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The radius $R_{1.4}$ of neutron stars (NSs) with a mass of 1.4 M$_{\odot}$has been extracted consistently in many recent studies in the literature. Usingrepresentative $R_{1.4}$ data, we infer high-density nuclear symmetry energy$E_{\rm{sym}}(\rho)$ and the associated nucleon specific energy $E_0(\rho)$ insymmetric nuclear matter (SNM) within a Bayesian statistical approach using anexplicitly isospin-dependent parametric Equation of State (EOS) for nucleonicmatter. We found that: (1) The available astrophysical data can already improvesignificantly our current knowledge about the EOS in the density range of$\rho_0-2.5\rho_0$. In particular, the symmetry energy at twice the saturationdensity $\rho_0$ of nuclear matter is determined to be$E_{\mathrm{sym}}(2\rho_0)$ =39.2$_{-8.2}^{+12.1}$ MeV at 68\% confidencelevel. (2) A precise measurement of the $R_{1.4}$ alone with a 4\% 1$\sigma$statistical error but no systematic error will not improve much the constraintson the EOS of dense neutron-rich nucleonic matter compared to what we extractedfrom using the available radius data. (3) The $R_{1.4}$ radius data and othergeneral conditions, such as the observed NS maximum mass and causalitycondition introduce strong correlations for the high-order EOS parameters.Consequently, the high-density behavior of $E_{\rm{sym}}(\rho)$ inferreddepends strongly on how the high-density SNM EOS $E_0(\rho)$ is parameterized,and vice versa. (4) The value of the observed maximum NS mass and whether it isused as a sharp cut-off for the minimum maximum mass or through a Gaussiandistribution affect significantly the lower boundaries of both the $E_0(\rho)$and $E_{\rm{sym}}(\rho)$ only at densities higher than about $2.5\rho_0$.

Bayesian Inference of High-density Nuclear Symmetry Energy from Radii of Canonical Neutron Stars