Abstract

In this study, we develop a Bayesian model to analyze the annual precipitation data. Our objective is to predict the probability of extreme rainfall events, which is crucial for water resource management and disaster preparedness.
The historical data spans several decades, providing a robust basis for our analysis. We adopt a Bayesian framework, allowing us to incorporate prior knowledge about precipitation trends and update our beliefs with observed data. This approach provides a coherent way to make probabilistic statements about future precipitation.
Our model employs a Gaussian likelihood to describe the annual precipitation amounts, with prior distributions chosen based on historical records and expert knowledge. We use Markov Chain Monte Carlo (MCMC) methods to sample from the posterior distribution of the model parameters, ensuring accurate and reliable inference.
To address the risk of extreme precipitation events, we integrate Extreme Value Theory (EVT) into our Bayesian model. Specifically, we model the tail behavior of the precipitation distribution using a Generalized Extreme Value (GEV) distribution. This approach enables us to estimate extreme precipitation events' return levels and return periods, providing valuable insights for policymakers and stakeholders in Lesotho.
The Bayesian model effectively captures this variability and provides credible intervals for future precipitation estimates, highlighting the benefits of the probabilistic approach. The integration of EVT reveals an increasing risk of extreme or below-average precipitation events, which has important implications for flood risk management and agricultural planning.
Bayesian modeling of Lesotho's annual precipitation data could offer a powerful tool for understanding and predicting precipitation patterns and extremes. By incorporating the risk of extreme events, our approach provides comprehensive insights that are essential for effective climate adaptation strategies. This study will not only contribute to the scientific understanding of precipitation dynamics in Lesotho but also demonstrate the applicability of Bayesian methods in climatological research.