Perhaps another way to phrase this is "sampling and evaluating the similarity of samples can determine the dispersion of a distribution, but not its correctness

Perhaps another way to phrase this is "sampling and evaluating the similarity of samples can determine the dispersion of a distribution, but not its correctness." I can sample a gaussian and tell you how sparse the samples are (standard deviation) but this in no way tells me whether the distribution is accurate (it is possible to have a highly accurate distribution of a high-entropy variable). On the other hand, its possible to have a tight distribution with low standard deviation that is simply inaccurate, but I can't know that simply by sampling from it (unless I already know apriori what the output should look like).