Bayesian analysis of the neutron star equation of state and model comparison: Insights from PSR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi mathvariant="normal">J</mml:mi> <mml:mn>0437</mml:mn> <mml:m

We perform a comprehensive Bayesian analysis to constrain the neutron star (NS) equation of state (EoS) using a wide range of terrestrial and astrophysical data. The terrestrial inputs include quantities related to symmetric nuclear matter (SNM) and symmetry energy up to two times saturation density (${\ensuremath{\rho}}_{0}\ensuremath{\simeq}0.16\text{ }\text{ }{\mathrm{fm}}^{\ensuremath{-}3}$), derived from finite nuclei and heavy ion collisions (HIC). The astrophysical constraints incorporate NS radii and tidal deformabilities from recent Neutron Star Interior Composition Explorer (NICER) observations and GW170817, respectively. We consider five different EoS models: Taylor, $n/3$, Skyrme, relative mean field, and sound speed (CS), and analyze them by sequentially updating the priors with (i) chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$)-based pure neutron matter, (ii) terrestrial, empirical, and earlier astrophysical data, (iii) case (ii) including NICER radii of PSR $\mathrm{J}0437+4715$ and $\mathrm{J}0614+3329$, (iv) all data combined, and (v) excluding empirical nuclear inputs. We also perform Bayesian model comparison, which favors the Skyrme model under all combined data [scenario (iv)], yielding tight constraints on symmetry energy parameters: ${L}_{0}=56\ifmmode\pm\else\textpm\fi{}3\text{ }\text{ }\mathrm{MeV}$ and ${K}_{\mathrm{sym}0}=\ensuremath{-}132\ifmmode\pm\else\textpm\fi{}15\text{ }\text{ }\mathrm{MeV}$, and also on SNM parameters: ${K}_{0}=265\ifmmode\pm\else\textpm\fi{}12\text{ }\text{ }\mathrm{MeV}$ and ${Q}_{0}=\ensuremath{-}366\ifmmode\pm\else\textpm\fi{}43\text{ }\text{ }\mathrm{MeV}$. The mass-radius and mass--tidal deformability posterior distributions are also well constrained. The radius and tidal deformability of a $1.4{M}_{\ensuremath{\bigodot}}$ neutron star are found to be ${R}_{1.4}=11.85\ifmmode\pm\else\textpm\fi{}0.11\text{ }\text{ }\mathrm{km}$ and ${\mathrm{\ensuremath{\Lambda}}}_{1.4}=354\ifmmode\pm\else\textpm\fi{}25$, respectively.