Abstract

Gaussian processes (GPs) have become a widely used tool for modeling unknown functions across various domains. In many applications, particular interest lies in a specific range of the response, with the goal of identifying inputs that lead to desired outputs. To enhance GP model performance in this setting, we employ weighted scoring rules to develop sequential design strategies that selectively augment the training dataset. Specifically, we study pointwise and integral criteria based on the threshold-weighted Continuous Ranked Probability Score (CRPS), using two different weighting measures. We showcase applications in synthetic chemistry, where the objective is to identify molecules with specific properties, and in plant selection, where the goal is to uncover combinations of genotypes and environmental factors that yield desirable performances in wheat. However, the presented acquisition strategies are applicable to a wide range of fields and pave the way to further developing sequential design relying on scoring rules.