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Bayesian analysis for extreme climatic events: A review

机译：极端气候事件的贝叶斯分析：综述

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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.
机译：本文回顾了应用于极端气候数据的贝叶斯分析方法。我们特别关注与极端气候事件相关的三个不同问题的应用，包括检测突然的政权转移，聚类热带气旋径迹以及季节性热带气旋活动的统计预测。为了识别极端事件计数序列中的潜在变化点，制定了一个涉及三层的数据，参数和假设的分层贝叶斯框架，以证明整个时间推移的后移概率。对于数据层，假定具有伽马分布速率的泊松过程。对于假设层，考虑具有不同变化点的多个候选假设。为了计算每个假设及其相关参数的后验概率，我们开发了精确的解析公式，马尔可夫链蒙特卡洛（MCMC）算法和更复杂的可逆跳跃马尔可夫链蒙特卡洛（RJMCMC）算法。该算法适用于几个罕见事件序列：北太平洋中部，东部和西部的年度热带气旋或台风计数；以及夏威夷马诺阿每年发生的特大降雨事件非常重要；以及法国的年度热浪频率。使用期望最大化（EM）算法，基于混合高斯模型建立的贝叶斯聚类方法被用于将北太平洋西部和南中国海的历史，类似意大利面条的热带气旋路径（1945-2007）客观地分类为八个不同的曲目类型。开发了一种基于回归的方法来预测一个地区的季节性热带气旋频率。具体而言，通过在热带气旋季节开始之前采用大规模环境条件，建立了泊松回归模型来预测季节性热带气旋数量，并针对二元分类问题开发了概率回归模型。在模型信息具有非信息性先验假设的情况下，并行推导了泊松回归模型和概率回归模型的贝叶斯推断。进一步设计了吉布斯采样器，以整合后验预测分布。所得的贝叶斯泊松回归算法用于预测季节性热带气旋活动。

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