Bayesian mixtures of multiple scale distributions

Florence Forbes (1) , Alexis Arnaud (1) , Russell Steele (2) , Benjamin Lemasson (3) , Emmanuel L. Barbier (4)

1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
2 Department of Mathematics and Statistics [Montréal]
3 ANTE-INSERM U836, équipe 5 - Neuro-imagerie fonctionnelle et métabolique
4 GIN - [GIN] Grenoble Institut des Neurosciences

Multiple scale distributions are multivariate distributions that exhibit a variety of shapes not necessarily elliptical while remaining analytical and tractable. In this work we consider mixtures of such distributions for their ability to handle non standard typically non-gaussian clustering tasks. We propose a Bayesian formulation of the mixtures and a tractable inference procedure based on variational approximation. The interest of such a Bayesian formulation is illustrated on an important mixture model selection task, which is the issue of selecting automatically the number of components. We derive promising procedures that can be carried out in a single-run, in contrast to the more costly comparison of information criteria.

Domaines: Statistiques [math.ST]

Florence Forbes, Alexis Arnaud, Russell Steele, Benjamin Lemasson, Emmanuel L. Barbier. Bayesian mixtures of multiple scale distributions. CMStatistics 2018 - 11th International Conference of the ERCIM WG on Computational and Methodological Statistics, Dec 2018, Pisa, Italy. ⟨hal-01941682⟩