This work develops a measurement-driven and model-based formal verification approach, applicable to dynamical systems with partly unknown dynamics. We provide a new principled method, grounded on 1 Bayesian inference and on reachability analysis respectively, to compute the confidence that a physical system driven by external inputs and accessed under noisy measurements verifies a given property expressed as a temporal logic formula. A case study discusses the bounded- and unbounded-time safety verification of a partly unknown system, encompassed within a class of linear, time-invariant dynamical models with inputs and output measurements. (C) 2017 Elsevier Ltd. All rights reserved.