5,798 research outputs found
Modeling for seasonal marked point processes: An analysis of evolving hurricane occurrences
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.Comment: Published at http://dx.doi.org/10.1214/14-AOAS796 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Degradation modeling applied to residual lifetime prediction using functional data analysis
Sensor-based degradation signals measure the accumulation of damage of an
engineering system using sensor technology. Degradation signals can be used to
estimate, for example, the distribution of the remaining life of partially
degraded systems and/or their components. In this paper we present a
nonparametric degradation modeling framework for making inference on the
evolution of degradation signals that are observed sparsely or over short
intervals of times. Furthermore, an empirical Bayes approach is used to update
the stochastic parameters of the degradation model in real-time using training
degradation signals for online monitoring of components operating in the field.
The primary application of this Bayesian framework is updating the residual
lifetime up to a degradation threshold of partially degraded components. We
validate our degradation modeling approach using a real-world crack growth data
set as well as a case study of simulated degradation signals.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS448 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary
Many researchers have investigated first hitting times as models for survival
data. First hitting times arise naturally in many types of stochastic
processes, ranging from Wiener processes to Markov chains. In a survival
context, the state of the underlying process represents the strength of an item
or the health of an individual. The item fails or the individual experiences a
clinical endpoint when the process reaches an adverse threshold state for the
first time. The time scale can be calendar time or some other operational
measure of degradation or disease progression. In many applications, the
process is latent (i.e., unobservable). Threshold regression refers to
first-hitting-time models with regression structures that accommodate covariate
data. The parameters of the process, threshold state and time scale may depend
on the covariates. This paper reviews aspects of this topic and discusses
fruitful avenues for future research.Comment: Published at http://dx.doi.org/10.1214/088342306000000330 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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