  Statistical solutions are time-parameterized probability measures on spaces
of integrable functions, that have been proposed recently as a framework for
global solutions and uncertainty quantification for multi-dimensional
hyperbolic system of conservation laws. By combining high-resolution finite
volume methods with a Monte Carlo sampling procedure, we present a numerical
algorithm to approximate statistical solutions. Under verifiable assumptions on
the finite volume method, we prove that the approximations, generated by the
proposed algorithm, converge in an appropriate topology to a statistical
solution. Numerical experiments illustrating the convergence theory and
revealing interesting properties of statistical solutions, are also presented.
