Screening the Discrepancy Function of a Computer Model

TL;DR

This paper introduces PIPS, a Bayesian screening method for identifying influential inputs in the discrepancy function of computer models, helping improve model calibration and prediction reliability.

Contribution

It develops a fast, Bayesian variable screening approach using posterior inclusion probabilities to detect active inputs in discrepancy functions, enhancing model validation.

Findings

Efficient MCMC-based computation of posterior inclusion probabilities.

Effective identification of influential discrepancy inputs.

Applicable to complex computer model calibration.

Abstract

Screening traditionally refers to the problem of detecting active inputs in the computer model. In this paper, 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 very intuitive and easy to interpret quantities, as the basis for selecting active inputs. For that reason, we name the methodology PIPS -- posterior inclusion probability screening.