Doubly Truncated Mode Kriging

Emilio Ruiz-Moreno, Baltasar Beferull-Lozano

Abstract: Ordinary kriging analytically constructs its estimates and credible intervals from the moments of a Gaussian Process (GP). Even though GPs can accommodate certain behavioral knowledge about the estimand, they are incapable of delimiting its range. This setback typically motivates using a truncated multivariate Gaussian distribution (TMGD) instead. On the other hand, it is well known that the mean and mode of a GP coincide. However, this is not necessarily true for a TMGD. In this context, a compelling aspect of the mode over the mean is that it can be computed by avoiding expensive integrals and specialized sampling. Consequently, this paper explores the implications of using the mode instead of the mean on a kriging-based method over a TMGD. We coin this method mode kriging to distinguish it from the ordinary one. Specifically, we show that finding the mode kriging estimates consists of i) solving a quadratic convex optimization problem followed by ii) an ordinary kriging estimation step. Lastly, we describe how this two-stage structure can be exploited to characterize and construct the associated credible intervals.