From a new working paper, Nassim Taleb (and co-author) with a formal proof of “statistical undecidability”. Highly technical, but interesting. [-]
Nassim Nicholas Taleb
October, 12 2010
Using the metadistribution of possible distributions for a given measure, we define a condition under which it is possible to make a decision based on the observation of random variable, which we call “statistical decidability”. We provide a sufficient condition on the metadistribution for the decision to be “statistically decidable” and conjecture that decisions based on a metadistribution with non compact support are always “statistically undecidable”. There is the need for a strong undefeasable a priori without which decisions are not statistically justified — an effect that is very significant for decisions affected by small probabilities.