Sensitivity analysis for bayesian networks with interval probabilities

Bayesian Networks (BNs) have more than once proven to be an extremely attractive tool in the field of complex systems reliability and risk analysis (Weber, Medina-Oliva, Simon, & Iung 2012). In spite of this, many studies have highlighted the limitations of the traditional BNs approach mainly restricted to the use of discrete variables and crisp probabilities, which cannot fully capture the nature of the information available and its unavoidable uncertainty (Spiegelhalter 1989). The use of probability bounds instead of crisp values can largely improve the accuracy of the models and the robustness of the analysis, representing the imprecision which affects both the data available and the projections inferred. The integration of BN approach with Interval probabilities present two main bottle-necks: one referred to the inference computation, the second to the uncertainty propagation among the variables involved. Regarding the inference computation, a nave approach to deriving precise bounds on a query node of the net is to apply the standard BN inference methods for each combination of probability bounds, minimizing and maximizing the final results. This approach is computationally expensive and suffers from combinatorial explosion (Thöne, Güntzer, & Kieβling 1997). Secondly, the use of probability bounds in BNs could result in large uncertainty affecting the output probabilities: high imprecision can make the analysis ineffective in terms of decision making support in spite of the accuracy of data representation. This can lead to the necessary to invest and refine the quality of the information in input in order reduce the uncertainty of the output but: this action, if not efficiently carried out, can be very expensive or even ineffective. The aim of this study is to develop theoretical and computational tools able to identify the main sources of uncertainty in the input affecting the overall results of the analysis. This information would allow to effectively tackling the uncertainty affecting the model results, obtaining the most accurate information at the lowest cost. The methods developed are based on well-known and robust inference algorithms and allow identifying the best possible strategy in terms of modification of single network parameters, in order to obtain the aimed level of imprecision in output. The approach has been implemented computationally in the general purpose software OpenCossan. Numerical examples are provided in order to test the validity of the methods proposed and compared with more traditional approaches.