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shminux comments on What is the best paper explaining the superiority of Bayesianism over frequentism? - Less Wrong Discussion

-1 Post author: Meni_Rosenfeld 01 January 2013 08:58PM

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Comment author: shminux 02 January 2013 07:52:10AM 0 points [-]

Note that instrumentally, there is little difference, according to Jaynes himself:

For example our system of probability could hardly, in style, philosophy, and purpose, be more different from that of Kolmogorov.

[...]

Yet when all is said and done we find ourselves, to our own surprise, in agreement with Kolmogorov and in disagreement with his critics, on nearly all technical issues.

Comment author: Oscar_Cunningham 02 January 2013 02:42:50PM *  6 points [-]

By "technical issues" I think that Jaynes means the measure theory basis of probability, not the everyday applications of statistics.

EDIT: And he's comparing Kolmogorov's definition of probability (which starts with a set of possible outcomes and then treats events as subsets) to his own view (IIRC he thinks you can calculate with events directly and need no underlying set). He's not comparing Frequentism and Bayesianism.

Comment author: shminux 02 January 2013 07:14:55PM *  1 point [-]

He's not comparing Frequentism and Bayesianism.

Not directly, no. But you would be hard-pressed to call Kolmogorov a Bayesian, at least when discussing axiomatic probability theory and not complexity/minimum description length, given that he never talked about "the degree of belief", only about axioms of probability. Yet his results match those of Jaynes (the other way around, really).

Further discussion on Kolmogorov and Bayes is in this paper posted on Luke's old blog. For example:

For an agent to be perfectly rational, her degrees of belief must obey the axioms of probability theory.

Comment author: [deleted] 02 January 2013 01:08:37PM 0 points [-]

For those curious, these quotes come from Probability Theory: The Logic of Science, p.xxi under the header "Foundations."

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