final_program_abstracts[1]

11 IMSC Session Program
Bayesian analysis for extreme events
Monday - Plenary Session 9
Pao-Shin Chu
Department of Meteorology, School of Ocean and Earth Science and Technology,
University of Hawaii, USA
Bayesian analysis for extreme events will be reviewed in the context of detecting
abrupt shifts in the series of extreme events. I will first introduce the Bayesian
change-point analysis applied to detect abrupt shifts in the time series of tropical
cyclone (TC) counts (Chu and Zhao, 2004). Specifically, a hierarchical Bayesian
approach involving three layers – data, parameter, and hypothesis – is formulated to
derive the posterior probability of the shifts throughout the time. For the data layer, a
Poisson process with gamma distributed intensity is presumed. For the hypothesis
layer, a “no change in the TC intensity” and a “single change in the intensity”
hypotheses are considered. In Chu and Zhao (2004), the method was only applicable
to detecting a single change in the extreme event series. To overcome this deficiency,
Zhao and Chu (2006) developed a scheme which extends from the two-hypothesis to
three-hypothesis (i.e., from a no change to a double change in the Poisson intensity).
Also new was the use of the Markov chain Monte Carlo (MCMC) method to solve for
complex integral quantities of posterior distributions. Moreover, Zhao and Chu (2006)
also devised an empirical approach, called the informative prior estimation (IPE), for
setting appropriate prior of Poisson rates. Results indicate that hurricane activity in
the eastern North Pacific has undergone two shifts since 1972 with three climate
regimes.
Although the MCMC imbedded with IPE method was demonstrated to be viable for a
multiple hypothesis model, it suffers from a shortcoming. That is, because parameter
spaces within different hypotheses are varying from each other, a simulation has to be
run independently for each of the candidate hypotheses. If the hypotheses have higher
dimension, this strategy is not efficient and is computationally prohibitive. In
principle, a standard MCMC algorithm is not appropriate for a model selection
problem because different candidate models or hypotheses do not share same
parameter sets. To address this issue, a reversible jump MCMC (RJMCMC) algorithm
is introduced to detect potential multiple shifts within an extreme event count series
(Zhao and Chu, 2010). Results of a simulated sample and some real-world cases (e.g.,
heavy rainfall, summer heat waves) will be given.
Chu, P.-S., and X. Zhao, 2004: Bayesian change-point analysis of tropical cyclone
activity: The central North Pacific case. J. Climate, 17, 2678-2689.
Zhao, X., and P.-S. Chu, 2006: Bayesian multiple changepoint analysis of hurricane
activity in the eastern North Pacific: A Markov Chain Monte Carlo approach. J.
Climate, 19, 564-578.
Zhao, X., and P.-S. Chu, 2010: Bayesian change-point analysis for extreme events
(Typhoons, Heavy Rainfall, and Heat Waves): A RJMCMC approach. J. Climate, 23,
1034-1046.
Abstracts 33