alex_zag_al comments on Putting in the Numbers - Less Wrong
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I thought so too, which is why I asked him what he thought a delta function in the distribution space meant.
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.
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.
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.