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Using the recent model-independent determination of the charge-weak formfactor difference $\Delta F_{\rm CW}$ in $^{48}$Ca and $^{208}$Pb by the CREXand PREX-2 collaborations together with some well-determined properties ofdoubly magic nuclei, we perform Bayesian inference of the symmetry energy$E_{\rm sym}(\rho)$ and the neutron skin thickness $\Delta r_{\rm np}$ of$^{48}$Ca and $^{208}$Pb within the Skyrme energy density functional (EDF). Wefind the inferred $E_{\rm sym}(\rho)$ and $\Delta r_{\rm np}$ separately fromCREX and PREX-2 are compatible with each other at $90\%$ C.L., although theyare inconsistent at $68.3\%$ C.L. with CREX (PREX-2) favoring a very soft(stiff) $E_{\rm sym}(\rho)$ and rather small (large) $\Delta r_{\rm np}$. Bycombining the CREX and PREX-2 data, we obtain a soft symmetry energy aroundsaturation density $\rho_0$ and thinner $\Delta r_{\rm np}$ of $^{48}$Ca and$^{208}$Pb, which are found to be closer to the corresponding results from CREXalone, implying the PREX-2 is less effective to constrain the $E_{\rmsym}(\rho)$ and $\Delta r_{\rm np}$ due to its lower precision of $\DeltaF_{\rm CW}$. Furthermore, we find the Skyrme EDF results inferred by combiningthe CREX and PREX-2 data nicely agree with the measured dipole polarizabilities$\alpha_D$ in $^{48}$Ca and $^{208}$Pb as well as the neutron matter equationof state from microscopic calculations. The implications of the inferred soft$E_{\rm sym}(\rho)$ around $\rho_0$ are discussed.

Bayesian Inference of the Symmetry Energy and the Neutron Skin in $^{48}$Ca and $^{208}$Pb from CREX and PREX-2