Geographically weighted regression (GWR) models handle geographical dependence through a spatially varying coefficient model and have been widely used in applied science, but its general Bayesian extension is unclear because it involves a weighted log-likelihood which does not imply a probability distribution on data. We present a Bayesian GWR model and show that its essence is dealing with partial misspecification of the model. Current modularized Bayesian inference models accommodate partial misspecification from a single component of the model. We extend these models to handle partial misspecification in more than one component of the model, as required for our Bayesian GWR model. Information from the various spatial locations is manipulated via a geographically weighted kernel and the optimal manipulation is chosen according to a Kullback-Leibler (KL) divergence. We justify the model via an information risk minimization approach and show the consistency of the proposed estimator in terms of a geographically weighted KL divergence.

翻译：地理加权回归模型(GWR)通过空间差异系数模型处理地理依赖问题,并在应用科学中广泛使用,但Bayesian通用扩展范围并不明确,因为它涉及加权日志相似性,并不意味着数据的概率分布。我们提出了一个Bayesian GWR模型,并表明其本质涉及该模型的局部偏差。目前模块化的Bayesian推理模型从该模型的单个组成部分中包含部分偏差。我们将这些模型扩展至处理该模型中不止一个组成部分的部分偏差,正如我们Bayesian GWR模型所要求的那样。来自不同空间地点的信息通过一个地理加权内核进行操纵,根据Kullback-Leber(KL)的差异选择最佳操作。我们通过信息风险最小化方法为该模型辩护,并以地理加权KL差异来显示拟议估算符的一致性。