  Excitations of colliding nuclei during a nuclear reaction considerably affect
fusion cross sections at energies around the Coulomb barrier. It has been
demonstrated that such channel coupling effects can be represented in terms of
a distribution of multiple fusion barriers. We here apply a Bayesian approach
to analyze the so called fusion barrier distributions. This method determines
simultaneously the barrier parameters and the number of barriers. We
particularly investigate the $^{16}$O+$^{144}$Sm and $^{16}$O+$^{154}$Sm
systems in order to demonstrate the effectiveness of the method. The present
analysis indicates that the fusion barrier distribution for the former system
is most consistent with three fusion barriers, even though the experimental
data show only two distinct peaks.
