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（computer model）中识别具有影响力的活跃输入（active inputs）的问题。我们开发了可应用于筛选任务的方法论，但本研究的核心聚焦点并非识别计算机模型自身的活跃输入，而是针对将计算机模型与实地观测数据（field observations）相连接时，为弥补模型不足而引入的差异函数（discrepancy function）来识别其中的活跃输入。我们认为这是一项极具价值的研究问题：它既能帮助建模者明确模型中可能处理不当的输入变量，也能指出在哪些方向下使用该模型进行预测并不适宜。本方法论采用贝叶斯（Bayesian）框架，其灵感来源于贝叶斯变量选择（Bayesian variable selection）领域文献中广泛推广的连续尖峰-板条先验（continuous spike-and-slab prior）。与既往研究方案不同，在我们的方法中，仅需从全模型中抽取一次马尔可夫链蒙特卡洛（MCMC）样本，即可计算所有竞争模型的后验概率（posterior probabilities），从而得到计算效率极高的方法论。该方法的核心在于能够获取输入变量的后验包含概率（posterior inclusion probabilities）——这是一类易于解读的统计量——并将其作为活跃输入变量选择的依据。基于此，我们将该方法论命名为PIPS——后验包含概率筛选（posterior inclusion probability screening）。