Screening the discrepancy of a computer model

Traditionally, screening refers to the problem of detecting 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.