  The belief propagation (BP) algorithm is widely applied to perform
approximate inference on arbitrary graphical models, in part due to its
excellent empirical properties and performance. However, little is known
theoretically about when this algorithm will perform well. Using recent
analysis of convergence and stability properties in BP and new results on
approximations in binary systems, we derive a bound on the error in BP's
estimates for pairwise Markov random fields over discrete valued random
variables. Our bound is relatively simple to compute, and compares favorably
with a previous method of bounding the accuracy of BP.
