  We present the implementation and validation of the techniques used to
efficiently evaluate parametric and perturbative theoretical uncertainties in
matrix-element plus parton-shower simulations within the Sherpa event-generator
framework. By tracing the full $\alpha_s$ and PDF dependences, including the
parton-shower component, as well as the fixed-order scale uncertainties, we
compute variational event weights on-the-fly, thereby greatly reducing the
computational costs to obtain theoretical-uncertainty estimates.
