  This paper is concerned with inverse acoustic scattering problem of inferring
the position and shape of a sound-soft obstacle from phaseless far-field data.
We propose the Bayesian approach to recover sound-soft disks, line cracks and
kite-shaped obstacles through properly chosen incoming waves in two dimensions.
Given the Gaussian prior measure, the well-posedness of the posterior measure
in the Bayesian approach is discussed. The Markov Chain Monte Carlo (MCMC)
method is adopted in the numerical approximation and the preconditioned
Crank-Nicolson (pCN) algorithm with random proposal variance is utilized to
improve the convergence rate. Numerical examples are provided to illustrate
effectiveness of the proposed method.
