  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.
