  For a single degree of freedom confined mechanical system with given energy,
we know that the motion is always periodic and action-angle variables are
convenient choice as conjugate phase-space variables. We construct action-angle
coherent states in view to provide a quantization scheme that yields precisely
a given observed energy spectrum ${E_n}$ for such a system. This construction
is based on a Bayesian approach: each family corresponds to a choice of
probability distributions such that the classical energy averaged with respect
to this probability distribution is precisely $E_n$ up to a constant shift. The
formalism is viewed as a natural extension of the Bohr-Sommerfeld rule and an
alternative to the canonical quantization. In particular, it also yields a
satisfactory angle operator as a bounded self-adjoint operator.
