eBitsVSodds

A simple but robust measure of evidence for true-false hypotheses, designed to accomodate new information as it comes in (additively if new bits of evidence are independent) turns out to be the surprisal that a hypothesis is false minus the surprisal that it is true (cf. items 7 and 9 here). The resulting mnemonic for this evidence in bits (ebits) becomes "odds ratio" = 2ebits. Thus "ebits" is just the binary-log version of good-old racetrack odds. It goes to zero when the odds of something are 50:50, and to negative and positive extremes slowly (like surprisal) as the probability approaches 0 or 1. An ebit of evidence for a proposition's truth means that it has 2:1 odds, two ebits means 4:1 odds, three ebits 8:1 odds, etc.

DETAILS

http://www.umsl.edu/~fraundorfp/egsurpri.html

See also items 7 and 9 here

Contributed by: P. Fraundorf

© The Wolfram Demonstrations Project & Contributors   |   Terms of Use