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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\u00a02419.<\/jats:p>","DOI":"10.1007\/s00180-020-01013-y","type":"journal-article","created":{"date-parts":[[2020,7,12]],"date-time":"2020-07-12T07:02:48Z","timestamp":1594537368000},"page":"577-601","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dirichlet process mixtures under affine transformations of the data"],"prefix":"10.1007","volume":"36","author":[{"given":"Julyan","family":"Arbel","sequence":"first","affiliation":[]},{"given":"Riccardo","family":"Corradin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1138-951X","authenticated-orcid":false,"given":"Bernardo","family":"Nipoti","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,12]]},"reference":[{"issue":"02","key":"1013_CR1","first-page":"326","volume":"8","author":"J Arbel","year":"2013","unstructured":"Arbel J, Nipoti B (2013) Discussion of \u201cBayesian nonparametric inference why and how comment\u201d, by M\u00fcller and Mitra. 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