© 2014 IEEE. Accurate displacement estimation can be a challenging task in acoustic radiation force elastography, where signal decorrelation can degrade the ability of a normalized cross-correlation (NCC) estimator to characterize the tissue response. In this work, we describe a Bayesian estimation scheme which models both signal decorrelation and thermal noise, and uses an edge-preserving, generalized Gaussian Markov random field prior. The performance of the estimator was evaluated in FEM simulations modeling the acoustic radiation force impulse response in a linearly-isotropic material. Bias, variance, and mean-square error were calculated over a range of estimator parameters, and compared to NCC. The results demonstrate that a significant reduction in mean-square error can be achieved with the proposed estimator. Finally, in vivo data of an radio-frequency ablation in a canine model are shown, demonstrating the in vivo feasibility of the proposed method.