Statistical mechanical Bayesian inference and its application

Based on the statistical mechanical Bayesian inference, we construct a method of phase unwrapping using multiple interferograms by making use of the maximizer of the posterior marginal (MPM) estimate due to the Monte Carlo simulation. In this method, we carry out phase unwrapping so as to maximize the marginal posterior probability. We clarify from the phase diagram in hyper-parameter space that the MPM estimate realizes phase unwrapping perfectly without using prior information under the constraint of the surface-consistency condition, if observed interferograms are not corrupted, and that prior information is useful for extending domain where phase unwrapping is realized with high degree of accuracy, if the interferograms are corrupted. Also, we find that results obtained by the extended mean-field theory are qualitatively confirmed by the MPM estimate due to the Monte Carlo simulation.