Location-scale Dirichlet process mixtures of Gaussians (DPM-G) have proved extremely useful in dealing with density estimation and clustering problems in a wide range of domains. Motivated by an astronomical application, in this work we address the robustness of DPM-G models to affine transformations of the data, a natural requirement for any sensible statistical method for density estimation and clustering. First, we devise a coherent prior specification of the model which makes posterior inference invariant with respect to affine transformations of the data. Second, we formalise the notion of asymptotic robustness under data transformation and show that mild assumptions on the true data generating process are sufficient to ensure that DPM-G models feature such a property. Our investigation is supported by an extensive simulation study and illustrated by the analysis of an astronomical dataset consisting of physical measurements of stars in the field of the globular cluster NGC 2419.

高斯的位置尺度Dirichlet过程混合（DPM-G）已被证明在处理广泛领域中的密度估计和聚类问题方面非常有用。受天文应用的推动，在这项工作中，我们解决了DPM-G模型对数据进行仿射变换的鲁棒性，这是任何用于密度估计和聚类的明智统计方法的自然要求。首先，我们设计了一个一致的模型先验规范，该模型使后验推断相对于数据的仿射变换是不变的。其次，我们将数据转换下的渐进鲁棒性概念形式化，并表明对真实数据生成过程的温和假设足以确保DPM-G模型具有这种特性。