Symbolic propagation and sensitivity analysis in Gaussian Bayesian networks with application to damage assessment

In this paper we show how Bayesian network models can be used to perform a sensitivity analysis using symbolic, as opposed to numeric, computations. An example of damage assessment of concrete structures of buildings is used for illustrative purposes. Initially, normal or Gaussian Bayesian network models are described together with an algorithm for numerical propagation of uncertainty in an incremental form. Next, the algorithm is implemented symbolically, in Mathematica code, and applied to answer some queries related to the damage assessment of concrete structures of buildings. Finally, the conditional means and variances of the nodes given the evidence are shown to be rational functions of the parameters, thus, discovering its parametric structure, which can be efficiently used in sensitivity analysis.

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