Dirichlet process mixtures for density estimation and clustering under affine transformations of the data

Bayesian nonparametric methods have proved very useful in problems of density estimation and clustering. In this area, the main tool is represented by the Dirichlet process mixture model (DPM). A natural requirement for statistical methods used to estimate densities is that they must be robust to rescaling of the data. Motivated by an application with astronomical data, we investigate the behavior of DPM when data are subject to affine transformations. First we devise a coherent prior specification of the model which makes posterior inference invariant with respect to the affine transformation of the data. Second we investigate asymptotic properties of the DPM, showing that, under certain assumptions, the method is asymptotically robust. Our investigation is supported by an extensive simulation study.