Frequentist and Bayesian Approaches in Modeling and Prediction of Extreme Rainfall Series: A Case Study from Southern Highlands Region of Tanzania

Abstract

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 Gen- eralized Extreme Value (GEV) model proved to be the best for modeling extreme rainfall in all stations. Tree 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. Te Bayesian MCMC approach demonstrated superior per- formance by incorporating noninformative priors to ensure that the prior information had minimal infuence 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 food protection measures and infrastructure design. Trend analysis using p value, Kendall’s tau, and Sen’s slope indicated no statistically signifcant 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 ft dis- tribution and Bayesian MCMC methodology for accurate parameter estimation and prediction, enabling effective measures and

infrastructure planning in the region.