Understanding how environmental drivers relate to vegetation condition motivates spatially varying regression models, but estimating a separate coefficient surface for every predictor can yield noisy patterns and poor interpretability when many predictors are irrelevant. Motivated by MODIS vegetation index studies, we examine predictors from spectral bands, productivity and energy fluxes, observation geometry, and land surface characteristics. Because these relationships vary with canopy structure, climate, land use, and measurement conditions, methods should both model spatially varying effects and identify where predictors matter. We propose a spatially varying coefficient model where each coefficient surface uses a tensor product B-spline basis and a Bayesian group lasso prior on the basis coefficients. This prior induces predictor level shrinkage, pushing negligible effects toward zero while preserving spatial structure. Posterior inference uses Markov chain Monte Carlo and provides uncertainty quantification for each effect surface. We summarize retained effects with spatial significance maps that mark locations where the 95 percent posterior credible interval excludes zero, and we define a spatial coverage probability as the proportion of locations where the credible interval excludes zero. Simulations recover sparsity and achieve prediction. A MODIS application yields a parsimonious subset of predictors whose effect maps clarify dominant controls across landscapes.

翻译：理解环境驱动因素与植被状况的关联关系，推动了空间变系数回归模型的发展。然而，当存在大量无关预测变量时，为每个预测因子单独估计系数曲面可能导致噪声模式并降低可解释性。基于MODIS植被指数研究的需求，本文考察了来自光谱波段、生产力与能量通量、观测几何以及地表特征等多类预测因子。由于这些关系随冠层结构、气候条件、土地利用及观测条件而变化，分析方法需同时具备空间变效应建模与预测变量重要性区位识别的能力。本文提出一种空间变系数模型，其中每个系数曲面采用张量积B样条基函数，并对基函数系数施加贝叶斯群套索先验。该先验能实现预测变量层面的收缩效应，在保持空间结构的同时将不显著的效应压缩至零。后验推断采用马尔可夫链蒙特卡罗方法，并为每个效应曲面提供不确定性量化。我们通过空间显著性图总结保留的效应，该图标记出95%后验可信区间不包含零的空间位置，并定义空间覆盖概率作为可信区间不包含零的位置比例。模拟实验验证了方法的稀疏恢复能力与预测性能。在MODIS数据应用中，该方法获得了简约的预测变量子集，其效应分布图清晰揭示了不同景观类型的主导控制因素。