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Keith Worden, University of Sheffield
Scott Ferson, Institute for Risk and Uncertainty, University of Liverpool
We are at a crossroads in our scientific appreciation of uncertainty. The traditional view is that there is only one kind of uncertainty and that probability theory with Bayes' rule is its calculus. But some engineers hold that, in practice, the quantitative results of traditional probabilistic models are often misconstrued and sometimes demonstrably misleading.
By relaxing a single axiom of traditional (von Neumann–Morgenstern) utility theory that assumes the decision maker can always decide which of any two nonidentical decision choices would be preferred, traditional decision theory devolves to a version entailing a richer concept of uncertainty and a broader framework for uncertainty analysis. The resulting theory admits a kind of uncertainty that is not handled by traditional Laplacian probability measures and might therefore be called non-Laplacian uncertainty. This non-Laplacian view argues that different kinds of uncertainty must be propagated differently through simulations, reliability and risk analyses, calculations for robust design, and other computations.
We suggest that these two views can be unified into a modern pragmatic approach to uncertainty quantification. Many, and perhaps most, practical calculations involving uncertainty may be well handled with traditional probability theory, implemented as standard applications of Bayes' rule and Monte Carlo simulations. But there are special cases involving epistemic uncertainty where it is difficult or impossible to fully specify probabilities or other measured quantities precisely, where a non-Laplacian approach can be useful. Such a unified approach would make practical solutions easier for engineering and physics-based models, and the inferences drawn from such models under this view would be more defensible.
Remarkably, this emerging consensus parallels the historical resolution of the initially extreme controversy in mathematics that produced the present balance between Euclidean and non-Euclidean approaches that forms modern geometry.
Speaker biosketches
Keith Worden began academic life as a theoretical physicist, with a degree from York University and a PhD in Mechanical Engineering from Heriot-Watt University eventually followed. A period of research at Manchester University led to a professorship at the University of Sheffield in 1995, where he has happily remained since. Keith's research is concerned with applications of advanced signal processing and machine learning methods to structural dynamics. The primary application is in the aerospace industry, although there has also been interaction with ground transport and offshore industries. One of the research themes concerns non-linear systems. The research conducted here is concerned with assessing the importance of non-linear modelling within a given context and formulating appropriate methods of analysis. The analysis of non-linear systems can range from the fairly pragmatic to the extremes of mathematical complexity. The emphasis within the research group here is on the pragmatic and every attempt is made to maintain contact with engineering necessity. Another major activity within the research group concerns structural health monitoring for aerospace systems and structures. The research is concerned with developing automated systems for inspection and diagnosis, with a view to reducing the cost-of-ownership of these high integrity structures. The methods used are largely adapted from pattern recognition and machine learning; often the algorithms make use of biological concepts e.g. neural networks, genetic algorithms and ant-colony metaphors. The experimental approaches developed range from global inspection using vibration analysis to local monitoring using ultrasound.
Scott Ferson is director of the Institute for Risk and Uncertainty at the University of Liverpool in the UK. For many years he was at Applied Biomathematics in the US. He holds a Ph.D. in Ecology and Evolution from Stony Brook University and an A.B. in biology from Wabash College. He has published five books, ten commercially distributed software packages, and over a hundred scholarly publications, mostly in environmental risk analysis, uncertainty propagation, and conservation biology. He is a fellow of the Society for Risk Analysis and was named Distinguished Educator by the Society. He has been a central figure in the development of probability bounds analysis, an approach to reliably computing with imprecisely specified probabilistic models. His research, funded primarily by the Engineering and Physical Sciences Research Council, National Institutes of Health, NASA, and Sandia National Laboratories, has focused on developing reliable statistical tools for uncertainty analysis when empirical information is very sparse in engineering, environmental and medical risk analyses.
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