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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
11 IMSC Session Program Softcore and hardcore Bayesianism in climate research Monday - Plenary Session 9 Armin Haas In many cases, climate researchers have sufficient data for applying strictly mathematical Bayesian learning routines. In my terms, they perform hardcore Bayesianism. In many other cases, researchers face a lack of sufficient data. In this case, their judgment rests on their understanding of the system or process under investigation. Nevertheless, they are able to come up with probability judgments and make decisions. The non-mathematical routines they use for making these judgments and taking these decisions I conceptualise as softcore Bayesianism. I will give examples of hardcore and softcore Bayesianism in climate research and argue that both approaches are intimately interwoven in our daily research. Abstracts 34
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