  A microscopic nuclear matter formalism with explicit chiral symmetry based on
the Nambu Jona-Lasinio model is considered to describe nuclear matter. To
reproduce nuclear matter properties adequately at the saturation density,
four-point and eight-point interactions are introduced. Within a Bayesian
inference approach, the parameters of the model are determined by imposing
nuclear matter, both experimental and from {\it ab-initio} calculations, and
neutron star observational constraints. Nuclear matter properties are well
reproduced with an effective mass of 0.75 to 0.8 nucleon mass at the saturation
density. At 90% confidence level, the radius of a $1.4 ~\rm M_\odot$ star
varies between 11.48 km and 13.20 km, masses as large as $\sim 2.2 ~\rm
M_\odot$ are predicted and the radius of a 2 M$_\odot$ star is above 10.5 km.
High-density perturbative QCD (pQCD) results exclude equations of state that
predict larger maximum masses and radii. The speed of sound increases
monotonically with density and reaches values as large as
$\sqrt{0.7}c$-$\sqrt{0.8}c$ in the center of massive stars. Several properties
such as the polytropic index or the renormalized trace anomaly, that have been
proposed to identify the deconfined phase transition, are analyzed.
Interestingly, the radius of the obtained posterior that also meets pQCD
constraints aligns closely with the mass-radius measurement of the recent PSR
J0437-4715, which contrasts with other relativistic mean field model results.
