DaFranker comments on 2012 Survey Results - Less Wrong
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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.
There already is such a theorem. From Wikipedia:
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.