Sampling Variance and Bias of the Wilks Conservative Estimate of Confidence Intervals

For evaluation of the uncertainty of nuclear power calculations, the Wilks approach has the appearance of an ideal tool. A conservatively estimated bound is obtained as the r’th most extreme model result, of a random sample of size determined by r. The methodology is noninvasive and simple and seems efficient and adequate. However, as this paper shows, these attributes come with a high price of large bias and substantial sampling variance. This jeopardizes its utilization as well as lowers its credibility and perceived efficiency. The unfortunate combination of random sampling and faithful estimation may result in a relative sampling uncertainty of the estimated bound(s) of no less than 100%. What is defined as credibility, i.e., the probability that the estimated bound is conservative relative to the true result, is well below the confidence relating the targeted bound(s) to the true result, which for the default application of the Wilks method translates into an expected failure rate of up to 10% (instead of 5%) of estimated bounds. To compensate for this deficit in credibility compared to the chosen level of confidence, adjustments of current practice are proposed. The application to modeling uncertainty is to be clearly distinguished from the original experimental sampling problem addressed by Wilks. Here, more is known but not utilized. A viable novel alternative based on so-called deterministic sampling with higher accuracy, precision, and efficiency will therefore be briefly discussed and illustrated.