A tutorial introduction to stochastic simulation algorithms for belief networks

Belief networks combine probabilistic knowledge with explicit information about conditional independence assumptions. A belief network consists of a directed acyclic graph in which the nodes represent variables and the edges express relationships of conditional dependence. When information about one variable's state is given to the network in the form of evidence, an update algorithm computes the posterior marginal probability distributions for the remaining variables in the network. Many algorithms for performing this inference task have been proposed. Exact algorithms report precise results for some classes of networks, but take exponential time (in the number of nodes) both in the worst case and for many interesting networks. Stochastic simulation algorithms estimate the posterior marginal probability distribution for many graph topologies that would require exponential time when using an exact algorithm. Nonetheless, for some belief networks, stochastic simulation algorithms are also known to have exponential worst case performance. This article describes at a tutorial level several stochastic simulation algorithms for belief networks, and illustrates them on some simple examples. In addition, the theoretical and empirical performance of the algorithms is briefly surveyed.