  In this work, we are interested in the determination of the shape of the
scatterer for the two dimensional time harmonic inverse medium scattering
problems in acoustics. The scatterer is assumed to be a piecewise constant
function with a known value inside inhomogeneities, and its shape is
represented by the level set functions for which we investigate the information
using the Bayesian method. In the Bayesian framework, the solution of the
geometric inverse problem is defined as a posterior probability distribution.
The well-posedness of the posterior distribution would be discussed, and the
Markov chain Monte Carlo (MCMC) methods will be applied to generate samples
from the arising posterior distribution. Numerical experiments will be
presented to demonstrate the effectiveness of the proposed method.
