论文标题
关于协变量依赖性混合物中破坏棒型模型的树观点
A tree perspective on stick-breaking models in covariate-dependent mixtures
论文作者
论文摘要
贝叶斯混合物模型中通常采用破坏性（SB）工艺来产生混合重量。当协变量影响簇的大小时，SB混合物特别方便，因为它们可以利用其与二元回归的连接以减轻协变量效应的规范和后验计算。现有的SB型号通常是基于不断破坏单元杆的剩余部分而构建的。我们从二元树的角度来看这是从仅在一侧延伸的偏斜树的角度来看的。我们表明，SB模型的两个不愉快特征实际上主要是由于这种偏斜的树结构。我们考虑了具有替代性分叉树结构的广义类型SB模型，并在先前的假设，后部不确定性和计算有效性方面检查了基础树拓扑对所得贝叶斯分析的影响。特别是，我们提供的证据表明，平衡的树拓扑与不断破坏单元棒的所有剩余部分相对应，可以解决或减轻依赖于偏斜树的SB模型的这些不良属性。
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 two 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 these undesirable properties of SB models that rely on a lopsided tree.
