  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.
