  Monte Carlo sampling has become a major vehicle for approximate inference in
Bayesian networks. In this paper, we investigate a family of related simulation
approaches, known collectively as quasi-Monte Carlo methods based on
deterministic low-discrepancy sequences. We first outline several theoretical
aspects of deterministic low-discrepancy sequences, show three examples of such
sequences, and then discuss practical issues related to applying them to belief
updating in Bayesian networks. We propose an algorithm for selecting direction
numbers for Sobol sequence. Our experimental results show that low-discrepancy
sequences (especially Sobol sequence) significantly improve the performance of
simulation algorithms in Bayesian networks compared to Monte Carlo sampling.
