Robustness of Wilks’ Conservative Estimate of Confidence Intervals

The striking generality and simplicity of Wilks’ method has made it popular for quantifying modeling uncertainty. A conservative estimate of the confidence interval is obtained from a very limited set of randomly drawn model sample values, with probability set by the assigned so-called stability. In contrast, the reproducibility of the estimated limits, or robustness, is beyond our control as it is strongly dependent on the probability distribution of model results. The inherent combination of random sampling and faithful estimation in Wilks’ approach is here shown to often result in poor robustness. The estimated confidence interval is consequently not a well-defined measure of modeling uncertainty. To remedy this deficiency, adjustments of Wilks’ approach as well as alternative novel, effective but less known approaches based on deterministic sampling are suggested. For illustration, the robustness of Wilks’ estimate for uniform and normal model distributions are compared.