Bayesian analysis for extreme climatic events: A review

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This article reviews Bayesian analysis methods applied to extreme climatic data. We particularly focus on applications to three different problems related to extreme climatic events including detection of abrupt regime shifts, clustering tropical cyclone tracks, and statistical forecasting for seasonal tropical cyclone activity. For identifying potential change points in an extreme event count series, a hierarchical Bayesian framework involving three layers – data, parameter, and hypothesis – is formulated to demonstrate the posterior probability of the shifts throughout the time. For the data layer, a Poisson process with a gamma distributed rate is presumed. For the hypothesis layer, multiple candidate hypotheses with different change-points are considered. To calculate the posterior probability for each hypothesis and its associated parameters we developed an exact analytical formula, a Markov Chain Monte Carlo (MCMC) algorithm, and a more sophisticated reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm. The algorithms are applied to several rare event series: the annual tropical cyclone or typhoon counts over the central, eastern, and western North Pacific; the annual extremely heavy rainfall event counts at Manoa, Hawaii; and the annual heat wave frequency in France.Using an Expectation-Maximization (EM) algorithm, a Bayesian clustering method built on a mixture Gaussian model is applied to objectively classify historical, spaghetti-like tropical cyclone tracks (1945–2007) over the western North Pacific and the South China Sea into eight distinct track types. A regression based approach to forecasting seasonal tropical cyclone frequency in a region is developed. Specifically, by adopting large-scale environmental conditions prior to the tropical cyclone season, a Poisson regression model is built for predicting seasonal tropical cyclone counts, and a probit regression model is alternatively developed toward a binary classification problem. With a non-informative prior assumption for the model parameters, a Bayesian inference for the Poisson regression model and the probit regression model are derived in parallel. A Gibbs sampler is further designed to integrate the posterior predictive distribution. The resulting Bayesian Poisson regression algorithm is applied to predicting the seasonal tropical cyclone activity.