论文标题
半层次结构的Dirichlet过程及其用于聚类均匀分布的应用
The semi-hierarchical Dirichlet Process and its application to clustering homogeneous distributions
论文作者
论文摘要
评估分布的同质性是一个旧问题，它受到了很大的关注，尤其是在非参数贝叶斯文学中。为此，我们提出了半层次的dirichlet过程，这是一个新的层次之前，扩展了Teh等人的层次差异过程。 （2006年），这避免了Camerlenghi等人最近描述的嵌套过程的变性问题。 （2019a）。我们超越了对同质性问题的简单/否答案，并将提出的先验嵌入随机分区模型中；该程序使我们能够对上述问题做出更全面的回应，实际上，当我考虑了大于2个这样的人群时，它们在内部具有同质性的人群。我们研究了i = 2时研究半层次差异过程的理论特性和同质性测试的贝叶斯因子的理论特性。还讨论了广泛的模拟研究和对教育数据的应用。
Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical prior that extends the hierarchical Dirichlet process of Teh et al. (2006) and that avoids the degeneracy issues of nested processes recently described by Camerlenghi et al. (2019a). We go beyond the simple yes/no answer to the homogeneity question and embed the proposed prior in a random partition model; this procedure allows us to give a more comprehensive response to the above question and in fact find groups of populations that are internally homogeneous when I greater or equal than 2 such populations are considered. We study theoretical properties of the semi-hierarchical Dirichlet process and of the Bayes factor for the homogeneity test when I = 2. Extensive simulation studies and applications to educational data are also discussed.
