  Ex ante forecast outcomes should be interpreted as counterfactuals (potential
histories), with errors as the spread between outcomes. Reapplying measurements
of uncertainty about the estimation errors of the estimation errors of an
estimation leads to branching counterfactuals. Such recursions of epistemic
uncertainty have markedly different distributial properties from conventional
sampling error. Nested counterfactuals of error rates invariably lead to fat
tails, regardless of the probability distribution used, and to powerlaws under
some conditions. A mere .01% branching error rate about the STD (itself an
error rate), and .01% branching error rate about that error rate, etc.
(recursing all the way) results in explosive (and infinite) higher moments than
1. Missing any degree of regress leads to the underestimation of small
probabilities and concave payoffs (a standard example of which is Fukushima).
The paper states the conditions under which higher order rates of uncertainty
(expressed in spreads of counterfactuals) alters the shapes the of final
distribution and shows which a priori beliefs about conterfactuals are needed
to accept the reliability of conventional probabilistic methods (thin tails or
mildly fat tails).
