Some new results for Dirichlet priors

Let p be a random probability measure chosen by a Dirichlet process whose parameter a is a finite measure with support contained in [0, +∞) and suppose that V = ∫ x²p(dx)-[∫ xp(dx)]² is a (finite)random variable. This paper deals with the distribution of V, which is given in a rather general case. A simple application to Bayesian bootstrap is also illustrated.