Bayesian Region Selection and Prediction in Poisson Regression with Spatially Dependent Global-Local Shrinkage Prior

2026-05-06

AI Summary

This study addresses the challenge of variable selection in high-dimensional Poisson regression when covariates exhibit spatial dependence. Conventional methods often fail to accurately recover sparse coefficient structures due to their neglect of spatial correlation, thereby compromising regional signal detection and predictive accuracy. To overcome this limitation, we propose a neighborhood-structured approach that integrates a conditional autoregressive (CAR) prior with a heavy-tailed global–local shrinkage prior, embedding spatial adjacency information directly into the coefficient prior. This formulation simultaneously enforces sparsity and captures spatial continuity, substantially enhancing the detection of weak yet spatially clustered signals. We develop a Metropolis-within-Gibbs sampling algorithm tailored for count data to enable efficient posterior inference. Extensive simulations and an application to North Atlantic hurricane frequency prediction demonstrate that the proposed method outperforms existing regression techniques under strong spatial correlation and achieves performance close to that of an oracle model.

Abstract

High-dimensional spatially correlated covariates are common in regression models encountered in environmental sciences and other fields. In such models, the regression coefficients often exhibit a sparse structure with spatial dependence. Although standard variable selection approaches can help detect the sparse structure, incorporating the dependence into variable selection helps recover spatially contiguous signals and improves prediction accuracy. Motivated by a real-world challenge in hurricane count prediction, we propose a novel neighborhood-structured global-local shrinkage prior for prediction and region selection in Poisson regression with spatial covariates. The proposed prior combines the Conditional Auto-Regressive (CAR) prior with a Super Heavy-tailed prior to introduce spatial dependence among the coefficients while ensuring appropriate shrinkage effects for covariate selection. We develop an efficient Metropolis-within-Gibbs sampler for computation that accommodates the count data. Extensive simulation studies demonstrate that the proposed model excels when signals are weak and adjacent and the spatial dependence in covariates is strong. In the application of hurricane prediction from the north Atlantic, our method outperforms traditional regression-based approaches and rivals the benchmark oracle model.

Problem

• spatial dependence
• variable selection
• Poisson regression
• high-dimensional covariates
• region selection

Innovation

• spatially dependent shrinkage prior
• Poisson regression
• Bayesian variable selection
• Conditional Auto-Regressive (CAR)
• Super Heavy-tailed prior