The Black Swan

"The Black Swan" is a best-seller by Nassim Nicholas Taleb, the author of another bigger best-seller "Fooled by Randomness." Both books received more than 300 reviews on Amazon.com. I flipped through the second book in the bookstore and thought it was an interesting book, especially for teaching statistics to curious and skeptical undergraduate students.

Today, I stumbled over a special issue in The American Statistician (August 2007) designated to the praises and criticisms (mainly the latter) of "The Black Swan." The reason for such strong reaction from the usually low-key statistical profession is pretty obvious from a small number of excerpts quoted in TAS:

“Statisticians . . . are computing people, not thinkers.”

“Statisticians, it has been shown, tend to leave their brains in the classroom, and engage in the most trivial inferential errors when they are let out on the streets.”

It is worth mentioning that this special issue even caught the attention of the Bloomberg news and the editor of TAS was interviewed for a news coverage of this book.

TAS also invited Taleb to write a response in this special issue. In this response, Taleb said the main criticism for statistics in his book is for

1. The unrigorous use of statistics, and reliance on probability in domains where the current methods can lead us to make consequential mistakes (the “high impact”)where, on logical grounds, we need to force ourselves to be suspicious of inference about low probabilities.

2. The psychological effects of statistical numbers in lowering risk consciousness and the suspension of healthy skepticism—in spite of the unreliability of the numbers
produced about low-probability events.

3. Finally TBS is critical of the use of commoditized metrics such as “standard deviation,” “Sharpe ratio,” “mean-variance,”and so on in fat-tailed domains where these terms have little practical meaning, and where reliance by the untrained has
been significant, unchecked and, alas, consequential.

This is essentially about cautions on prediction (extrapolation) based on models, effects of outliers and rare events, and uses of statistics that are motivated by specific probability models. I don't think any good applied statistican will deny the importance of cautionary interpretation of statistical analysis and will not "commit" the mistakes outlined above. Actually, sometimes I feel the conclusion that can be made from data analysis is very limited. The usefulness of statistical inference and analysis lies primarily in narrowing down hypotheses and possbilities.