An Empirical Evaluation of a Randomized Algorithm for Probabilistic
  Inference
  In recent years, researchers in decision analysis and artificial intelligence
(Al) 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. K N ET, 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. In this article, we describe a randomized algorithm for
probabilistic inference and analyze its performance mathematically. Then, we
devote the major portion of the paper to a discussion of the algorithm's
empirical behavior. The results indicate that the generation of good trials
(that is, trials whose distribution closely matches the true distribution),
rather than the computation of numerous mediocre trials, dominates the
performance of stochastic simulation. Key words: probabilistic inference,
belief networks, stochastic simulation, computational complexity theory,
randomized algorithms.
