Abstract:
Traditional spatial-temporal models either use separable models to separate spatial processes from temporal processes, which often results in a loss of information, or use nonseparable models through the introduction of correlation functions. These functions typically have to be complicated enough to address the real problem and additionally the implementation requires the integral of these functions. In this dissertation, with a focus on contribution to the interdisciplinary area of statistics and GIS (geographic information system), I have developed methods extending EM (expectation-maximization) algorithm to Poisson point processes with incomplete data structure to undercover the underlying components characterizing highway loss events. With component information in the dissertation, I have developed methods that use classification and regression trees along with visualization procedures to identify key features influencing highway loss intensities, and detect key feature patterns of the "hot spot" loss areas. Instead of examining the correlation between spatial space and temporal space, I have developed methods using a k-means based algorithm and specially tailored distance functions to partition the key feature space into homogeneous clusters, and map this partition to the spatial space partition. Then, I have built the Bayesian hierarchical model (BHM) that use the current time point loss information and most recent past loss information to predict the future losses for each cluster. The BHM in this dissertation has a good updating mechanism and is adaptive. Finally, I have successfully applied the methods to 2009-11 FARS (Fatality Analysis Reporting System) data of U.S. Department of Transportation. The application is a good example that methods developed in this dissertation can be widely used on any loss types whose events exhibit a Poisson-point-pattern.
