Department Seminar Series: Joshua French, Credible Regions for Exceedance Sets of Geostatistical Data

Identifying regions in a spatial domain where the response is large or unusual is frequently of interest in environmental and public health contexts. These regions are frequently the ones most impacted by an environmental event or where there is greatest concern for public health. Regions where the response is large are frequently called exceedance sets, exceedance regions, or excursion sets. We propose Bayesian methodology for constructing credible regions that either contain the exceedance set or are contained within the exceedance set with a specified level of probability. The methodology is simple to implement using samples from the joint posterior predictive distribution of the process of interest. We show that the methodology has the desired asymptotic coverage level and also has good coverage properties in practice. Simulation experiments are used to investigate the empirical coverage and power of the methodology. We apply this methodology in identifying regions of high zinc concentration using soil samples collected in southwestern Wyoming.