>>>
the one case where I have allowed that physical probabilities *might*
exist is in QM. But even this case is in dispute among physicists,
many of whom do not accept the Copenhagen interpretation of QM.
>>>
Uh, no it isn't. My PhD and original post-graduate work was in
theoretical physics. Not once did I encounter a practicing (!)
physicist who seriously considered the degree of belief interpretation
of probability as applying to quantum phenomena. (For all of the
brilliance of his contributions to science, Jaynes hardly qualifies
anymore as a practicing physicist.) There is no dispute that the
probabilities in quantum mechanics are objective. Especially in light
of Bell's theorems (which you should read, by the way).
Moreover, a good 99.99% of physicists are perfectly happy with the
Copenhagen interpretation, and proponents of the other interpretations
(many worlds, etc.) would simply respond with astonishment to the idea
that probabilities aren't objective - where the interpretations
diverge is in their assessment of the source of the probabilities, not
in the physical nature of those probabilities.
>>>
even if QM does in fact exhibit physical probabilities, this would
be of little practical importance in most statistical problems, in
which QM effects are negligible, and the physics of the situation is,
to a high degree of accuracy, entirely deterministic.
>>>
You should be more careful before you speak, my friend. You are right
now reading this on a transistor-based computer, I assume? Do you
happen to know what field of physics is responsible for the phenomena
behind transistors? You are also reading this visually I presume - do
you happen to know what field of physics is responsible for the
interplay between photons and the rods and cones in your retina?
In any case, the important point is not whether the universe is based
on objective probabilities, but that it *could be* and still be fully
self-consistent mathematically. I.e., there is NO logical necessity to
the degree of belief interprtation. The universe does not demand
it. Rather it is (at most) a viewpoint imposed on the universe, by
humans.
>>>
Perhaps you are confusing maximum a posteriori (MAP) methods with a full
Bayesian analysis.
>>>
Um, in point of fact, I have several published papers explicating the
dangers of using MAP rather than hierarchical Bayesian methods. I
refer you my ftp site, ftp.santafe.edu/pub/dhw_ftp.
David Wolpert
NASA Ames Research Center