Continuous and reliable risk and uncertainty analysis of complex systems is essential for developing timely risk mitigation strategies and optimal operation of the systems. It is, therefore, imperative to constantly understand and predict the behavior of the system under often incomplete and imperfect observations of the system. Ignoring the uncertainty stemming from imperfect observations may lead to a lack of preparedness for unforeseen scenarios. In this work, we aim to develop efficient uncertainty quantification methodologies that take into account the imperfections in observations and facilitate reliable risk estimation and management.