Nonparametric statistical methods will be developed for spatial data arising from random fields and point processes. A nonparametric approach is appealing for analyzing spatial data because it avoids detailed assumptions about the typically unknown and usually complicated underlying probability structure in terms of marginal distributions of the observations or shapes of spatial boundaries that partition the observations into homogeneous groups. Two specific types of nonparametric methods will be developed: resampling methods, which describe the sampling distribution of a general statistic computed from spatial data; and boundary estimators, which separate nonhomogeneous spatial data into homogeneous subsets. Spatial data is data that is laid out on a map or grid; it arises naturally in geology, ecology, meteorology, agriculture, epidemiology, medical imaging and other areas of scientific investigation. Often there is a natural boundary running through spatial data such as a seismic fault line or the edge of an object in an image. One goal of this project is to develop methods for identifying such boundaries accurately; another is to develop methods for assessing the sampling error in quantities calculated from spatial data.
