Abstract In recent years, researchers in decision analysis and artificial intelligence (AI) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in the field have shown that the problem of probabilistic inference in belief networks is difficult and almost certainly intractable. KNET, a software environment for constructing knowledge-based systems within the axiomatic framework of decision theory, contains a randomized approximation scheme for probabilistic inference. The algorithm can, in many circumstances, perform efficient approximate inference in large and richly interconnected models of medical diagnosis. Unlike previously described stochastic algorithms for probabilistic inference, the randomized approximation scheme computes a priori bounds on running time by analyzing the structure and contents of the belief network.