包含概率（posterior inclusion probability）——这是一类易于解读的统计量——并将其作为筛选活跃输入项的依据。基于此，我们将该方法命名为PIPS——后验包含概率筛选（posterior inclusion probability screening）。