[gpsx]

I enjoyed reading the chapter but I didn't have enough time to put into it to understand all his derivations as well as I would like. So I may be incorrect here but I don't think he is proving the gaussian distribution is correct, just that it is a good (or the best) one to use.

Does someone have a dart board? It would be nice to take a look at some real data. Maybe 20 throws? Or 200?

I don't think the results will fit a gaussian particularly well. I think there will more darts at large distances than expected. For that matter I would guess, if there is enough data, that the mean would be slightly below the maximal likelihood (as in closer to the floor).

[BenoitEssiambre]

Jaynes usually tries to move away from an interpretation of probability distributions being "correct" as in representing a fact about the world, and towards a definition that is more about a state of knowledge and uncertainty about the world. Distributions are a property of a model or of a knowledgeable agent, not of an object or situation. See Chapter 10: "Physics of 'Random Experiments'". However the two definitions sorta become indistinguishable when you are dealing with experiments that are repeated enough times.