On the multimodality of random probability measures

Abstract

Nonparametric methods for density estimation are examined here. Within a Bayesian setting the construction of an absolutely continuous random probability measure is often required for nonparametric statistical analysis. To achieve this we propose a "partial convexification" procedure of a process, such as the Dirichlet, resulting in a multimodal distribution function with a finite expected number of modes. In agreement with convexity theory results, it is shown that the derived random probability measure admits a density with respect to Lebesgue measure.