  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 region. A simulation study is used to validate the
approach for several levels of spatial and temporal dependence. The methodology
is used to identify regions of Oregon having high precipitation levels and also
used in comparing climate models and assessing climate change using climate
models from the North American Regional Climate Change Assessment Program.
