Stochastic simulation algorithms such as likelihood weighting often give fast, accurate approximations to posterior probabilities in probabilistic networks, and are the methods of choice for very large networks. Unfortunately, the special characteristics of dynamic probabilistic networks (DPNs), which are used to represent stochastic temporal processes, mean that standard simulation algorithms perform very poorly. In essence, the simulation trials diverge further and further from reality as the process is observed over time. In this paper, we present simulation algorithms that use the evidence observed at each time step to push the set of trials back towards reality. The first algorithm, "evidence reversal " (ER) restructures each time slice of the DPN so that the evidence nodes for the slice become ancestors of the state variables. The second algorithm, called "survival of the fittest " sampling (SOF), "repopulates " the set of trials at each time step using a stochastic reproduction rate weighted by the likelihood of the evidence according to each trial. We compare the performance of each algorithm with likelihood weighting on the original network, and also investigate the benefits of combining the ER and SOF methods. The ER/SOF combination appears to maintain bounded error independent of the number of time steps in the simulation.

We introduce a variant of Aldous and Vazirani's "Go with the winners" algorithm that can be used for search graphs that are not trees. We analyze the algorithm in terms of the properties of a tree-decomposition of the search graph. We show a large class of distributions for search graphs so that "Go with the winners" works well with high probability for almost all graphs from the distribution. We also give a sufficient combinatorial property that ensures good performance.

We analyze "Go with the winners" for graph bisection. We introduce a weaker version of expansion called "local expansion". We show that "Go with the winners" works well in any search space whose sub-graphs with solutions at least as good as a certain threshold have local expansion, and where these sub-graphs do not shrink more than by a polynomial factor when the threshold is incremented. We give a general technique for showing that solution spaces for random instances of problems have local expansion. We apply this technique to the minimum bisection problem for random graphs. We conclude that "Go with the winners" approximates the best solution in random graphs of certain densities with planted bi-sections in polynomial time, and finds the optimal solution in quasi-polynomial time. Although other methods also solve this problem for the same densities, the set of tools we develop may be useful in the analysis of similar problems. In particular, our results easily extend to hypergraph b...