shortest goddamn bayes guide ever

lemonhope

// ODDS = YEP:NOPE
YEP, NOPE = MAKE UP SOME INITIAL ODDS WHO CARES
FOR EACH E IN EVIDENCE
	YEP *= CHANCE OF E IF YEP
	NOPE *= CHANCE OF E IF NOPE
	ASSUME E // DO NOT DOUBLE COUNT

The thing to remember is that yeps and nopes never cross. The colon is a thick & rubbery barrier. Yep with yep and nope with nope.

bear : notbear =
1:100 odds to encounter a bear on a camping trip around here in general
* 20% a bear would then scratch my tent : 50% a notbear would
* 10% a bear would then flip my tent over : 1% a notbear would
* 95% a bear would then look exactly like a fucking bear inside my tent : 1% a notbear would
* 0.01% chance a bear would then eat me alive : 0.001% chance a notbear would

As you die you conclude 1*20*10*95*.01 : 100*50*1*1*.001 = 190 : 5 odds that a bear is eating you.

// ODDS = YEP:NOPE
YEP, NOPE = MAKE UP SOME INITIAL ODDS WHO CARES
FOR EACH E IN EVIDENCE
	YEP *= CHANCE OF E IF YEP
	NOPE *= CHANCE OF E IF NOPE
	ASSUME E // DO NOT DOUBLE COUNT

The thing to remember is that yeps and nopes never cross. The colon is a thick & rubbery barrier. Yep with yep and nope with nope.

As you die you conclude 1*20*10*95*.01 : 100*50*1*1*.001 = 190 : 5 odds that a bear is eating you.

Kicks open the door

Alright, here's the current state of affairs:

Premise: Bayes Theorem is held up as the most important part of rationality. ACX has the tagline "P(A|B) = [P(A)P(B|A)]/P(B), all the rest is commentary." Yudkowsky mentions it approximately a million times in the Sequences.
Premise: The average rationalist cannot use Bayes theorem. No, I will be stronger and more specific: when I ask a room full of people at a LessWrong meetup whether they can write the formula for Bayes Theorem on a piece of paper, less than half of them can.
Conclusion: Less than half of the rationalist community understands the most important part of rationality.

Or in other words, we suck. Lest anyone think I'm merely throwing stones, I screwed up Bayes the first time I tried to use it in public. I would not bet a lot on me getting any particular problem right. I suck too.

This version though? This I think most people could remember. I can do this version in my head. I've read a half-dozen explainers for Bayes, some with very nice pictures. This beats all of them, and it's in less than two hundred words! Maybe this is a case of Writing A Thousand Roads To Rome where this version happened to click with me but it's fundamentally just as good as many other versions. I suspect this is a simpler formulation.

Either someone needs to point out where this math is wrong, or I'm just going to use this version for myself and for explaining it to others. A much simpler version of the only non-commentary part of rationality seems a worthy use of Best of LessWrong space to me.

2abstractapplic9mo

Nitpick: I think that second sentence is actually weaker-and-more-specific. I'm very confident I can do a Bayesian update right, I not infrequently use Bayes in my dayjob, I once made a videogame about Bayesian reasoning . . . and if you asked me to write the formula without checking Wikipedia I'd have to spend a minute or two deriving it from first principles. I suspect at least a few people are in a similar boat.

If it's just about remembering the formula, would it be helpful to point out that "the fractions on the right simplifies"? If I write P(B|A)=P(A|B)P(B)/P(A) and just look at the symbols (A|B)B/A you can see it as a fraction that reduces to 1.

The next step would be to replace B and A with T and D for Theory and Data (or H for Hypothesis if you want to be fancy).

From someone who cannot use Bayes theorem in real life... probably.

3goldfine9mo

I'm 13 and I consider myself to have a sufficient understanding of Bayes, or at least I'd be able to write it out and use it in basic situations. This community seems to be filled of pretty smart people, I haven't been to enough events to make a sustained argument on this. I find this guide to be even more confusing than learning the formula itself, but maybe that's just my perception.

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