  The neutron skin thickness $\Delta r_{np}$ in heavy nuclei has been known as
one of the most sensitive terrestrial probes of the nuclear symmetry energy
around $\frac{2}{3}$ of the saturation density $\rho_0$ of nuclear matter.
Existing neutron skin data mostly from hadronic observables suffer from large
uncertainties and their extraction from experiments are often strongly model
dependent. While waiting eagerly for the promised model-independent and
high-precision neutron skin data for $^{208}$Pb and $^{48}$Ca from the
parity-violating electron scattering experiments (PREX-II and CREX at JLab as
well as MREX at MESA), within the Bayesian statistical framework using the
Skyrme-Hartree-Fock model we infer the posterior probability distribution
functions (PDFs) of the slope parameter $L$ of the nuclear symmetry energy at
$\rho_0$ from imagined $\Delta r_{np}(^{208}$Pb$)=0.15$, 0.20, and 0.30 fm as
well as $\Delta r_{np}(^{48}$Ca$)=0.12$, 0.15, and 0.25 fm, with different
$1\sigma$ error bars. The results are compared with the PDFs of $L$ inferred
using the same approach from the available $\Delta r_{np}$ data for Sn isotopes
from hadronic probes. They are also compared with results from a recent
Bayesian analysis of the radius and tidal deformability data of canonical
neutron stars from GW170817 and NICER. The neutron skin data for Sn isotopes
gives $L=45.5^{+26.5}_{-21.6}$ MeV surrounding its mean value or
$L=53.4^{+18.6}_{-29.5}$ MeV surrounding its maximum {\it a posteriori} value,
respectively, with the latter smaller than but consistent with the
$L=66_{-20}^{+12}$ MeV from the neutron star data within their 68\% confidence
intervals. In order to provide additionally useful information on $L$ extracted
from the $\Delta r_{np}$ of Sn isotopes, the experimental error bar of $\Delta
r_{np}(^{208}$Pb) should be at least smaller than 0.06 fm aimed by some current
experiments.
