  We apply Bayesian approach to construct a large number of minimally
constrained equations of state (EOSs) and study their correlations with a few
selected properties of a neutron star (NS). Our set of minimal constraints
includes a few basic properties of saturated nuclear matter and low-density
pure neutron matter EOS which is obtained from a precise
next-to-next-to-next-to-leading-order (N$^{3}$LO) calculation in chiral
effective field theory. The tidal deformability and radius of NS with mass $1-2
M_\odot$ are found to be strongly correlated with the pressure of
$\beta$-equilibrated matter at densities higher than the saturation density
($\rho_0 = 0.16$ fm$^{-3}$) in a nearly model-independent manner. These
correlations are employed to parametrize the pressure for $\beta$-equilibrated
matter, around 2$\rho_0$, as a function of neutron star mass and the
corresponding tidal deformability. The maximum mass of neutron star is also
found to be strongly correlated with the pressure of $\beta$-equilibrated
matter at densities $\sim 4.5\rho_0$.
