The parametrized equation of state (EOS) of neutron stars is investigated by the Bayesian inference method with various constraints from both nuclear physics and modern astronomical observations, where the energy per particle is expanded as a polynomial function of the density. The expansion coefficients correspond to the properties of symmetric nuclear matter and the density dependence of the symmetry energy. The empirical values of the symmetry energy at subsaturation density and the density of crust-core phase transition are considered to limit the low-density behavior of EOS, i.e., $L_{\mathrm{sym}}$, while the speed of sound of neutron star matter and mass-radius observations of millisecond pulsars PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$ are adopted to eliminate the high-order expansion coefficients, such as $Q_{\mathrm{sat}}$ and $Q_{\mathrm{sym}}$. Finally, our analysis reveals that the skewness coefficient $Q_{\mathrm{sat}}$ of the energy per nucleon in symmetric nuclear matter exhibits the strongest correlation with the speed of sound, constrained to $Q_{\mathrm{sat}}=-69.50_{-31.93}^{+16.52}\mathrm{MeV}$, whose uncertainties are much smaller than those of the experiments of heavy-ion collisions. The symmetry energy parameters are determined as follows: slope $L_{\mathrm{sym}}=34.32_{-11.85}^{+13.66}\mathrm{MeV}$, curvature $K_{\mathrm{sym}}=-58.45_{-89.46}^{+88.47}\mathrm{MeV}$, and skewness $Q_{\mathrm{sym}}=302.28_{-231.89}^{+251.62}\mathrm{MeV}$. Additionally, the radii of canonical ($1.4M_{\odot }$) and massive ($2.0M_{\odot }$) neutron stars are predicted as $R_{1.4}=11.85_{-0.15}^{+0.06}\mathrm{km}$ and $R_{2.0}=11.42_{-0.35}^{+0.23}\mathrm{km}$, respectively, with a maximum mass of $M_{\max }=2.12_{-0.05}^{+0.11}{M}_{\odot }$. The tidal deformability is ${\mathrm{\Lambda }}_{1.4}=303.57_{-45.22}^{+47.95}$ at $1.4M_{\odot }$, which is consistent with the analysis of the GW170817 event. The trace anomaly $\mathrm{\Delta }$ in the high density region increases when the causality of the speed of sound is taken.

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• Nuclear matter in neutron stars