Nonparametric Methods for Point Processes and Geostatistical Data

In this dissertation, we explore the properties of correlation structure for spatio-temporalpoint processes and a quantitative spatial process. Spatio-temporal pointprocesses are often assumed to be separable; we propose a formal approach for testingwhether a particular data set is indeed separable. Because of the resampling methodology,the approach requires minimal conditions on the underlying spatio-temporalprocess to perform the hypothesis test, and thus is appropriate for a wide class ofmodels.Africanized Honey Bees (AHBs, Apis mellifera scutellata) abscond more frequentlyand defend more quickly than colonies of European origin. That they alsoutilize smaller cavities for building colonies expands their range of suitable hive locationsto common objects in urban environments. The aim of the AHB study isto create a model of this quantitative spatial process to predict where AHBs weremore likely to build a colony, and to explore what variables might be related to theoccurrences of colonies. We constructed two generalized linear models to predictthe habitation of water meter boxes, based on surrounding landscape classifications,whether there were colonies in surrounding areas, and other variables. The presenceof colonies in the area was a strong predictor of whether AHBs occupied a watermeter box, suggesting that AHBs tend to form aggregations, and that the removal ofa colony from a water meter box may make other nearby boxes less attractive to thebees.