The main objective of this thesis is to combine the advantages of probabilistic graphical model learning and formal verifica- tion in order to build a novel strategy for secu- rity assessments. The second objective is to assess the security of a given system by veri- fying whether it satisfies given properties and, if not, how far is it from satisfying them. We are interested in performing formal verification of this system based on event sequences col- lected from its execution. Consequently, we propose a model-based approach where a Re- cursive Timescale Graphical Event Model (RT- GEM), learned from the event streams, is con- sidered to be representative of the underlying system. This model is then used to check a se- curity property. If the property is not verified, we propose a search methodology to find an- other close model that satisfies it. We discuss and justify the different techniques we use in our approach and we adapt a distance mea- sure between Graphical Event Models. The distance measure between the learned "fittest" model and the found proximal secure model gives an insight on how far our real system is from verifying the given property. For the sake of completeness, we propose series of exper- iments on synthetic data allowing to provide experimental evidence that we can attain the desired goals.