Interval-valued kriging for geostatistical mapping with imprecise inputs

Abstract

Many geosciences data are imprecise due to various limitations and uncertainties in the measuring process. In other situations, collocated measurements of variables from the same, yet unknown, distribution are characterized with separate models that may not respect the relatedness of the measurements. One way to preserve this imprecision or relatedness in a geostatistical mapping framework is to characterize the measurements as intervals rather than single numbers. To effectively analyze the interval-valued data, this paper develops an interval-valued kriging based on the modification of a previous attempt and the recent development of the random sets theory. Numerical implementation of our interval-valued kriging is provided using a penalty-based constrained optimization algorithm. An interval-valued kriging of design ground snow loads in Ohio, USA, demonstrates the applicability and advantages of the proposed methodology.