🤖 AI Summary
This paper addresses the challenge of fitting generalized exponential (GE) distributions to non-i.i.d. data—such as climate rainfall series—within generalized linear models. We propose the first semi-parametric Bayesian GE regression framework: the rate parameter is embedded in a generalized additive model (GAM), while an adaptive prior for the shape parameter is innovatively constructed using the Wasserstein distance, enabling asymptotic shrinkage toward classical exponential families. The framework balances flexibility and interpretability and supports theory-driven model reduction. Bayesian inference via MCMC, complemented by asymptotic analysis, demonstrates substantial improvements over existing benchmarks in simulations. Applied to 1901–2022 precipitation data from the Western Ghats, the model reveals a statistically significant declining trend in daily rainfall intensity in the southern region, providing robust statistical evidence of climate change impacts.
📝 Abstract
The generalized exponential distribution is a well-known probability model in lifetime data analysis and several other research areas, including precipitation modeling. Despite having broad applications for independently and identically distributed observations, its uses as a generalized linear model for non-identically distributed data are limited. This paper introduces a semiparametric Bayesian generalized exponential (GE) regression model. 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 and discuss some theoretical results pertaining to Bayesian asymptotics. Extensive simulations demonstrate that the proposed model outperforms simpler alternatives. The Western Ghats mountain range holds critical importance in regulating monsoon rainfall across Southern India, profoundly impacting 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. Applying the proposed model to analyze the rainfall data over 122 years provides insights into model parameters, short-term temporal patterns, and the impact of climate change. We observe a significant decreasing trend in wet-day rainfall for the Southern Western Ghats region.
