Interval data are widely used in real applications to represent the values of quantities in uncertain situations. However, the implied probabilistic causal relationships among interval-valued variables with interval data cannot be represented and inferred by general Bayesian networks with point-based probability parameters. Thus, it is desired to extend the general Bayesian network with effective mechanisms of representation, learning and inference of probabilistic causal relationships implied in interval data. In this paper, we define the interval probabilities, the bound-limited weak conditional interval probabilities and the probabilistic description, as well as the multiplication rules. Furthermore, we propose the method for learning the Bayesian network structure from interval data and the algorithm for corresponding approximate inferences. Experimental results show that our methods are feasible, and we conclude that the Bayesian network with interval probability parameters is the expansion of the general Bayesian network.
Dynamic Bayesian networks for evaluation of Granger causal relationships in climate reanalyses
