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Inference for belief networks using Gibbs sampling produces a distributionfor unobserved variables that differs from the correct distribution by a(usually) unknown error, since convergence to the right distribution occursonly asymptotically. The method of "coupling from the past" samples fromexactly the correct distribution by (conceptually) running dependent Gibbssampling simulations from every possible starting state from a time far enoughin the past that all runs reach the same state at time t=0. Explicitlyconsidering every possible state is intractable for large networks, however. Wepropose a method for layered noisy-or networks that uses a compact, but oftenimprecise, summary of a set of states. This method samples from exactly thecorrect distribution, and requires only about twice the time per step asordinary Gibbs sampling, but it may require more simulation steps than would beneeded if chains were tracked exactly.

Inference for Belief Networks Using Coupling From the Past