Comparisons of the Kullback–Leibler distances for different
sample sizes are shown in Figure 5. It can be seen that the predictive
distribution derived from the score intervals can approximate
the true binomial distribution more accurately than that
derived from the adjusted interval.
Theorem 1 shows that the variance of the distribution with
respect to the density function f s(y|x) is closer to the true variance
than that of the distribution with respect to f a(y|x). This
can provide an intuitive explanation for the results in Figure 5.