On a Posterior Predictive Density Sample Size Criterion

Let Ω be a space of densities with respect to some "σ"-finite measure "μ" and let <b>Π</b> be a prior distribution having support Ω with respect to some suitable topology. Conditional on "f", let <b>X</b>-super-<b>n</b> = ("X"₁&hairsp;,…, &hairsp;"X"_"n") be an independent and identically distributed sample of size <b>"n"</b> from <b>"f"</b>. 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. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..