  In the era of precision physics measurements at the LHC, efficient and
exhaustive estimations of theoretical uncertainties play an increasingly
crucial role. In the context of Monte Carlo (MC) event generators, the
estimation of such uncertainties traditionally requires independent MC runs for
each variation, for a linear increase in total run time. In this work, we
report on an automated evaluation of the dominant (renormalization-scale and
non-singular) perturbative uncertainties in the PYTHIA 8 event generator, with
only a modest computational overhead. Each generated event is accompanied by a
vector of alternative weights (one for each uncertainty variation), with each
set separately preserving the total cross section. Explicit scale-compensating
terms can be included, reflecting known coefficients of higher-order splitting
terms and reducing the effect of the variations. The formalism also allows for
the enhancement of rare partonic splittings, such as $g \to b \bar{b}$ and
$q\to q \gamma$, to obtain weighted samples enriched in these splittings while
preserving the correct physical Sudakov factors.
