标题： 使用预测生成树方法的一致贝叶斯空间域划分 显示英文标题

标题： Consistent Bayesian Spatial Domain Partitioning Using Predictive Spanning Tree Methods

摘要： 基于贝叶斯模型的空间聚类方法因其在估计具有未知聚类数的潜在聚类时的灵活性而被广泛使用，同时考虑空间邻近性。许多现有方法是为聚类有限的空间单元设计的，限制了它们的预测能力，或者可能对子区域的形状施加了严格的几何约束。此外，空间聚类模型的后验聚类一致性理论在文献中仍大多未被探索。在本研究中，我们提出了一种空间域随机划分模型（Spat-RPM），并展示了其在空间聚类回归中的应用，该模型通过将空间域划分为不相交的块，并使用生成树切割来诱导连续域划分，从而扩展了基于生成树的贝叶斯空间聚类。在填充域渐近框架下，我们引入了一种新的距离度量来研究域划分的后验集中度。我们证明了Spat-RPM能够实现域划分的一致估计，包括聚类数量，并推导了划分、参数和预测的后验集中率。我们还建立了先验超参数和块数的条件，为超参数选择提供了重要的实际指导。最后，我们通过模拟研究检验了我们模型的渐近性质，并将其应用于大西洋海洋数据。 显示英文摘要

摘要： Bayesian model-based spatial clustering methods are widely used for their flexibility in estimating latent clusters with an unknown number of clusters while accounting for spatial proximity. Many existing methods are designed for clustering finite spatial units, limiting their ability to make predictions, or may impose restrictive geometric constraints on the shapes of subregions. Furthermore, the posterior clustering consistency theory of spatial clustering models remains largely unexplored in the literature. In this study, we propose a Spatial Domain Random Partition Model (Spat-RPM) and demonstrate its application for spatially clustered regression, which extends spanning tree-based Bayesian spatial clustering by partitioning the spatial domain into disjoint blocks and using spanning tree cuts to induce contiguous domain partitions. Under an infill-domain asymptotic framework, we introduce a new distance metric to study the posterior concentration of domain partitions. We show that Spat-RPM achieves a consistent estimation of domain partitions, including the number of clusters, and derive posterior concentration rates for partition, parameter, and prediction. We also establish conditions on the hyperparameters of priors and the number of blocks, offering important practical guidance for hyperparameter selection. Finally, we examine the asymptotic properties of our model through simulation studies and apply it to Atlantic Ocean data.