Statistical naturalness and non-gaussianity in a finite universe

We study the behavior of n-point functions of the primordial curvature perturbations, assuming our observed Universe is only a subset of a larger space with statistically homogeneous and isotropic perturbations. If the larger space has arbitrary n-point functions in a family of local type non-Gaussian statistics, sufficiently biased smaller volumes will have statistics from a "natural" version of that family with moments that are weakly non-Gaussian and ordered, regardless of the statistics of the original field. We also describe the effect of this bias on the shape of the bispectrum.