It appears to me that this paper merely
restates Bayesian decision theory and then
asks the reader to interpret the prior as
referring to an ensemble instead of viewing
it as a subjective prior. Other than this,
I don't see much else going on here.
1. The first sentence of the abstract
is mysterious. It makes it seem that there
is no frequentist theory of decision making.
There is of course a very well developed
frequentist decision theory and it is by far
the dominant theory in statistics.
Similarly, the second sentence
promises a unification of hypothesis testing
and estimation but such a unification already
exists in the current decision theory.
2. Continuing on this theme,
on page 3 you say: ``In all cases the
classical theory of estimation appears to have
lost its frequentist foundations.''
Again I am mystified. Minimax decision theory
is alive and well and is purely frequentist
in nature. The modern theory of optimal nonparametric
function estimation is completely dominated by
minimax fequentist decision theory, for example.
3. The definition of the likelihood in section 6
appears to be the usual Radon-Nikodym derivative.
4. Typo in ``continuos'' after Theorem 1.
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