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：分裂棍（SB）过程常被用于贝叶斯混合模型中生成混合权重。当协变量影响聚类规模时，SB混合模型尤其便利，因其可利用与二元回归的联系来简化协变量效应的设定及后验计算。现有SB模型通常基于对单位棍棒剩余片段的持续分割构建。我们从二元树视角将其视为仅单侧延伸的不平衡分叉树模型。研究表明，SB模型若干不良特性实际上很大程度上源于这种不平衡树结构。我们考虑具有替代分叉树结构的广义SB模型类，并从先验假设、后验不确定性和计算效率三方面考察底层树拓扑结构对贝叶斯分析的影响。特别地，我们提供证据表明：持续分割单位棍棒所有剩余片段的平衡树拓扑结构，能够解决或缓解依赖不平衡树的SB模型的多项不良特性。