Exact Multivariate Bayesian Bootstrap Distributions of Moments

The common unknown probability law P of a random sample Y₁,…, Yₙ is assigned a Dirichlet process prior with index α. It is shown that the posterior joint density of several moments of P converges, as α(R)→ 0, to a multivariate B-spline, which is, therefore, the Bayesian bootstrap joint density of the moments. The result provides the basis for possible default nonparametric Bayesian inference on unknown moments.