Dirichlet process mixtures are particularly sensitive to the value of the so-called precision parameter, which controls the behavior of the underlying latent partition. Randomization of the precision through a prior distribution is a common solution, which leads to more robust inferential procedures. However, existing prior choices do not allow for transparent elicitation, due to the lack of analytical results. We introduce and investigate a novel prior for the Dirichlet process precision, the Stirling-gamma distribution. We study the distributional properties of the induced random partition, with an emphasis on the number of clusters. Our theoretical investigation clarifies the reasons of the improved robustness properties of the proposed prior. Moreover, we show that, under specific choices of its hyperparameters, the Stirling-gamma distribution is conjugate to the random partition of a Dirichlet process. We illustrate with an ecological application the usefulness of our approach for the detection of communities of ant workers.

翻译：狄利克雷过程混合模型对所谓的精度参数值特别敏感，该参数控制底层潜划分的行为。通过先验分布对精度进行随机化是一种常见解决方案，可生成更稳健的推断程序。然而，由于缺乏解析结果，现有先验选择无法实现透明的信息提取。我们引入并研究了一种新型狄利克雷过程精度先验——斯特林-伽马分布。我们探讨了由此诱导的随机划分的分布特性，重点关注聚类数目。理论分析阐明了所提先验改进稳健性的原因。此外，我们证明，在其超参数的特定选择下，斯特林-伽马分布与狄利克雷过程的随机划分共轭。通过一项生态学应用实例，我们展示了该方法在检测蚂蚁工群落中的实用性。