Abstract
Spatial cluster detection is an important problem in a variety of scientific disciplines such as environmental sciences,epidemiology and sociology. However, there appears to be very limited statistical methodology for quantifying theuncertainty of a detected cluster. In this paper, we develop a new method for the quantification and visualizationof uncertainty associated with a detected cluster. Our approach is defining a confidence set for the true cluster andvisualizing the confidence set, based on the maximum likelihood, in time or in one-dimensional space. We evaluatethe pivotal property of the statistic used to construct the confidence set and the coverage rate for the true clustervia empirical distributions. For illustration, our methodology is applied to both simulated data and an Alaska borealforest dataset