Inference in hybrid Bayesian networks with large discrete and continuous domains

•Bayesian inference algorithm for a large domain of discrete variables is proposed.•Classification tree algorithm identifies conditional probability tables.•Tree based factor production and marginalization methods are proposed.•Efficient inference algorithm for tree structured Bayesian network is developed.•Estimation of most likely production times for steel plates production. Inference in Bayesian networks with large domain of discrete variables requires significant computational effort. In order to reduce the computational effort, current approaches often assume that discrete variables have some bounded number of values or are represented at an appropriate size of clusters. In this paper, we introduce decision-tree structured conditional probability representations that can efficiently handle a large domain of discrete and continuous variables. These representations can partition the large number of values into some reasonable number of clusters and lead to more robust parameter estimation. Very rapid computation and ability to treat both discrete and continuous variables are accomplished via modified belief propagation algorithm. Being able to compute various types of reasoning from a single Bayesian network eliminates development and maintenance issues associated with the use of distinct models for different types of reasoning. Application to real-world steel production process data is presented.