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

Plots of the cumulative differences between observed and expected values of ordered Bernoulli variates