alex_zag_al comments on Putting in the Numbers - Less Wrong

8 Post author: Manfred 30 January 2014 06:41AM

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Comment author: Vaniver 02 February 2014 07:58:19AM 0 points [-]

I think it's pretty clear you're talking about different things here.

I thought so too, which is why I asked him what he thought a delta function in the distribution space meant.

One of them, (1/3, 1/3, 1/3), represents fairness, and is just one among many possibilities.

Right; but putting a delta function there means you're infinitely certain that's what it is, because you give probability 0 to all other possibilities.

It could equally well represent being certain that it's biased to land on only one side every time, but you have no idea which side.

Knowing that the die is completely biased, but not which side it is biased towards, would be represented by three delta functions, at (1,0,0), (0,1,0), and (0,0,1), each with a coefficient of (1/3). This is very different from the uniform case and the delta at (1/3,1/3,1/3) case, as you can see by calculating the posterior distribution for observing that the die rolled a 1.

Comment author: alex_zag_al 03 February 2014 05:24:31AM 0 points [-]

okay, and you were just trying to make sure that Manfred knows that all this probability-of-distributions speech you're speaking isn't, as he seems to think, about the degree-of-belief-in-my-current-state-of-ignorance distribution for the first roll. Gotcha.