  In this work, we focus on reduced order modeling (ROM) techniques for
hyperbolic conservation laws with application in uncertainty quantification
(UQ) and in conjunction with the well-known Monte Carlo sampling method.
Because we are interested in model order reduction (MOR) techniques for
unsteady non-linear hyperbolic systems of conservation laws, which involve
moving waves and discontinuities, we explore the parameter-time framework and
in the same time we deal with nonlinearities using a POD-EIM-Greedy algorithm
\cite{Drohmann2012}. We provide under some hypothesis an error indicator, which
is also an error upper bound for the difference between the high fidelity
solution and the reduced one.
