A Semiparametric Generalized Exponential Regression Model with a Principled Distance-based Prior for Analyzing Trends in Rainfall

Abstract: The Western Ghats mountain range holds critical importance in regulating monsoon rainfall across Southern India, with a profound impact on regional agriculture. Here, we analyze daily wet-day rainfall data for the monsoon months between 1901-2022 for the Northern, Middle, and Southern Western Ghats regions. Motivated by an exploratory data analysis, we introduce a semiparametric Bayesian generalized exponential (GE) regression model; despite the underlying GE distribution assumption being well-known in the literature, including in the context of rainfall analysis, no research explored it in a regression setting, as of our knowledge. Our proposed approach involves modeling the GE rate parameter within a generalized additive model framework. An important feature is the integration of a principled distance-based prior for the GE shape parameter; this allows the model to shrink to an exponential regression model that retains the advantages of the exponential family. We draw inferences using the Markov chain Monte Carlo algorithm. Extensive simulations demonstrate that the proposed model outperforms simpler alternatives. Applying the model to analyze the rainfall data over 122 years provides insights into model parameters, temporal patterns, and the impact of climate change. We observe a significant decreasing trend in wet-day rainfall for the Southern Western Ghats region.