  In reply to hep-ph/0701204 we demonstrate why the arguments made therein do
not address the criticism exposed in hep-ph/0607246 on the fundamental
shortcomings of the Bayesian approach when it comes to the extraction of
parameters of Nature from experimental data. As for the isospin analysis and
the CKM angle alpha it is shown that the use of uniform priors for the observed
quantities in the Explicit Solution parametrization is equivalent to a
frequentist construction resulting from a change of variables, and thus relies
neither on prior PDFs nor on Bayes' theorem. This procedure provides in this
particular case results that are similar to the Confidence Level approach, but
the treatment of mirror solutions remains incorrect and it is far from being
general. In a second part it is shown that important differences subsist
between the Bayesian and frequentist approaches, when following the proposal of
hep-ph/0701204 and inserting additional information on the hadronic amplitudes
beyond isospin invariance. In particular the frequentist result preserves the
exact degeneracy that is expected from the remaining symmetries of the problem
while the Bayesian procedure does not. Moreover, in the Bayesian approach
reducing inference to the 68% or 95% credible interval is a misconception of
the meaning of the posterior PDF, which in turn implies that the significant
dependence of the latter to the chosen parametrization cannot be viewed as a
minor effect, contrary to the claim in hep-ph/0701204.
