  Within the Bayesian statistical framework we infer the incompressibility
$K_0$, skewness $J_0$ and kurtosis $Z_0$ parameters of symmetric nuclear matter
(SNM) at its saturation density $\rho_0$ using the constraining bands on the
pressure in cold SNM in the density range of 1.3$\rho_0$ to 4.5$\rho_0$ from
transport model analyses of kaon production and nuclear collective flow in
relativistic heavy-ion collisions. As the default option assuming the $K_0$,
$J_0$ and $Z_0$ have Gaussian prior probability distribution functions (PDFs)
with the means and variances of $235\pm 30$, $-200\pm 200$ and $-146\pm 1728$
MeV, their posterior most probable values are narrowed down to
192$^{+12}_{-16}$ MeV, -180$^{+100}_{-110}$ MeV and 200$^{+250}_{-250}$ at 68\%
confidence level, respectively. The results are largely independent of the
prior PDFs of $J_0$ and $Z_0$ used. However, if one adopts the strong belief
that the incompressibility $K_0$ has a uniform prior PDF within its absolute
boundary of 220-260 MeV as one can find easily in the literature, the posterior
most probable values of $K_0$, $J_0$ and $Z_0$ shift to $K_0=220^{+6}_{-0}$
MeV, $J_0=-390^{+60}_{-70}$ MeV and $Z_0=600^{+200}_{-200}$ MeV, respectively.
While the posterior PDFs of the SNM EOS parameters depend somewhat on the prior
PDF of $K_0$ used, the results from using different prior PDFs are
qualitatively consistent. The uncertainties of all three parameters are
significantly reduced especially for the $J_0$ and $Z_0$ parameters compared to
their current values.
