Response to “Closure on the Discussion of “Models, Uncertainty, and the Sandia V&V Challenge Problem” ” (Oberkampf, W. L., and Balch, M. S., ASME J. Verif. Valid. Uncert., 2020, 5(3), p. 035501-1)

Abstract

We write to address comments made in Closure on the Discussion of “Models, Uncertainty, and the Sandia V&V Challenge Problem” by Oberkampf and Balch. We feel that the title of these comments is unfortunate because it misrepresents our article and continues to espouse what we believe is a dangerous and uninformed viewpoint on certain mathematical constructs interpreted and employed in every-day engineering practice. We offer this brief rebuttal in recognition that the Oberkampf and Balch article certainly provides no closure to the discussion.The central message of our paper is that engineers should operate with an understanding of state-of-the-art physical principles and, equivalently, with an understanding of state-of-the-art mathematical principles as well. Both are particularly important in a decision-making context such as that presented by the Sandia Challenge Problem. Two such principles are particularly important to engineers, namely, those addressing uncertainty and those addressing decision making (the latter encompassing optimization). There is wide consensus in the world of mathematics on the theory of probability as axiomatically proposed by Kolmogorov to address the quantification of uncertainty. The Kolmogorov interpretation of probability is wholly consistent with the widely accepted intuitive interpretation of the word. Other quantifications of uncertainty are not probabilities and should not be referred to as such. The foundations of decision science are built specifically on the Kolmogorov axiomatic theory of probability. This does not mean that the current theory adequately addresses all aspects of decision-making under uncertainty, nor that it answers all questions that engineers might ask when analyzing decisions. But the extant theory clearly does address the Sandia Challenge Problem. We agree that there are many ways to characterize uncertainty, but it is unclear how alternative characterizations can be used in support of a normative decision-making process as we know of no axiomatically rigorous mathematical framework that supports their use in a normative decision-making process. For this and several additional reasons, other characterizations of uncertainty do not enjoy the broad support of the mathematics community and should not be considered for use by the engineering community. Indeed, if Oberkampf and Balch wish to propose the use of alternative quantifications of uncertainty in support of engineering decision making, they should preface their proposal with the derivation of an axiomatically sound framework for the use of their proposed alternative quantification in a normative decision-making context. Absent such a framework, alternative quantifications of uncertainty lack coherent interpretation.