  We investigate the capabilities of the Nambu--Jona-Lasinio model to describe
and reproduce fundamental vacuum properties of Quantum Chromodynamics, notably
the hadronic spectrum. Mesons are described as quark-antiquark bound states at
the level of the random phase approximation of the Bethe-Salpeter equation,
while baryons are characterized as quark-diquark bound states within the static
approximation of the Faddeev equation. Within a Bayesian framework, we
constrain the model by phenomenologically known quantities and study the
implications on its parameters and predictions in vacuum, as well as the
correlations between the two. We find that within our framework, the vacuum
masses of mesons and baryons can be reasonably well reproduced. Scalar diquarks
need to be significantly bound in order to correctly reproduce the masses of
the baryon octet, therefore enforcing values of the scalar diquark coupling
larger than what is suggested by the canonical Fierz values. These findings
could have important implications on the phenomenology of strongly-interacting
matter at high temperature and density as well as of compact star physics.
