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MrMind comments on Some thoughts on meta-probabilties - Less Wrong Discussion

0 Post author: iarwain1 21 September 2015 05:23PM

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Comment author: MrMind 22 September 2015 09:32:49AM *  3 points [-]

If I remember correctly, Jaynes discusses this in Probability Theory

He does, it's in the chapter about Ap distribution, which are basically meta-probability, or better, Ap is the probability assigned to receive a future evidence that will put the probability of A at p. Formally P(A|Ap) = p.
From this you can show that P(A) is the expected value of the Ap distribution.

Comment author: buybuydandavis 23 September 2015 02:37:24AM 2 points [-]

The Chapter is "Inner and Outer Robots", available here:

http://www-biba.inrialpes.fr/Jaynes/cc18i.pdf

The outer robot, thinking about the real world, uses Aristotelian propositions referring to that world. The inner robot, thinking about the activities of the outer robot, uses propositions that are not Aristotelian in reference to the outer world; but they are still Aristotelian in its context, in reference to the thinking of the outer robot; so of course the same rules of probability theory will apply to them. The term `probability of a probability' misses the point, since the two probabilities are at different levels.

This always seemed like a real promising idea to me. Alas, I have a day job, and it isn't as a Prof.

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