  Efficiency corrected single ratios of neutron and proton spectra in central
$^{112}$Sn+$^{112}$Sn and $^{124}$Sn+$^{124}$Sn collisions at 120 MeV/u are
combined with double ratios to provide constraints on the density and momentum
dependencies of the isovector mean-field potential. Bayesian analyses of these
data reveal that the isoscalar and isovector nucleon effective masses, $m_s^* -
m_v^*$ are strongly correlated. The linear correlation observed in $m_s^* -
m_v^*$ yields a nearly independent constraint on the effective mass splitting
$\Delta m_{np}^*= (m_n^*-m_p^*)/m_N = -0.05_{-0.09}^{+0.09}\delta$. The
correlated constraint on the standard symmetry energy, $S_0$ and the slope, $L$
at saturation density yields the values of symmetry energy
$S(\rho_s)=16.8_{-1.2}^{+1.2}$ MeV at a sensitive density of $\rho_s/\rho_0 =
0.43_{-0.05}^{+0.05}$.
