  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 exact probabilistic
inference on belief networks almost certainly requires exponential computation
in the worst ease [3]. We have previously described a randomized approximation
scheme, called BN-RAS, for computation on belief networks [ 1, 2, 4]. We gave
precise analytic bounds on the convergence of BN-RAS and showed how to trade
running time for accuracy in the evaluation of posterior marginal
probabilities. We now extend our previous results and demonstrate the
generality of our framework by applying similar mathematical techniques to the
analysis of convergence for logic sampling [7], an alternative simulation
algorithm for probabilistic inference.
