  Rank and PIT histograms are established tools to assess the calibration of
probabilistic forecasts. They not only check whether an ensemble forecast is
calibrated, but they also reveal what systematic biases (if any) are present in
the forecasts. Several extensions of rank histograms have been proposed to
evaluate the calibration of probabilistic forecasts for multivariate outcomes.
These extensions introduce a so-called pre-rank function that condenses the
multivariate forecasts and observations into univariate objects, from which a
standard rank histogram can be produced. Existing pre-rank functions typically
aim to preserve as much information as possible when condensing the
multivariate forecasts and observations into univariate objects. Although this
is sensible when conducting statistical tests for multivariate calibration, it
can hinder the interpretation of the resulting histograms. In this paper, we
demonstrate that there are few restrictions on the choice of pre-rank function,
meaning forecasters can choose a pre-rank function depending on what
information they want to extract from their forecasts. We introduce the concept
of simple pre-rank functions, and provide examples that can be used to assess
the location, scale, and dependence structure of multivariate probabilistic
forecasts, as well as pre-rank functions tailored to the evaluation of
probabilistic spatial field forecasts. The simple pre-rank functions that we
introduce are easy to interpret, easy to implement, and they deliberately
provide complementary information, meaning several pre-rank functions can be
employed to achieve a more complete understanding of multivariate forecast
performance. We then discuss how e-values can be employed to formally test for
multivariate calibration over time. This is demonstrated in an application to
wind speed forecasting using the EUPPBench post-processing benchmark data set.
