This paper addresses the problem of Bayesian off-line change-point detection in synthetic aperture radar images. The minimum mean square error and maximum a posteriori estimators of the changepoint positions are studied. Both estimators cannot be implemented because of optimization or integration problems. A practical implementation using Markov chain Monte Carlo methods is proposed. This implementation requires a priori knowledge of the so-called hyperparameters. A hyperparameter estimation procedure is proposed that alleviates the requirement of knowing the values of the hyperparameters. Simulation results on synthetic signals and synthetic aperture radar images are presented.