Identification of multi-modal random variables through mixtures of polynomial chaos expansions

Abstract : A methodology is introduced for the identification of a multi-modal real-valued random variable from a collection of samples. The random variable is seen as a finite mixture of uni-modal random variables. A functional representation of the random variable is used, which can be interpreted as a {mixture of polynomial chaos expansions}. After a suitable separation of samples into sets of uni-modal samples, the coefficients of the expansion are identified by using an empirical projection technique. This identification procedure allows for a generic representation of a large class of multi-modal random variables with low-order generalized polynomial chaos representations.
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Anthony Nouy. Identification of multi-modal random variables through mixtures of polynomial chaos expansions. Comptes Rendus Mécanique, Elsevier Masson, 2010, 338 (12), pp.698-703. ⟨10.1016/j.crme.2010.09.003⟩. ⟨hal-00521932⟩

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