## Jeffreys at the bar

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!

### 6 Responses to “Jeffreys at the bar”

1. And, if I may, the bar is exactly where you lot would be spending your time without physicists !!!
:-]

• Just as forecasted, the comments degenerate towards the inebriated category… But so far restricted to my Italian readers! I meant bar as in “bar of a tribunal”, not as “drunken bar fights”!!!

2. Steve Stigler gives the reference:

Shafer, Glenn and Vladimir Vovk (2006). The sources of Kolmogorov’s Grundbegriffe. Statistical Science 21: 70-98.

And indeed Shafer and Vovk indicate Jeffreys (1931) as the origin of the notation. This paper is actually very interesting in terms of the discussion of Burdzy’s book as it also covers the notion of collectives whom refutation the authors attribute to Ville (1939).

3. Footnote 10 of Cox’s 1946 paper says that Keynes did some investigation into the history of conditioning notation. A notation (possibly the first?) was introduced by McColl, although not the vertical bar:

“H. McColl, Proc. Lond Math. Soc. 11, 113 (1880). McColl uses the symbol $x_a$ for the probability of the proposition $x$ on the hypothesis $a$.”

4. Following DeGroot, the most important thing for a Bayesian is “where is the bar”!!
in this perspective, Jeffreys was the one who found the bar!!!

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