  The Brier Score is a widely-used criterion to assess the quality of
probabilistic predictions of binary events. The expectation value of the Brier
Score can be decomposed into the sum of three components called reliability,
resolution, and uncertainty which characterize different forecast attributes.
Given a dataset of forecast probabilities and corresponding binary
verifications, these three components can be estimated empirically. Here,
propagation of uncertainty is used to derive expressions that approximate the
sampling variances of the estimated components. Variance estimates are provided
for both the traditional estimators, as well as for refined estimators that
include a bias correction. Applications of the derived variance estimates to
artificial data illustrate their validity, and application to a meteorological
prediction problem illustrates a possible use case. The observed increase of
variance of the bias-corrected estimators is discussed.
