This study focuses on modeling and predicting extreme rainfall based on data from the Southern Highlands region, the critical for rain-fed agriculture in Tanzania. Analyzing 31 years of annual maximum rainfall data spanning from 1990 to 2020, the Generalized Extreme Value (GEV) model proved to be the best for modeling extreme rainfall in all stations. Three estimation methods–L-moments, maximum likelihood estimation (MLE), and Bayesian Markov chain Monte Carlo (MCMC)–were employed to estimate GEV parameters and future return levels. The Bayesian MCMC approach demonstrated superior performance by incorporating noninformative priors to ensure that the prior information had minimal influence on the analysis, allowing the observed data to play a dominant role in shaping the posterior distribution. Furthermore, return levels for various future periods were estimated, providing guidance for flood protection measures and infrastructure design. Trend analysis using value, Kendall’s tau, and Sen’s slope indicated no statistically significant trends in rainfall patterns, although a weak positive trend in extreme rainfall events was observed, suggesting a gradual and modest increase over time. Overall, the study contributes valuable insights into extreme rainfall patterns and underscores the importance of L-moments in identifying the best fit distribution and Bayesian MCMC methodology for accurate parameter estimation and prediction, enabling effective measures and infrastructure planning in the region.

中文翻译：

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极端降雨系列建模和预测中的频率论和贝叶斯方法：坦桑尼亚南部高地地区的案例研究

这项研究的重点是根据南部高地地区的数据对极端降雨进行建模和预测，该地区对于坦桑尼亚的雨养农业至关重要。通过分析 1990 年至 2020 年 31 年的年度最大降雨量数据，广义极值 (GEV) 模型被证明是模拟所有站点极端降雨的最佳模型。采用三种估计方法——L矩、最大似然估计 (MLE) 和贝叶斯马尔可夫链蒙特卡罗 (MCMC)——来估计 GEV 参数和未来回报水平。贝叶斯 MCMC 方法通过结合非信息性先验来证明其优越的性能，以确保先验信息对分析的影响最小，从而使观察到的数据在塑造后验分布中发挥主导作用。此外，还估计了未来各个时期的回报水平，为防洪措施和基础设施设计提供指导。使用值、Kendall's tau 和 Sen 斜率进行的趋势分析表明，降雨模式没有统计上显着的趋势，尽管观察到极端降雨事件呈微弱的正趋势，表明随着时间的推移逐渐适度增加。总体而言，该研究为极端降雨模式提供了宝贵的见解，并强调了L矩在确定最佳拟合分布和贝叶斯 MCMC 方法中的重要性，以实现准确的参数估计和预测，从而在该地区实现有效的措施和基础设施规划。