Block prediction intervals
In environmental assessment, such as clean up of contaminated regions (e.g. with dioxin), it is important for scientists (or decision makers) to predict the average amount (called block averages in the geostatistical literature) of contaminant present in the region in order to more effectively remediate the contamination. In geostatistics, block averages are regarded as an integral of random fields over bounded regions. An important problem in predictive inference of block average is the prediction interval of block average value when the distribution of the random fields is not Gaussian. In this dissertation, we propose methods to construct prediction intervals for integrals of Gaussian and non-Gaussian random fields over bounded regions based on observations at a finite set of sampling locations. For Gaussian random fields, we propose two bootstrap calibration algorithms, termed indirect and direct, aimed at improving upon plug-in prediction intervals in terms of coverage probability. We also propose two bootstrap methods for non-Gaussian random fields. The first method relies on the lognormal distributional assumption while the second method does not require any distributional assumptions. Simulation studies are performed to show the effectiveness of all four methods, and these methods are applied to estimate spatial averages of chromium and cadmium traces in a potentially contaminated region in Switzerland.