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

**Authors:** Arijit Dey, Arnab Hazra  
**arXiv:** [2309.03165](https://arxiv.org/abs/2309.03165)  
**Date:** 2023-09-06  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2309.03165v1/

## Key points

- The Western Ghats mountain range shapes precipitation patterns in Southern India during the monsoon season
- It contributes a substantial portion of annual rainfall necessary for ecosystem vitality and agriculture
- Wet-day rainfall varies across the Northern, Middle, and Southern regions of the Western Ghats
- Researchers have developed a semiparametric Bayesian generalized exponential regression model to analyze wet-day rainfall data from 1901 to 2022
- The proposed model incorporates a principled distance-based prior for the GE shape parameter within a generalized additive model framework
- The model allows for shrinking to an exponential regression model while retaining advantages of the exponential family
- Inferences are drawn using the Markov chain Monte Carlo algorithm, and extensive simulations show that the proposed model outperforms simpler alternatives
- Analysis of 122 years of rainfall data reveals insights into model parameters, temporal patterns, and climate change impacts
- There is a significant decreasing trend in wet-day rainfall observed in the Southern Western Ghats region
- The research is valuable for policymakers and stakeholders involved in agriculture and water resource management in the region
- Findings highlight temporal trends and potential impacts of climate change on wet-day rainfall, which affects regional agriculture.

## Summary

The Western Ghats mountain range holds critical importance in shaping precipitation patterns in Southern India during the monsoon season. It is responsible for a substantial portion of annual rainfall essential for ecosystem vitality and agricultural sustenance. Divided into Northern, Middle, and Southern regions, these areas experience varying levels of wet-day rainfall. To analyze the wet-day rainfall data for the monsoon months between 1901 and 2022, researchers have introduced a semiparametric Bayesian generalized exponential (GE) regression model. While the GE distribution assumption is well-known in the literature, it has not been explored in a regression setting until now. The proposed model incorporates a principled distance-based prior for the GE shape parameter within a generalized additive model framework. One important feature of this approach is that it allows the model to shrink to an exponential regression model while retaining the advantages of the exponential family. Inferences are drawn using the Markov chain Monte Carlo algorithm, and extensive simulations demonstrate that the proposed model outperforms simpler alternatives. Applying this model to analyze 122 years of rainfall data reveals insights into various aspects such as model parameters, temporal patterns, and the impact of climate change. Notably, there is a significant decreasing trend in wet-day rainfall observed for the Southern Western Ghats region. This research serves as an important resource for policymakers and stakeholders involved in agriculture and water resource management in the region. The findings highlight both temporal trends and potential impacts of climate change on wet-day rainfall which has a significant impact on regional agriculture. Overall, this study contributes valuable insights into understanding and predicting rainfall patterns in Southern India's Western Ghats region.