Evidential reasoning using stochastic simulation of causal models
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Convergence rates for Markov chains
SIAM Review
Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Exact sampling and approximate counting techniques
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
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Inference for belief networks using Gibbs sampling produces a distribution for unobserved variables that differs from the correct distribution by a (usually) unknown error, since convergence to the right distribution occurs only asymptotically. The method of "coupling from the past" samples from exactly the correct distribution by (conceptually) running dependent Gibbs sampling simulations from every possible starting state from a time far enough in the past that all runs reach the same state at time t = 0. Explicitly considering every possible state is intractable for large networks, however. We propose a method for layered noisy-or networks that uses a compact, but often imprecise, summary of a set of states. This method samples from exactly the correct distribution, and requires only about twice the time per step as ordinary Gibbs sampling, but it may require more simulation steps than would be needed if chains were tracked exactly.