  Multilevel Monte Carlo can efficiently compute statistical estimates of
discretized random variables, for a given error tolerance. Traditionally, only
a certain statistic is computed from a particular implementation of multilevel
Monte Carlo. This paper considers the multilevel case when one wants to verify
and evaluate a single ensemble that forms an empirical approximation to many
different statistics, namely an ensemble forecast. We propose a simple
algorithm that, in the univariate case, allows one to derive a statistically
consistent single ensemble forecast from the hierarchy of ensembles that are
formed during an implementation of multilevel Monte Carlo. This ensemble
forecast then allows the entire multilevel hierarchy of ensembles to be
evaluated using standard ensemble forecast verification techniques. We
demonstrate the case of evaluating the calibration of the forecast in this
paper.
