A main purpose of spatial data analysis is to predict the objective variable for the unobserved locations. Although Geographically Weighted Regression (GWR) is often used for this purpose, estimation instability proves to be an issue. To address this issue, Bayesian Geographically Weighted Regression (BGWR) has been proposed. In BGWR, by setting the same prior distribution for all locations, the coefficients' estimation stability is improved. However, when observation locations' density is spatially different, these methods do not sufficiently consider the similarity of coefficients among locations. Moreover, the prediction accuracy of these methods becomes worse. To solve these issues, we propose Bayesian Geographically Weighted Sparse Regression (BGWSR) that uses Bayesian Fused Lasso for the prior distribution of the BGWR coefficients. Constraining the parameters to have the same values at adjacent locations is expected to improve the prediction accuracy at locations with a low number of adjacent locations. Furthermore, from the predictive distribution, it is also possible to evaluate the uncertainty of the predicted value of the objective variable. By examining numerical studies, we confirmed that BGWSR has better prediction performance than the existing methods (GWR and BGWR) when the density of observation locations is spatial difference. Finally, the BGWSR is applied to land price data in Tokyo. Thus, the results suggest that BGWSR has better prediction performance and smaller uncertainty than existing methods.

翻译：空间数据分析的主要目的是预测未观测位置的目标变量。尽管地理加权回归（GWR）常用于此目的，但其存在估计不稳定的问题。为解决该问题，学界提出了贝叶斯地理加权回归（BGWR）。通过为所有位置设定相同的先验分布，BGWR提升了系数的估计稳定性。然而，当观测位置密度存在空间差异时，这些方法未能充分考虑位置间系数的相似性，导致预测精度下降。针对这些问题，我们提出贝叶斯地理加权稀疏回归（BGWSR），该方法将贝叶斯融合套索作为BGWR系数的先验分布。通过约束相邻位置参数取值相同，有望提升低邻近位置数量的预测精度。此外，基于预测分布还可评估目标变量预测值的不确定性。数值实验表明，当观测位置密度存在空间差异时，BGWSR的预测性能优于现有方法（GWR和BGWR）。最后将BGWSR应用于东京地价数据，结果证实BGWSR相较现有方法具有更优的预测性能和更小的不确定性。