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Lumifer comments on Open thread, Mar. 2 - Mar. 8, 2015 - Less Wrong Discussion

4 Post author: MrMind 02 March 2015 08:19AM

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Comment author: Lumifer 02 March 2015 05:57:03PM 2 points [-]

the problem seems to be using expected values, which is highly distorted by even a single outlier ... Why not "median expected utility"?

This is a common problem which is handled by robust statistics. Means, while efficient, are notably not robust. The median is a robust alternative from the class of L-estimators (L is for Linear), but a popular alternative for location estimates nowadays is something from the class of M-estimators (M is for Maximum Likelihood).

Comment author: Houshalter 02 March 2015 07:15:44PM 0 points [-]

Maximum Likelihood doesn't really lead to desirable behavior when the number of possibilities is very large. E.g. i roll a dice with a 2 and a 3 give you a dollar, and unrelated but horrible things happen on any other number.

Comment author: Lumifer 02 March 2015 07:29:26PM 0 points [-]

Huh?

Comment author: Houshalter 02 March 2015 07:35:47PM 0 points [-]

Maximum likelihood means taking the outcome with the highest probability relative to everything else, correct? This isn't really desirable since the outcome with the highest probability, might still have very low absolute probability.

Comment author: Lumifer 02 March 2015 07:41:58PM *  1 point [-]

Maximum likelihood means taking the outcome with the highest probability relative to everything else, correct?

No, not at all, what you are talking about is called the mode of the distribution.

Why don't you look at the links in my post?

Comment author: Houshalter 02 March 2015 08:00:17PM 1 point [-]

a maximum-likelihood estimate is often defined to be a zero of the derivative of the likelihood function with respect to the parameter

And the equation.

I don't see how it's different than the mode. Even the graphs show it as being the same: 1 2.

Comment author: Lumifer 02 March 2015 08:10:25PM 1 point [-]

I don't see how it's different than the mode

Think about a bimodal distribution, for example. But in any case, we're talking about M-estimates, weren't we?

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