Spatio-Temporal Exceedance Locations and Confidence Regions

An exceedance region is the set of locations in a spatial domain where a process exceeds some threshold. Examples of exceedance regions include areas where ozone concentrations exceed safety standards, there is high risk for tornadoes or floods, or heavy-metal levels are dangerously high. Identifying these regions in a spatial or spatio-temporal setting is an important responsibility in environmental monitoring. Exceedance regions are often estimated by finding the areas where predictions from a statistical model exceed some threshold. Even when estimation error is quantifiable at individual locations, the overall estimation error of the estimated exceedance region is still unknown. A method is presented for constructing a confidence region containing the true exceedance region of a spatio-temporal process at a certain time. The underlying latent process and any measurement error are assumed to be Gaussian. Conventional techniques are used to model the spatio-temporal data, and then conditional simulation is combined with hypothesis testing to create the desired confidence