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Steve_Rayhawk comments on Log-odds (or logits) - Less Wrong Discussion

20 Post author: brilee 28 November 2011 01:11AM

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Comment author: Steve_Rayhawk 30 November 2011 06:43:51PM *  5 points [-]

The natural unit of ratio, the neper (Np), is easier to interpret for small ratio contributions, where the derivative of exp(x) is ≈1:

0.1Np = exp( 0.1) ∶ 1 ≈ 1.1 ∶ 1
-0.1Np = exp(-0.1) ∶ 1 ≈ 0.9 ∶ 1

This could make for an easy upgrade path to use of nepers or centinepers instead of percents in comparatives involving rates, which would reduce semantic confusion. "50% faster" can mean "gets 150% as far" (so .41Np faster, or 41 cNp, or perhaps 41Np%) or "takes 50% as much time" (so .69Np faster, or 69cNp, or 69Np%). That's an argument for using nepers as a standard base outside communications of probability.

(trivia: Nepers and radians are each other turned sideways, being respectively the real and imaginary parts of eigenvalues of linear differential equation systems.)