Stick-breaking priors are often adopted in Bayesian nonparametric mixture models for generating mixing weights. When covariates influence the sizes of clusters, stick-breaking mixtures can leverage various computational techniques for binary regression to ease posterior computation. Existing stick-breaking priors are typically based on continually breaking a single remaining piece of the unit stick. We demonstrate that this ``single-piece'' scheme can induce three highly undesirable behaviors; these behaviors are circumvented by our proposed model which continually breaks off all remaining pieces of a unit stick while keeping posterior computation essentially identical. Specifically, the new model provides more flexibility in setting cross-covariate prior correlation among the generated random measures, mitigates the impact of component label switching when posterior simulation is performed using Markov chain Monte Carlo, and removes the imposed artificial decay of posterior uncertainty on the mixing weights according to when the weight is ``broken off'' the unit stick. Unlike previous works on covariate-dependent mixtures, which focus on estimating covariate-dependent distributions, we instead focus on inferring the effects of individual covariates on the mixture weights in a fashion similar to classical regression analysis, and propose a new class of posterior predictives for summarizing covariate effects.

中文翻译：

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协变量相关混合模型的树棒破坏先验

贝叶斯非参数混合模型中经常采用断棒先验来生成混合权重。当协变量影响集群的大小时，断棒混合可以利用各种计算技术进行二元回归，以简化后验计算。现有的断棒先验通常基于不断地破坏单位棒的单个剩余部分。我们证明了这种“单件”方案可以引发三种非常不受欢迎的行为；这些行为被我们提出的模型所规避，该模型不断地断开单位棒的所有剩余部分，同时保持后验计算基本相同。具体来说，新模型在设置生成的随机度量之间的交叉协变量先验相关性方面提供了更大的灵活性，当使用马尔可夫链蒙特卡罗执行后验模拟时，减轻组件标签切换的影响，并根据权重何时“断开”单位棒消除对混合权重的后验不确定性的人为衰减。与以前关于协变量相关混合的工作（侧重于估计协变量相关分布）不同，我们专注于以类似于经典回归分析的方式推断单个协变量对混合权重的影响，并提出一类新的后验预测总结协变量效应。单位坚持。与以前关于协变量相关混合的工作（侧重于估计协变量相关分布）不同，我们专注于以类似于经典回归分析的方式推断单个协变量对混合权重的影响，并提出一类新的后验预测总结协变量效应。单位坚持。与以前关于协变量相关混合的工作（侧重于估计协变量相关分布）不同，我们专注于以类似于经典回归分析的方式推断单个协变量对混合权重的影响，并提出一类新的后验预测总结协变量效应。