Modeling for seasonal marked point processes: An analysis of evolving hurricane occurrences

TL;DR

This paper introduces a nonparametric Bayesian framework for modeling seasonal marked point processes, specifically applied to hurricane landfalls, capturing their evolving intensity, marks, and damages over a century.

Contribution

It develops a novel nonparametric mixture model with dependent Dirichlet processes for dynamic seasonal point process analysis, including marks and damages.

Findings

Hurricane landfall occurrences increased over time.

Median maximum wind speed at peak season decreased.

No significant trend in hurricane damages over time.

Abstract

Seasonal point processes refer to stochastic models for random events which are only observed in a given season. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We assume the point process is a nonhomogeneous 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 the intensity of the process of hurricane landfall occurrences, and the respective maximum wind speed and associated damages. Our results indicate an increase in the number of hurricane landfall occurrences and a decrease in the median maximum wind speed at the peak of the season. Introducing standardized damage as a mark, such that reported damages are comparable both in time and space, we find that there is no significant rising trend in hurricane damages over time.