Fig. 32

\(n =\) 100; \(S_1\), \(S_2\), ..., \(S_n\) are equispaced; Kuiper’s statistic is \(0.1388 / \sigma = 3.399\), Kolmogorov’s and Smirnov’s is \(0.1388 / \sigma = 3.399\). Figure 33 displays the ground-truth reliability diagram. The conventional plots become increasingly problematic as n reduces to 100 from 10,000 and 1000 in Figures 28 and 30, whereas the cumulative plot still detects roughly the right level of miscalibration for \(0 \lesssim S_k \lesssim 0.2\) and \(0.8 \lesssim S_k \lesssim 1\); the cumulative plot indicates that too little data is available for \(0.2 \lesssim S_k \lesssim 0.8\) to detect any statistically significant miscalibration in that range of \(S_k\) (note the size of the triangle centered at the origin of the plot)