Title: Bayesian Hierarchical Point-Pattern-Based Intensity Model in Prediction of Highway Losses
- Speaker: Yongping Yan, PhD, Highway Loss Data Institute
- Date: February 28, 2014
- Time: 10:30 a.m. Refreshments, 10:45 a.m. Colloquium Talk
- Location: Exploratory Hall, Room 1004, Fairfax Campus, George Mason University, 4400 University Drive, Fairfax, VA 22030
- Sponsor: George Mason University SPACS/CCDS/Statistics Colloquium
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 non-separable 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 talk, with a focus on contribution to the interdisciplinary area of statistics and GIS (geographic information system), we develop 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, we develop 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, we develop 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, we build a Bayesian hierarchical model (BHM) that uses 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, we apply the methods to 2009-11 FARS (Fatality Analysis Reporting System) data of U.S. Department of Transportation. The application is a good example that the methods developed can be widely used on any loss types, whose events exhibit a Poisson-point-pattern.
