Bayesian Change-Point Modelling of Rainfall Distributions In Nigeria

Abstract

A Bayesian framework is developed to detect single change abrupt shift in a time series of the annual amount of rainfall in Nigeria. The annual amount of rainfall is modelled by a Normal probability distribution where the means are codified by a normal probability distribution and inverted gamma probability distribution for the variance. Based on the sampling from an estimated informative prior for the parameters and the posterior distribution of hypotheses, the methodology is applied to the time series of amount of rainfall in six states in Nigeria. Although, the model under study seems quite simple, but no analytic solutions for parameter inference are available, and recourse to approximations is needed. It was shown that the Gibbs sampler is particularly suitable for change-point analysis, and this Markovian updating scheme is used. The result from the analysis showed that, in all the six states considered displayed that indeed a single change point occurred.