Bayesian Discrete-Time Markov Chain Analysis of Rainfall Dynamics in Makurdi, Nigeria

Abstract

Rainfall variability is crucial in the management of water resources, hydrological processes, and agricultural productivity, especially in climate-sensitive areas like Makurdi, Benue State, Nigeria. This paper predicts monthly rainfall occurrence using a first-order discrete-time Markov chain within a Bayesian inference framework. The Climate Research Unit Time Series (CRU TS) dataset provided monthly rainfall data from 2014 to 2023, which were transformed into binary, wet and dry states using a threshold-based transformation. Both noninformative (Beta(1, 1)) and weakly informative (Beta(2, 2)) prior distributions were used to estimate the transition probabilities between rainfall state. Bayesian posterior distributions of the transition probabilities were derived analytically via Beta-Bernoulli conjugacy, allowing explicit quantification of parameter uncertainty. Results revealed strong persistence in the wet state, with posterior mean probabilities showing a high probability of remaining wet after rainfall. Sensitivity analysis shows that while symmetric transitions are largely unaffected by prior choice, weakly informative priors provide regularization for highly persistent transitions. The stationary distribution indicates long-run dominance of the wet state, while mean recurrence times confirm more frequent returns to wet conditions compared to dry periods. The Bayesian Markov chain framework provides a reliable and transparent probabilistic method for simulating the occurrence of rainfall, with significant ramifications for Makurdi’s water resource planning and climate risk assessment.