We study a relativistic Hartree–Fock Lagrangian model which considers confinement, chiral symmetry breaking, nucleon form factor and short range correlations. The chiral potential originally based on the linear sigma model is compared to an improved potential generated by the Nambu–Jona–Lasino (NJL) model for quark interaction. Our model is also anchored in fundamental hadronic properties predicted by Lattice-QCD calculations and a few nuclear empirical properties. We explore in a Bayesian approach the role of the saturation density, the energy per particle and the incompressibility modulus for the model selection. We find that most of our models could not reproduce these empirical quantities, unless a phenomenological “missing” energy is added. The properties of this “missing” energy are therefore inferred from our Bayesian analysis and we obtain that it shall be attractive. Finally we analyse the origin of the break down density in relativistic approaches and we relate it to the properties of the scalar potential.