Performance modeling for dynamic Bayesian networks

In recent decades, Bayesian Network (BN) has shown its power to solve probabilistic inference problems because of its expressive representation of dependence relationships among random variables and the dramatic development of inference algorithms. They have been applied for decision under uncertainty in many areas such as data fusion, target recognition, and medical diagnosis, etc. In general, the problem of probabilistic inference for a dynamic BN is to compute the posterior probability distribution of a specific variable of interest given a set of observations cumulated over time. The accuracy of the resulting posterior probability distribution is essential since the correct decision in any partially observable environment depends on this distribution. However, there is no general evaluation methodology available to predict the inference performance for a BN other than extensive Monte Carlo simulation methods. In this paper, we first present a method to model the inference performance for a static BN. This approximate method is designed to predict the inference performance analytically without extensive simulation. We then propose a sequential simulation method based on the particle filter concept to evaluate the inference performance for a dynamic BN. The specific model we deal with is the hybrid partial dynamic BN consists of discrete and continuous variables with arbitrary relationships. Since no exact inference algorithm available for such a model, we use likelihood weighting (LW) method on an unrolled DBN to estimate its true performance bound for comparison with the predicted performance. Comparison and analysis of the experimental results show the potential capability of the sequential simulation method for evaluating the performance of dynamic Bayesian networks.