Stick-breaking (SB) processes are often adopted in Bayesian mixture models for generating mixing weights. When covariates influence the sizes of clusters, SB mixtures are particularly convenient as they can leverage their connection to binary regression to ease both the specification of covariate effects and posterior computation. Existing SB models are typically constructed based on continually breaking a single remaining piece of the unit stick. We view this from a dyadic tree perspective in terms of a lopsided bifurcating tree that extends only in one side. We show that several unsavory characteristics of SB models are in fact largely due to this lopsided tree structure. We consider a generalized class of SB models with alternative bifurcating tree structures and examine the influence of the underlying tree topology on the resulting Bayesian analysis in terms of prior assumptions, posterior uncertainty, and computational effectiveness. In particular, we provide evidence that a balanced tree topology, which corresponds to continually breaking all remaining pieces of the unit stick, can resolve or mitigate several undesirable properties of SB models that rely on a lopsided tree.

翻译：Stick-breaking（SB）过程常被用于贝叶斯混合模型中生成混合权重。当协变量影响聚类大小时，SB混合模型因其能通过二元回归框架同时简化协变量效应的设定与后验计算而尤为便利。现有SB模型通常基于对单位长度棍棒剩余部分进行连续断裂而构建。本文从二元树视角将其视为仅单侧延伸的偏斜分叉树。研究表明，SB模型的若干不良特性实际上主要源于这种偏斜树结构。我们考虑具有替代分叉树结构的广义SB模型类别，并考察底层树拓扑结构对先验假设、后验不确定性及计算效率等贝叶斯分析结果的影响。特别地，我们提供证据表明：对应持续断裂单位棍棒所有剩余部分的平衡树拓扑结构，能够解决或缓解依赖偏斜树的SB模型中的若干不良性质。