Extreme inaccuracies in Gaussian Bayesian networks

To evaluate the impact of model inaccuracies over the network's output, after the evidence propagation, in a Gaussian Bayesian network, a sensitivity measure is introduced. This sensitivity measure is the Kullback-Leibler divergence and yields different expressions depending on the type of parameter to be perturbed, i.e. on the inaccurate parameter. In this work, the behavior of this sensitivity measure is studied when model inaccuracies are extreme, i.e. when extreme perturbations of the parameters can exist. Moreover, the sensitivity measure is evaluated for extreme situations of dependence between the main variables of the network and its behavior with extreme inaccuracies. This analysis is performed to find the effect of extreme uncertainty about the initial parameters of the model in a Gaussian Bayesian network and about extreme values of evidence. These ideas and procedures are illustrated with an example.