  Many predictions are probabilistic in nature; for example, a prediction could
be for precipitation tomorrow, but with only a 30 percent chance. Given both
the predictions and the actual outcomes, "reliability diagrams" (also known as
"calibration plots") help detect and diagnose statistically significant
discrepancies between the predictions and the outcomes. The canonical
reliability diagrams are based on histogramming the observed and expected
values of the predictions; several variants of the standard reliability
diagrams propose to replace the hard histogram binning with soft kernel density
estimation using smooth convolutional kernels of widths similar to the widths
of the bins. In all cases, an important question naturally arises: which widths
are best (or are multiple plots with different widths better)? Rather than
answering this question, plots of the cumulative differences between the
observed and expected values largely avoid the question, by displaying
miscalibration directly as the slopes of secant lines for the graphs. Slope is
easy to perceive with quantitative precision even when the constant offsets of
the secant lines are irrelevant. There is no need to bin or perform kernel
density estimation with a somewhat arbitrary kernel.
