Practical Aspects of Solving Hybrid Bayesian Networks Containing Deterministic Conditionals

In this paper we discuss some practical issues that arise in solving hybrid Bayesian networks that include deterministic conditionals for continuous variables. We show how exact inference can become intractable even for small networks, due to the difficulty in handling deterministic conditionals (for continuous variables). We propose some strategies for carrying out the inference task using mixtures of polynomials and mixtures of truncated exponentials. Mixtures of polynomials can be defined on hypercubes or hyper-rhombuses. We compare these two methods. A key strategy is to re-approximate large potentials with potentials consisting of fewer pieces and lower degrees/number of terms. We discuss several methods for re-approximating potentials. We illustrate our methods in a practical application consisting of solving a stochastic PERT network.