Nassim Taleb, of Black Swan fame (or infamy), has elaborated on the concept and developed what he calls "a map of the limits of Statistics". His basic argument is that there is one kind of decision problem where the use of any statistical model is harmful. These would be any decision problems where the consequence of making the wrong decision could be inordinately high, and the underlying PDF is hard to know.
One example would be shorting a stock option. This kind of operation can lead to limitless (in theory, at least) loss; and the probability of such a loss is unknown. Many people in fact model the probability, but Taleb argues that the financial markets aren't old enough to allow one to be confident about any model. Just because every swan you have ever seen is white, that doesn't mean black swans are impossible or even unlikely.
So here's the question: is there such a thing as a consensus in the Statistics community about Mr. Taleb's arguments?
Maybe this should be community wiki. I don't know.
I was at a meeting of the ASA (American Statistical Association) a couple years ago where Taleb talked about his "fourth quadrant" and it seemed his remarks were well received. Taleb was much more careful in his language when addressing an auditorium of statisticians than he has been in his popular writing.
Some statisticians are offended by the provocative hyperbole in Taleb's books, but when he states his ideas professionally there's not too much to object to. It's hard to argue that one can confidently estimate the probability of rare events with little or no data, or that one should make high-stakes decisions on such estimates if they can at all be avoided.
(Here's a blog post I wrote about Taleb's ASA talk shortly after the event.)
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