  The equations of state (EoSs) governing neutron star (NS) matter obtained for
both non-relativistic and relativistic mean-field models are systematically
confronted with a diverse set of terrestrial data and astrophysical
observations within the Bayesian framework. The terrestrial data, spans from
bulk properties of finite nuclei to the heavy-ion collisions, constrain the
symmetric nuclear matter EoS and the symmetry energy up to twice the saturation
density ($\rho_0$= 0.16 fm$^{-3}$). The astrophysical observations encompass
the NS radius, the tidal deformability, and the lower bound on maximum mass.
Three distinct posterior distributions of EoSs are generated by gradually
updating the priors with different constraints: (i) only the maximum NS mass,
(ii) incorporating additional terrestrial data, (iii) combining both the
terrestrial data and astrophysical observations. These EoS distributions are
then compared using the Kullback-Liebler divergence which highlights the
significant constraints imposed on the EoSs by the currently available lower
bound of NS maximum mass and terrestrial data. The remaining astrophysical
observations marginally refine the EoS within the density range $\sim$
2-3$\rho_0$. It is observed that the relativistic mean field model yields
stiffer EoS around the saturation density, but predict smaller values of the
speed of sound and proton fraction in the interior of massive stars.
