Behavior of relative to the uniform distribution under Scenario 2, depending on the interval housing the statistical prior sharpness parameter .

Kolomogorov-Smirnov distance (D) between the simulated and the uniform distribution and frequency ( and ) of found at the 5% and 1% extremities of the unit interval for the Poisson model with in Scenario 2 based on 100,000 different datasets. In this Scenario, the statistical prior , has a different sharpness to the probabilistic prior . The statistics for the overall sample were , and . These results illustrate that for to be approximately uniform when the statistical prior is not the same as the probabilistic prior, it is preferable for the statistical prior to be less informative rather than more informative compared with the probabilistic prior. Similar results were found for other test statistics and other probability distributions (cf. Text S2).
NOTE: The notation for the significance of the tests is as follows: (*) means that the test is significant at a level between .05 and .1; * between .01 and .05; ** between .0001 and .01; *** less than .0001. The notation system for the study of the negligibility of departures from expected values is as follows, for : 00 (respectively, 0) means 95% of the estimated values of the underlying p-value are in the interval (resp. ); ++ (respectively, +) means 95% of the estimated values are in the interval (resp. ); – (respectively, -) means 95% of the estimated values are in the interval (resp. ). For , the notations are the same but with cutoff points divided by 5.