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Posted by Inya Ivkovic Apr 6, 2008 |
Taleb’s discussion on rare events continues with a brief analysis why statisticians cannot successfully detect rare events. He says that statistics “is based on one simple notion; the more information you have, the more you are confident about the outcome.” The only problem is determining the level of that confidence.
Common statistics models are based on establishing the confidence level under an assumption that it will increase in non-linear proportion to the number of observations. In layman’s terms, the larger the sample, the better the statisticians knowledge about the behavior of its variables.
Where statistics becomes complicated, and by extension, yields fallacies, is when the distribution is not normal, but asymmetrical. Taleb offers an example. Suppose there is an urn full of red and black tennis balls. We don’t know how many balls are in the urn, only that red balls are significantly outnumbered by black balls. Having that in mind, knowing about “the absence of red balls will increase very slowly,” while “our knowledge of the presence of red balls will dramatically improve once one of them is found.”
In the investment context, assessing performance requires more precise and less intuitive techniques and models. Otherwise, performance assessments will have to be measured independent of how often rare events may or may not occur.