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owencb comments on What Bayesianism taught me - Less Wrong

62 Post author: Tyrrell_McAllister 12 August 2013 06:59AM

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Comment author: owencb 12 August 2013 10:10:13AM 8 points [-]

You cannot expect that future evidence will sway you in a particular direction. "For every expectation of evidence, there is an equal and opposite expectation of counterevidence."

Well ... you can have an expected direction, just not if you account for magnitudes.

For example if I'm estimating the bias on a weighted die, and so far I've seen 2/10 rolls give 6's, if I roll again I expect most of the time to get a non-6 and revise down my estimate of the probability of a 6; however on the occasions when I do roll a 6 I will revise up my estimate by a larger amount.

Sometimes it's useful to have this distinction.

Comment author: Tyrrell_McAllister 13 August 2013 10:18:49PM *  4 points [-]

Well ... you can have an expected direction, just not if you account for magnitudes.

Yes, on reflection it was a poor choice of words. I was using "expect" in that sense according to which one expects a parameter to equal zero if the expected value of that parameter is zero. However, while "expected value" has a well-established technical meaning, "expect" alone may not. It is certainly reasonably natural to read what I wrote as meaning "my opinion is equally likely to be swayed in either direction," which, as you point out, is incorrect. I've added a footnote to clarify my meaning.

Comment author: [deleted] 13 August 2013 10:22:38AM 2 points [-]

That's not what “expected” means in these contexts.

Comment author: owencb 13 August 2013 10:44:47AM 1 point [-]

I'm well aware of this. My point was that there's a subtle difference between "direction of the expectation" and "expected direction".

The expectation of what you'll think after new evidence has to be the same as you think now, so can't point in any particular direction. However "direction" is a binary variable (which you might well care about) and this can have a particular non-zero expectation.

I'm being slightly ambiguous as to whether "expected" in "expected direction" is meant to be the technical sense or the common English one. It works fine for either, but to interpret it as an expectation you have to choose an embedding of your binary variable in a continuous space, which I was avoiding because it didn't seem to add much to the discussion.

Comment author: RyanCarey 15 August 2013 12:37:00PM 1 point [-]

Maybe 'on expectation' is clearer?