Modeling for Seasonal Marked Point Processes: An Analysis of Evolving Hurricane Occurrences

• Activity Number: 552
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Sai Xiao*+ and Athanasios Kottas and Bruno Sanso
• Companies: University of California, Santa Cruz and University of California, Santa Cruz and University of California, Santa Cruz
• Keywords: Bayesian nonparametrics ; Dependent Dirichlet process ; Hurricane intensity ; Marked Poisson process ; Markov chain Monte Carlo ; Risk assessment

Abstract

Seasonal point processes refer to stochastic models for random events which are only observed in a given season. There are several relevant applications in the environmental sciences, biology, finance and marketing. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We assume the point process is a non-homogeneous Poisson process, and propose a nonparametric mixture of beta densities to model dynamically evolving temporal Poisson process intensities. Dependence structure is built through a dependent Dirichlet process prior for the seasonally-varying mixing distributions. We extend the nonparametric model to incorporate time-varying marks resulting in flexible inference for both the seasonal point process intensity and for the conditional mark distribution. The motivating application involves the analysis of hurricane landfalls with reported damages along the U.S. Gulf and Atlantic coasts from 1900 to 2010. We focus on studying the evolution of hurricane intensity, the respective maximum wind speed and associated damages.