Classical and Bayesian Markov Chain Monte Carlo (MCMC) modeling of extreme rainfall (1979-2014) in Makurdi, Nigeria

Abstract

This study presents a probabilistic model for daily extreme rainfall. The Annual Maximum Series (AMS) data of daily rainfall in Makurdi was fitted to Generalized Extreme Value (GEV) distribution using Maximum Likelihood Estimation (MLE) and Bayesian Markov Chain Monte Carlo (Bayesian MCMC) simulations. MLE is a reliable principle to derive an efficient estimator for a model as sample size approaches infinity. Results in this study show that despite the asymptotic requirement of the MLE, its performance can be improved when adopting Bayesian MCMC. The comparison between the performance of MLE and Bayesian MCMC methods using Percent Bias (PBIAS), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) proved Bayesian MCMC is the better method to estimate the distribution parameters of extreme daily rainfall amount in Makurdi. Based on the 36-year record of rainfall (1979-2014) in Makurdi, return levels for the next 10, 100, 500, 1000 and 10000 years were derived.