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Dirichlet process mixtures under affine transformations of the data

Julyan Arbel 1 Riccardo Corradin 2 Bernardo Nipoti 3
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : 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. First, we devise a coherent prior specification of the model which makes posterior inference invariant with respect to affine transformation 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.
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Julyan Arbel, Riccardo Corradin, Bernardo Nipoti. Dirichlet process mixtures under affine transformations of the data. 2019. ⟨hal-01950652v2⟩

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