发表机构
Department of Statistics Texas A&M University（德克萨斯农工大学统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种基于Bregman几何的广义似然框架，用于复杂对象（如分布、网络）的空间聚类，通过折叠分数和MCMC实现后验推断，并证明了一致性及在休斯顿数据上的有效性。
AI 中文摘要
空间聚类日益涉及复杂对象，包括概率分布、网络和结构化矩阵，对于这些对象，传统的参数似然可能难以指定。我们通过对响应的固定表示进行聚类特定的Bregman损失取幂来构造广义似然，从而避免为每个响应类别指定参数采样模型的需要。每个聚类与一个未知的代表相关联，广义似然通过所表示观测与该代表之间的Bregman散度来度量聚类内同质性。与Bregman几何匹配的先验族产生共轭的广义后验更新，并允许对聚类特定代表进行精确边缘化。由此产生的折叠分数将聚类内Bregman离散度与代表的不确定性相结合，而生成树划分先验将后验划分支持限制为空间连续的聚类。这种折叠表示还导致用于后验计算的可处理MCMC算法。该框架在共同的推断构造内适应多个复杂对象响应类别。我们在填充域渐近下建立了空间划分和聚类特定代表的后验一致性。针对不同复杂对象响应的模拟研究证明了空间划分和聚类特定代表的准确恢复。我们进一步分析了休斯顿空间单元中的种族构成分布，展示了具有不同人口构成的地理上连贯的聚类。
英文摘要
Spatial clustering increasingly involves complex objects, including probability distributions, networks, and structured matrices, for which conventional parametric likelihoods may be difficult to specify. We construct a generalized likelihood by exponentiating a cluster-specific Bregman loss on fixed representations of the responses, avoiding the need to specify a parametric sampling model for each response class. Each cluster is associated with an unknown representative, and the generalized likelihood measures within-cluster homogeneity through the Bregman divergence between the represented observations and that representative. A prior family matched to the Bregman geometry yields conjugate generalized posterior updates and permits exact marginalization of the cluster-specific representatives. The resulting collapsed scores combine within-cluster Bregman dispersion with uncertainty in the representatives, while a spanning-tree partition prior restricts posterior partition support to spatially contiguous clusters. This collapsed representation also leads to a tractable MCMC algorithm for posterior computation. The framework accommodates multiple complex-object response classes within a common inferential construction. We establish posterior consistency for the spatial partition and cluster-specific representatives under infill-domain asymptotics. Simulation studies with different complex-object responses demonstrate accurate recovery of spatial partitions and cluster-specific representatives. We further analyze racial-composition distributions across spatial units in Houston, illustrating geographically coherent clusters with distinct demographic compositions.
