Improvements and enhancements for empirical simulation for the risk analysis of hurricanes

For many problems, a primary goal is to model the link between certain causes and effects. Often, this link is highly nonlinear. Usual parametric approaches for modeling may fail due to lack of data and/or dependence among the variables. In this dissertation, nonparametric methods to model this link are discussed. The procedure is explained referring to an application involving hurricanes, because this example originally motivated our research and also because of its inherent interest. In this case, "causes" are hurricane variables, such as maximum wind speed and radius to maximum wind velocity; effects are coastal impact variables, such as maximum storm surge and shoreline erosion.; In the hurricane example, selection of a training set that minimizes the processing cost (CPU-time) is important. A general method to select a training set is given. After computing coastal impacts for the training set hurricanes, a smoothing technique has been used to smooth the coastal impacts for the remaining hurricanes in the total set. Multivariate Adaptive Regression Splines (Friedman, 1991), are introduced and shown to perform better than Kernel smoothing, the current method. Two new approaches to model the number of occurrences of storms over time are given. One method is based on the nonhomogeneous Poisson process and the other is based on the simulated annealing algorithm. After deciding the number of occurrences, coastal impacts are simulated using a modified version of the Taylor-Thompson method (Thompson, 1986).