Title: "Bayesian Poisson Regression with Spatially Dependent Global-Local Shrinkage Prior."
For hurricane prediction problems, the challenge often lies in the small sample sizes and high-dimensional, spatially correlated covariates. Traditional regularized regression models, such as Poisson regression with an elastic net penalty, struggle with these data characteristics, leading to bad predictions. We propose a Bayesian Poisson regression model that incorporates spatially dependent global-local shrinkage priors. It is designed to discern subtle signals within global field data and simultaneously generate predictions. Our model employs a Conditional Autoregressive (CAR) Gaussian prior for the spatially dependent covariates to account for spatial correlations. Additionally, it applies global-local shrinkage factors to the CAR prior to effectively mitigate the influence of inactive regions while maintaining the significance of active ones, which also helps to decouple the correlation effects between active and inactive regions. The shrinkage factors themselves are assigned with half-Cauchy and log-Cauchy priors, with the latter demonstrating superior performance in scenarios of weak signals and strong spatial correlation among covariates. A Metropolis-within-Gibbs sampler is developed for computational implementation. Simulation studies affirm the efficacy of the proposed model. When applied to the North Atlantic hurricane prediction problem, our model outperforms both the elastic net approach and traditional climatology, closely rivaling the University of Arizona's (UA) model, which serves as the benchmark "oracle" in this context.