  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.
