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shminux comments on Rationality Quotes January 2013 - Less Wrong
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For coin bias estimate, as for most other things, the self-consistent updating procedure follows maximum likelihood.
Max liklihood tells you which is most likely, which is mostly meaningless without further assumptions. For example, if you wanted to bet on what the next flip would be, a max liklihood method won't give you the right probability.
Yes.
OTOH, the expected value of the beta distribution with parameters a and b happens to equal the mode of the beta distribution with parameters a - 1 and b - 1, so maximum likelihood does give the right answer (i.e. the expected value of the posterior) if you start from the improper prior B(0, 0).
(IIRC, the same thing happens with other types of distributions, if you pick the ‘right’ improper prior (i.e. the one Jaynes argues for in conditions of total ignorance for totally unrelated reasons) for each. I wonder if this has some particular relevance.)