[Link] Better results by changing Bayes’ theorem

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If it ever turns out that Bayes fails - receives systematically lower rewards on some problem, relative to a superior alternative, in virtue of its mere decisions - then Bayes has to go out the window.

-- Eliezer Yudkowsky, Newcomb's Problem and Regret of Rationality

Don't worry, we don't have to abandon Bayes’ theorem yet. But changing it slightly seems to be the winning Way given certain circumstances. See below:

In Peter Norvig’s talk The Unreasonable Effectiveness of Data, starting at 37:42, he describes a translation algorithm based on Bayes’ theorem. Pick the English word that has the highest posterior probability as the translation. No surprise here. Then at 38:16 he says something curious.

So this is all nice and theoretical and pure, but as well as being mathematically inclined, we are also realists. So we experimented some, and we found out that when you raise that first factor [in Bayes' theorem] to the 1.5 power, you get a better result.

In other words, if we change Bayes’ theorem (!) we get a better result. He goes on to explain

Link: johndcook.com/blog/2012/03/09/monkeying-with-bayes-theorem/

Peter Norvig - The Unreasonable Effectiveness of Data

If it ever turns out that Bayes fails - receives systematically lower rewards on some problem, relative to a superior alternative, in virtue of its mere decisions - then Bayes has to go out the window.

-- Eliezer Yudkowsky, Newcomb's Problem and Regret of Rationality

Don't worry, we don't have to abandon Bayes’ theorem yet. But changing it slightly seems to be the winning Way given certain circumstances. See below:

In Peter Norvig’s talk The Unreasonable Effectiveness of Data, starting at 37:42, he describes a translation algorithm based on Bayes’ theorem. Pick the English word that has the highest posterior probability as the translation. No surprise here. Then at 38:16 he says something curious.

So this is all nice and theoretical and pure, but as well as being mathematically inclined, we are also realists. So we experimented some, and we found out that when you raise that first factor [in Bayes' theorem] to the 1.5 power, you get a better result.

In other words, if we change Bayes’ theorem (!) we get a better result. He goes on to explain

Link: johndcook.com/blog/2012/03/09/monkeying-with-bayes-theorem/

Peter Norvig - The Unreasonable Effectiveness of Data

You could have got positive karma here too if you didn't present it incorrectly as a challenge to...

As a "challenge to"? I incorrectly assumed that it is a good example in support of something Eliezer said, namely that you choose the winning way and not your favorite heuristic.

As a "challenge to"? I incorrectly assumed that it is a good example in support of something Eliezer said, namely that you choose the winning way and not your favorite heuristic.

I suppose it would actually be a support of Eliezer's 'choose the winning way' theme while simultaneously undermining everything he said about probability theory.

Either way, it is the incorrect framing not just the location that dampened reception here.