Estimation of distribution parameters as a tool for model-based system engineering and model identification

The estimation of the parameters of a probability distribution (e.g., moments) plays an important role both in the model-based system engineering (e.g., analysis and verification through Statistical Model Checking (SMC)) and in the identification of parameters of predictive models (e.g., systems biology, social networks). The contribution of this PhD thesis is both on the algorithm side and on the modeling side. On the algorithm side, we overview a set of Monte Carlo-based Statistical Model Checking tools and algorithms for the verification of Cyber-Physical Systems, and we provide selection criteria for the verification problem at hand. Furthermore, we present an efficient Monte Carlo-based algorithm to estimate the expected value of a multivariate random variable, when marginal density functions are not known. We prove the correctness of our algorithm, we give an Upper Bound and a Lower Bound to its complexity and we present experimental results confirming our evaluations. On the modeling side, we present a mechanistic and identifiable model to predict, at the node level and at a set of nodes level, the expected value of the retweeting rate of a message inside a social network, at a certain time. Our model parameters are random variables, whose distribution parameters are estimated from an available dataset. We experimentally show that our model reliably predicts both the qualitative and the quantitative time behavior of retweeting rates. This is confirmed by the high correlation between the predicted and the observed data. These results enable a simulation-based analysis of users or of a set of users' behaviors inside a network.