Thasvaddef comments on 2012 Survey Results - Less Wrong

80 Post author: Yvain 07 December 2012 09:04PM

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Comment author: Thasvaddef 09 January 2013 03:23:43PM 1 point [-]

If you choose maths as one of your A-levels, there's a good chance you will cover stats 1 which includes the formula for Bayes' Theorem and how to apply it to calculate medical test false positives/false negatives (and equivalent problems). However it isn't named and the significance to science/rationality is not explained, so it's just seen as "one more formula to learn".

Comment author: Larks 09 January 2013 04:01:49PM 1 point [-]

Offhand, 1/2 young people do A levels, 1/4 of those do maths, and 2/3 of those do stats, giving us 1/12 of young people. I don't think any of these numbers are off by enough to push the fraction over 25%

Comment author: Peterdjones 09 January 2013 03:25:51PM -1 points [-]

the significance to science/rationality is not explained,

Maybe you guys could solve that problem by publishing some results demonstrating its exteme significance

Comment author: DaFranker 09 January 2013 03:45:53PM *  4 points [-]

As far as I know, it's been formally demonstrated to be the absolutely mathematically-optimal method of achieving maximal hypothesis accuracy in an environment with obscured, limited or unreliable information.

That's basically saying: "There is no possible way to do better than this using mathematics, and as far as we know there doesn't yet exist anything more powerful than mathematics."

What more could you want? A theorem proving that any optimal decision theory must necessarily use Bayesian updating? ETA: It has been pointed out that there already exists such a theorem. I could've found that out by looking it up. Oops.

Comment author: [deleted] 10 January 2013 01:56:22PM *  3 points [-]

What more could you want? A theorem proving that any optimal decision theory must necessarily use Bayesian updating?

There already is such a theorem. From Wikipedia:

A decision-theoretic justification of the use of Bayesian inference was given by Abraham Wald, who proved that every Bayesian procedure is admissible. Conversely, every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.

Comment author: pengvado 10 January 2013 11:50:31PM 2 points [-]

As far as I can tell from wikipedia's description of admissibility, it makes the same assumptions as CDT: That the outcome depends only on your action and the state of the environment, and not on any other properties of your algorithm. This assumption fails in multi-player games.

So your quote actually means: If you're going to use CDT then Bayes is the optimal way to derive your probabilities.

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