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性催生了空间变系数回归模型，但为每个预测变量单独估计系数曲面会导致：当众多预测变量不相关时，产生噪声干扰模式并降低模型可解释性。基于MODIS植被指数研究，本文考察来自光谱波段、生产力与能量通量、观测几何特征及地表特性的预测变量。由于这些关系随冠层结构、气候条件、土地利用和测量环境而变化，研究方法应同时具备空间变异效应建模与预测变量重要性区域识别的能力。我们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组套索先验。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可忽略效应压缩至零。后验推断采用马尔可夫链蒙特卡洛方法，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效应，该图标记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。MODIS实际应用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。