Kriging‐Informed Coverage Sampling: An Integer Programming Approach to Optimizing Information Collection

ABSTRACT Accurately mapping spatial phenomena with limited observations hinges on selecting sampling sites that minimize predictive uncertainty. We model this task by quantifying unsampled‐location uncertainty with ordinary Kriging and framing site selection as an optimization problem. Because the resulting Kriging prediction‐variance objective is nonlinear, we derive an integer program approximation called Kriging‐informed coverage sampling that bounds the Kriging variance with a set of linear constraints. We prove that Kriging‐informed coverage sampling is isomorphic to the classical Maximal Coverage Location Problem, thereby linking geostatistical uncertainty reduction to a well‐studied family of location problems and enabling the use of well‐established solution techniques. Computational experiments on synthetic landscapes and a remote‐sensing case study show that Kriging‐informed coverage sampling attains 90% of the information gain achieved by exact non‐linear solution methods while reducing solution times by up to two orders of magnitude.