Comment author:potato
27 July 2011 06:55:26PM
2 points
[-]

Please elaborate EY.

I think it would be a wonderfully clarifying post if you were to write a technical derivation of frequentest probability from the "probability in the mind" concept o Bayesian probability. If you decide to do this, or anyone knows where i could find such a text, please let me know.

related question:

Is there an algebra that describes the frequentest interpretation of probability? If so, where is it isomorphic to Bayesian algebra and where does it diverge? I want to know if the dispute has to do just with the semantic interpretation of 'P(a)', or if the 'P(a)' of the frequentest actually behaves differently than the Bayesian 'P(a)' syntactically.

Comment author:JGWeissman
27 July 2011 07:15:19PM
*
3 points
[-]

If a well calibrated rationalist, for a given probability p, independantly believes N different things each with probability p, then you can expect about p*N of those beliefs to be correct.

Jayne's book shows how frequencies are estimated in his system, and somewhere, maybe his book, he compares and contrasts his ideas with frequentists and Kolmogorov. In fact, he expends great effort in contrasting his views to those of frequentists.

## Comments (186)

OldYou can derive frequentist probabilities from subjective probabilities but not the other way around.

Please elaborate EY.

I think it would be a wonderfully clarifying post if you were to write a technical derivation of frequentest probability from the "probability in the mind" concept o Bayesian probability. If you decide to do this, or anyone knows where i could find such a text, please let me know.

related question:

Is there an algebra that describes the frequentest interpretation of probability? If so, where is it isomorphic to Bayesian algebra and where does it diverge? I want to know if the dispute has to do just with the semantic interpretation of 'P(a)', or if the 'P(a)' of the frequentest actually behaves differently than the Bayesian 'P(a)' syntactically.

*3 points [-]If a well calibrated rationalist, for a given probability p, independantly believes N different things each with probability p, then you can expect about p*N of those beliefs to be correct.

See the discussion of calibration in the Technical Explanation.

Jayne's book shows how frequencies are estimated in his system, and somewhere, maybe his book, he compares and contrasts his ideas with frequentists and Kolmogorov. In fact, he expends great effort in contrasting his views to those of frequentists.