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Structure formation in our Universe creates non-Gaussian random fields thatwill soon be observed over almost the entire sky by the Euclid satellite, theVera-Rubin observatory, and the Square Kilometre Array. An unsolved problem ishow to analyze best such non-Gaussian fields, e.g. to infer the physical lawsthat created them. This problem could be solved if a parametric non-Gaussiansampling distribution for such fields were known, as this distribution couldserve as likelihood during inference. We therefore create a samplingdistribution for non-Gaussian random fields. Our approach is capable ofhandling strong non-Gaussianity, while perturbative approaches such as theEdgeworth expansion cannot. To imitate cosmological structure formation, weenforce our fields to be (i) statistically isotropic, (ii) statisticallyhomogeneous, and (iii) statistically independent at large distances. Wegenerate such fields via a Monte Carlo Markov Chain technique and find thateven strong non-Gaussianity is not necessarily visible to the human eye. Wealso find that sampled marginals for pixel pairs have an almost genericGauss-like appearance, even if the joint distribution of all pixels is markedlynon-Gaussian. This apparent Gaussianity is a consequence of the highdimensionality of random fields. We conclude that vast amounts of non-Gaussianinformation can be hidden in random fields that appear nearly Gaussian insimple tests, and that it would be short-sighted not to try and extract it.

MCMC generation of cosmological fields far beyond Gaussianity