In Bayesian statistics, one's prior beliefs about underlying model parameters
are revised with the information content of observed data from which, using
Bayes' rule, a posterior belief is obtained. A non-trivial example taken from
the isospin analysis of B-->PP (P = pi or rho) decays in heavy-flavor physics
is chosen to illustrate the effect of the naive "objective" choice of flat
priors in a multi-dimensional parameter space in presence of mirror solutions.
It is demonstrated that the posterior distribution for the parameter of
interest, the phase alpha, strongly depends on the choice of the
parameterization in which the priors are uniform, and on the validity range in
which the (un-normalizable) priors are truncated. We prove that the most
probable values found by the Bayesian treatment do not coincide with the
explicit analytical solution, in contrast to the frequentist approach. It is
also shown in the appendix that the alpha-->0 limit cannot be consistently
treated in the Bayesian paradigm, because the latter violates the physical
symmetries of the problem.Comment: 17 pages, 10 figure