Bayesian networks (BNs) offer a compact, intuitive, and efficient graphical representation of uncertain relationships among the variables in a domain and have proven their value in many disciplines over the last two decades. However, two challenges become increasingly critical in practical applications of Bayesian networks. First, real models are reaching the size of hundreds or even thousands of nodes. Second, some decision problems are more naturally represented by hybrid models which contain mixtures of discrete and continuous variables and may represent linear or nonlinear equations and arbitrary probability distributions. Both challenges make building Bayesian network models and reasoning with them more and more difficult.; In this dissertation, I address the challenges by developing representational and computational solutions based on importance sampling. I First develop a more solid understanding of the properties of importance sampling in the context of Bayesian networks. Then, I address a fundamental question of importance sampling in Bayesian networks, the representation of the importance function. I derive an exact representation for the optimal importance function and propose an approximation strategy for the representation when it is too complex. Based on these theoretical analysis, I propose a suite of importance sampling-based algorithms for (hybrid) Bayesian networks. I believe the new algorithms significantly extend the efficiency, applicability, and scalability of approximate inference methods for Bayesian networks. The ultimate goal of this research is to help users to solve difficult reasoning problems emerging from complex decision problems in the most general settings.
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