On the Statistical Formalism of Uncertainty Quantification

Posted: 3 May 2019

See all articles by James O. Berger

James O. Berger

Duke University

Lenny Smith

London School of Economics & Political Science (LSE)

Date Written: March 2019


The use of models to try to better understand reality is ubiquitous. Models have proven useful in testing our current understanding of reality; for instance, climate models of the 1980s were built for science discovery, to achieve a better understanding of the general dynamics of climate systems. Scientific insights often take the form of general qualitative predictions (i.e., “under these conditions, the Earth's poles will warm more than the rest of the planet”); such use of models differs from making quantitative forecasts of specific events (i.e. “high winds at noon tomorrow at London's Heathrow Airport”). It is sometimes hoped that, after sufficient model development, any model can be used to make quantitative forecasts for any target system. Even if that were the case, there would always be some uncertainty in the prediction. Uncertainty quantification aims to provide a framework within which that uncertainty can be discussed and, ideally, quantified, in a manner relevant to practitioners using the forecast system. A statistical formalism has developed that claims to be able to accurately assess the uncertainty in prediction. This article is a discussion of if and when this formalism can do so. The article arose from an ongoing discussion between the authors concerning this issue, the second author generally being considerably more skeptical concerning the utility of the formalism in providing quantitative decision-relevant information.

Suggested Citation

Berger, James O. and Smith, Leonard A., On the Statistical Formalism of Uncertainty Quantification (March 2019). Annual Review of Statistics and Its Application, Vol. 6, Issue 1, pp. 433-460, 2019, Available at SSRN: https://ssrn.com/abstract=3382105 or http://dx.doi.org/10.1146/annurev-statistics-030718-105232

James O. Berger

Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

Leonard A. Smith (Contact Author)

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

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