What happens when the expert’s median coincides with the realization? It would seem that the expert provides the “best” prediction, right?

Well, let’s see what calibration score does this “best” prediction correspond to.

But first, we employ the following convention:

– when the realization coincides with the expert’s 5% quantile, we assume that the realization falls in the first interquantile range, IQ1
– when the realization coincides with the expert’s 50% quantile, we assume that the realization falls in the second interquantile range, IQ2
– when the realization coincides with the expert’s 95% quantile, we assume that the realization falls in the third interquantile range, IQ3