Spatio-Temporal Exceedance Locations and Confidence Regions

• Activity Number: 456
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Joshua P. French*+ and Stephan Sain
• Companies: University of Colorado at Denver and National Center for Atmospheric Research
• Keywords: exceedance regions ; hotspots ; confidence regions ; environmental monitoring ; spatio-temporal

Abstract

An exceedance region is the set of locations in a spatial domain where a process exceeds some threshold. Examples 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 an estimated model exceeds 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 future time. Conventional techniques are used to model the spatio-temporal data, and then conditional simulation is combined with hypothesis testing to create the desired confidence region. A simulation study is used to validate the approach for several levels of spatial and temporal dependence. The methodology is applied in assessing climate change using data from the National Center for Atmospheric Research.