Some new results on random Dirichlet variances
Ilenia Epifani, Alessandra Guglielmi, Eugenio Melilli · CNR SOLAR (Scientific Open-access Literature Archive and Repository) (University of Southampton) · 2004
A fundamental problem in a nonparametric Bayesian framework is the computation of the laws of functionals of random probability measures. For instance, in this context, testing hypotheses about the variance of the frequency distribution of a characteristic in a population requires the knowledge of its posterior distribution. The aim of this paper is to show some new results concerning the law of the functional variance V of a Dirichlet process P. In particular, we establish a simple distributional relationship between V and the random variable (X-Y)^2, where X and Y are independent copies of the random mean of the Dirichlet process P. Useful expressions for some integral transforms of V are also obtained and illustrative examples are given. Moreover, we discuss the correspondence between the distribution of the variance and the parameter of the Dirichlet process with given total mass. Finally two approximation procedures of the law of V are suggested