  We consider systems under uncertainty whose dynamics are partially unknown.
Our aim is to study satisfaction of temporal logic properties by trajectories
of such systems. We express these properties as signal temporal logic formulas
and check if the probability of satisfying the property is at least a given
threshold. Since the dynamics are parameterized and partially unknown, we
collect data from the system and employ Bayesian inference techniques to
associate a confidence value to the satisfaction of the property. The main
novelty of our approach is to combine both data-driven and model-based
techniques in order to have a two-layer probabilistic reasoning over the
behavior of the system: one layer is related to the stochastic noise inside the
system and the next layer is related to the noisy data collected from the
system. We provide approximate algorithms for computing the confidence for
linear dynamical systems.
