  Inverse scattering problems have many important applications. In this paper,
given limited aperture data, we propose a Bayesian method for the inverse
acoustic scattering to reconstruct the shape of an obstacle. The inverse
problem is formulated as a statistical model using the Baye's formula. The
well-posedness is proved in the sense of the Hellinger metric. The extended
sampling method is modified to provide the initial guess of the target
location, which is critical to the fast convergence of the MCMC algorithm. An
extensive numerical study is presented to illustrate the performance of the
proposed method.
