  We present an a posteriori error analysis for one-dimensional random
hyperbolic systems of conservation laws. For the discretization of the random
space we consider the Non-Intrusive Spectral Projection method, the
spatio-temporal discretization uses the Runge--Kutta Discontinuous Galerkin
method. We derive an a posteriori error estimator using smooth reconstructions
of the numerical solution, which combined with the relative entropy stability
framework yields computable error bounds for the space-stochastic
discretization error. Moreover, we show that the estimator admits a splitting
into a stochastic and deterministic part.
