  In Monte Carlo simulations of lattice field theory with a $\theta$ term, one
confronts the complex weight problem, or the sign problem. This is circumvented
by performing the Fourier transform of the topological charge distribution
$P(Q)$. This procedure, however, causes flattening phenomenon of the free
energy $f(\theta)$, which makes study of the phase structure unfeasible.
  In order to treat this problem, we apply the maximum entropy method (MEM) to
a Gaussian form of $P(Q)$, which serves as a good example to test whether the
MEM can be applied effectively to the $\theta$ term. We study the case with
flattening as well as that without flattening. In the latter case, the results
of the MEM agree with those obtained from the direct application of the Fourier
transform. For the former, the MEM gives a smoother $f(\theta)$ than that of
the Fourier transform. Among various default models investigated, the images
which yield the least error do not show flattening, although some others cannot
be excluded given the uncertainty related to statistical error.
