Credible regions for exceedance sets of geostatistical data

Identifying regions having large or unusual response in a spatial domain is frequently of interest in environmental and public health contexts. These regions having a large response are frequently called exceedance sets, exceedance regions, or excursion sets. We propose Bayesian methodology for constructing credible regions that either contain the exceedance sets or are contained within the exceedance sets with a specified level probability. The algorithms are simple to implement and use samples from the joint posterior predictive distribution of the process of interest. The R package ExceedanceTools implements the proposed methodology. We study the coverage properties of the methodology and also show that it has good coverage properties in practice. Simulation experiments demonstrate that the proposed method has good performance with respect to the empirical coverage and power. We apply this methodology to identify regions of high zinc concentration using soil samples collected in southwestern Wyoming. Copyright © 2015 John Wiley & Sons, Ltd.