  Bayesian analyses on both isoscalar and isovector nuclear interaction
parameters are carried out based on the Korea-IBS-Daegu-SKKU (KIDS) model under
the constraints of nuclear structure data of $^{208}$Pb and $^{120}$Sn. Under
the constraint of the neutron-skin thickness, it is found that incorporating
the curvature parameter $K_{sym}$ of nuclear symmetry energy as an independent
variable significantly broadens the posterior probability distribution function
(PDF) of the slope parameter $L$, and affects the related correlations.
Typically, the anticorrelation between $L$ and the symmetry energy at
saturation density disappears, while a positive correlation between $L$ and
$K_{sym}$ is observed. Under the constraint of the isoscalar giant monopole
resonance (ISGMR), incorporating the skewness parameter as an independent
variable also significantly broadens the posterior PDF of the nuclear matter
incompressibility $K_0$. Even with the broad uncertainties of higher-order
parameters of the equation of state (EOS), robust constraints of $L<90$ MeV and
$K_0<270$ MeV are obtained. Our study quantifies the consistency between the
constraints on $L$ from the neutron-skin data of PREXII and isovector giant
dipole resonance (IVGDR) data, and the constraints on $K_0$ from the data of
ISGMR in $^{208}$Pb and $^{120}$Sn.
