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

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.

Noise-Driven Return Statistics: Scaling and Truncation in Stochastic Storage Processes

“…Many natural and engineered systems may be conceptualized as perturbed by external noise. Examples span geology 1 , seismology 2 , forestry 3 , medicine 4 , hydrology 5 , hurricane climatology 6 , avalanche prediction 7 , ecology 8 , insurance 9 , trade 10 , and social sciences 11 , among others. In such systems under variable forcing, understanding return periods to desirable (resilience) or undesirable (risk) states is of paramount importance for design and decision making.…”

Seasonal warranty prediction based on recurrent event data

“…Wu (2012, Section 3.5) gives a brief review of different types of coarse warranty data and methods to analyze such data. Xiao et al (2015) develop nonparametric Bayesian methodology using a seasonal marked point process to predict hurricane occurrences. Cifuentes-Amado and Cepeda-Cuervo (2015) and Ngailo et al (2016) use NHPP models with seasonality described by trigonometric functions of time in health diseases and seasonal rainfall events, respectively.…”

Compound Dirichlet Processes

“…As a consequence of its construction, these processes could be use to model renewal phenomena. Examples of applied Bayesian nonparametric models to analyze Renewal theory phenomena are presented in Bulla and Muliere [2007], Frees [1986], Xiao et al [2015]. One of the principal reasons to combine these methodologies is the fact that in many cases the renewal phenomena have complex random structures.…”