Nuclear Physics Hamiltonians, Inverse Problem And The Related Issue Of Predictive Power

In this paper we formulate and discuss the strategy of constructing theories capable of providing not only the numerical predictions sensu strict but also the distributions of probability that such predictions apply in the predefined physics context. Examples of applications of the presented ideas are illustrated using as a choice the nuclear mean-field theory with two realistic realizations of the underlying Hamiltonians: Phenomenological Woods-Saxon and self-consistent Skyme-Hartree-Fock.