On functional central limit theorems of Bayesian nonparametric priors

A general approach to derive the weak convergence, when centered and rescaled, of certain Bayesian nonparametric priors is proposed. This method may be applied to a wide range of processes including, for instance, nondecreasing nonnegative pure jump Levy processes and normalized nondecreasing nonnegative pure jump Levy processes with known finite dimensional distributions. Examples clarifying this approach involve the beta process in latent feature models and the Dirichlet process.