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::GN- Bayesjutsu

Ghost Net 1
Image from Bernd Helfert
So, you want to learn Bayesjutsu? Well, here's one of the preliminary lessons.

It's a lot easier for us baselines and nebs and other smallminds to add up small integers than it is for us to multiply fractions and decimals. One of the first tricks invented by the smarty-pants who came up with Bayesjutsu was the measurement of probability in terms of decibels of evidence (or "Jaynes"), which measure probability logarithmically rather than linearly, and rounding them off to the nearest round number. This let us combine probabilities by just adding up their Jaynes, rather than multiplying their probabilities.

Positive numbers of Jaynes indicate evidence for the truth of a proposition; negative Jaynes indicate evidence against it; no Jaynes at all indicate agnosticism.

Some of the earliest aioids were designed to use this form of measurement of the truth of statements, because it allowed the representation of the aioid's belief or disbelief in nearly all propositions in the form of a single signed byte, with a value ranging between -127 and 127. (You'll notice that that's only using up 127+127+1=255 out of 256 values of a byte; the 256'th possibility, which corresponds to a value of 128 or -0 depending on which way you're coming at it, is a flag for when those aioids have to use something more complicated than this simple trick.)

The ease with which this technique allows baselines to mentally deal with probabilities was a foundation for a wide variety of more advanced techniques, which this memetic payload is too small to compress.


If you can absorb all of that, then it just might be worth your time to go looking for Bayesian masters who can increase your understanding still further, and help guide you through such thorny issues as meta-evidence - that is, trying to figure out how reliable eyewitness testimony is - and on to deeper insights. Of course, being the smartest Bayesian around won't do you a lick of good if you're going up against even the dumbest transap, and only some good against a transav, but hey, at least it'll help you deal with the rest of us pieces of meat, right?


Jaynes / Level of belief / Rough Odds / notes

-oo / 0% / 1:oo / complete disbelief, unachievable by Bayesjutsu save
for paradoxes

-6 / 20.0% / 1:4 /
-5 / 24.0% / 1:3 /
-4 / 28.5% / 2:5 / a reasonable doubt
-3 / 33.3% / 1:2 /
-2 / 38.7% / 2:3 / probable cause
-1 / 44.3% / 4:5 /
0 / 50.0% / 1:1 / neither belief nor disbelief; agnosticism
1 / 55.7% / 5:4 / preponderance of the evidence
2 / 61.3% / 3:2 /
3 / 66.6% / 2:1 / clear and convincing evidence
4 / 71.5% / 5:2 /
5 / 76.0% / 3:1 / beyond a reasonable doubt
6 / 80.0% / 4:1 /
7 / 83.3% / 5:1 /
8 / 86.3% / 6:1 /
9 / 88.8% / 8:1 /
10 / 90.9% / 10:1 / one nine

13 / 95.2% / 20:1 / lone studies with p=0.05
20 / 99.0% / 100:1 / two nines, lone studies with p=0.01
26 / 99.7% / 400:1 / confirmed studies with p=0.05
30 / 99.9% / 1,000:1 / three nines
40 / 99.99% / 10,000:1 / four nines, confirmed studies with p=0.01
42 / 99.993% / 16,000:1 / 4 standard deviations
50 / 99.999% / 100,000:1 / five nines
60 / 99.9999% / 1,000,000:1 / six nines
62 / 99.99994% / 1,500,000:1 / 5 standard deviations
87 / 99.9999998% / 500,000,000:1 / 6 standard deviations
116 / 99.9999999997% / 390,000,000,000:1 / 7 standard deviations
127 / 99.99999999998% / 5,000,000,000,000:1 / max belief storable in
one signed byte

oo / 100% / oo:1 / complete certainty, unachievable by Bayesjutsu save
for tautologies


Where LevelOfBelief is measured between 0 and 1 (eg, 0.5 or 50%):
Jaynes = 10 * log(10) (LevelOfBelief / (1 - LevelOfBelief))
10 ^ (Jaynes/10) = LevelOfBelief / (1-LevelOfBelief)
 
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Development Notes
Text by Daniel Eliot Boese

Initially published on 16 February 2011.

 
 
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