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.
翻译:评估分布的同质性是一个老问题,特别是在非对称贝耶斯文献中,这个问题已经受到相当重视。为此,我们提议采用半等级二分立进程,这是一个新的等级,将Teh等人(2006年)的分级进程扩大,避免Camerlenghi等人(2019年a)最近描述的巢状进程的脱皮问题。我们超越了简单是/不回答的同质问题,将先前提出的同质问题纳入随机分割模式;这一程序使我们能够更全面地回答上述问题,并在考虑我大于或等于2人时,发现内部同质的人口群体。我们研究半等级二分立进程和同质测试的巴耶斯因素的理论性质,同时讨论我=2的大规模模拟研究和教育数据应用。