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

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 (Formula presented.) 90% of the information gain achieved by exact non-linear solution methods while reducing solution times by up to two orders of magnitude.