On a posterior predictive density sample size criterion

Let Omega be a space of densities with respect to some sigma-finite measure mu and let Pi be a prior distribution having support Omega with respect to some suitable topology. Conditional on f, let X-n = (X-1 ,..., X-n) be an independent and identically distributed sample of size n from f. This paper introduces a Bayesian non-parametric criterion for sample size determination which is based on the integrated squared distance between posterior predictive densities. An expression for the sample size is obtained when the prior is a Dirichlet mixture of normal densities.