Bayesian Variable Selection for Spatially Varying Coefficient Models via Spike-and-Slab Group Lasso

Thomas M. Menino Convention & Exhibition Center 

We propose a Bayesian spatial variable selection method for massive datasets using spatially varying coefficient models. Coefficients share low-rank basis functions for dimension reduction and scalable computation. A spike and slab group lasso, SSGL, prior induces structured sparsity, selecting predictors and their spatial effects without manual tuning. We build a conjugate Bayesian model with an efficient MCMC sampler and closed-form updates. Cross-validation chooses the number of basis functions and shrinkage settings to balance fit and speed. Simulations across varied sample sizes and numbers of predictors show gains over generalized additive models and multiscale geographically weighted regression in prediction, surface recovery, and variable selection. The method lowers MSE for active coefficients, improves detection of zero effects in high dimensions, and delivers calibrated uncertainty with near nominal coverage. The approach is rigorous and scalable, with possible future extensions to non-Gaussian outcomes, spatiotemporal settings, and adaptive bases.

Spatially Varying Coefficients

Bayesian Variable Selection

Spike-and-Slab Prior

Group Lasso

Basis Functions 

Section on Bayesian Statistical Science