Sampling strategies to detect threshold excursions in random fields

摘要

Sampling strategies are considered for efficiently detecting threshold excursions within realizations of random fields. By considering costs of sampling and costs of non-detection of excursions, a risk-based sampling framework is described. Computation of excursion probabilities, conditional upon observations from samples, is performed by using a conditional simulation technique to generate realizations of random fields that are consistent with the observed values. Simple numerical examples are used to demonstrate the use of the approach, and to illustrate how it might be used to identify adaptive sampling schemes that will aid in efficiently detecting threshold excursions. The problem is motivated by geotechnical sampling problems, where a limited testing budget is available to obtain information about the potential presence of interesting features underground (e.g., pockets of weak or liquefiable soil).