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Bayesian nonparametric inference for unimodal and multimodal random probability measures on a finite dimensional Euclidean space is examined. After a short discussion on several concepts of multivatiate unimodality, we introduce and study a new class of nonparametric prior distributions on the subspace of random multivariate multimodal distributions. This class in a way generalizes the very restrictive class of random unimodal distributions. A flexible constructional approach is developed using a variant of Khinchin's representation theorem for unimodal distributions.

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