## Jeffreys at the bar

Posted in Books, Statistics with tags , , on February 1, 2010 by xi'an

This morning, I found out, thanks to Steve Stiegler, that the most useful tool in Bayesian statistics, namely…the bar notation for conditioning, as in

$\pi(\theta|x)$,

is due to none but Harold Jeffreys! It was used in his 1931 edition of Scientific Inference … (Surprisingly, you can buy Scientific Inference on amazon.fr, but not on amazon.com!) And, indeed, in Keynes’ A Treatise On Probability, the conditioning is done using slanted bars. So it may be that, despite the influence of his introduction of Bayes factors and non-informative priors on the Bayesian community, his most lasting influence (in probability and statistics at least) remains this notational device!

## Re-reading Jeffreys’ Theory of Probability

Posted in Books, Statistics with tags , , , on January 20, 2010 by xi'an

Our paper with Nicolas Chopin and Judith Rousseau, Harold Jeffreys’s Theory of Probability Revisited, has now appeared in Statistical Science, 2009, Vol. 24, No. 2, 141-172, along with six discussions and our reply. It is very nice that the paper appeared in the 2009 volume of Statistical Science, as it made it as a 70th anniversary celebration for this important book. (In a similar spirit, I will start a reading class in March at CREST on Keynes’ A Treatise On Probability. With the hope that this can lead to another reassessment.)

## Shorter, clearer, with no swan in the pond

Posted in Books, Statistics with tags , , , , on March 28, 2009 by xi'an

In the current issue of Significance, there is a four page discussion by Bill Janeway on the current financial crisis and the role of statistical models. If you remove the pictures and the quotes from Alice, it is more like three pages and they tell you much more than the three-hundred-somes of The Black Swan. For instance, the paper relates to references that appeared much earlier than the book to point out the distinction between uncertainty and randomness, a point on which The Black Swan is always vague, it also spells out that there are not always true models and that time-series are not always stationary, two points that The Black Swan misses, and that ergodicity does not apply and that markets are not rational. As in The Black Swan, there are mentions there of black swans as events that “happen once in five hundred years”, too, as well as of the inadequacy of models like Value at Risk (which provides a quantile estimate on the risk but no loss evaluation) and of Gaussian assumptions, but the paper also blames the crisis on the abandonment of the essential balance-sheet by banks. In its conclusion about the rise of behavioural finance, Janeway relates to Taleb by quoting from his hero, John Maynard Keynes, but for reasons different from Fooled by Randomness. Ending on “bad models are bad” by calling for models that explore inefficiencies in the markets is not going to solve the crisis, but, again, the paper gives a much clearer and more informative message than The Black Swan did.