Spatial mixture modeling for analyzing a rainfall pattern: A case study in Ireland

Abstract

This study investigates the spatial heterogeneity in the maximum monthly rainfall amounts reported by stations in Ireland from January 2018 to December 2020. The heterogeneity is modeled by the Bayesian normal mixture model with different ranks. The selection of the best model or the degree of heterogeneity is implemented using four criteria which are the modified Akaike information criterion, the modified Bayesian information criterion, the deviance information criterion, and the widely applicable information criterion. The estimation and model selection process is implemented using the Gibbs sampling. The results show that the maximum monthly rainfall amounts are accommodated in two and three components. The goodness of fit for the selected models is checked using the graphical plots including the probability density function and cumulative distribution function. This article also contributes via the spatial determination of return level or rainfall amounts at risk with different return periods using the prediction intervals constructed from the posterior predictive distribution.

Keywords

• rainfall amounts
• bayesian mixture modeling
• cumulative distribution
• prediction interval
• posterior predictive distribution