An Elementary Approach To Thinking Under Uncertainty

Flow Randomness and epistemic uncertainty in the extreme value distribution. Lack of knowledge and natural variability of river bed and friction conditions. Final goal of the uncertainty study. Accredit measurement result and comply with metrological criterion. Understand and reduce main sources of uncertainty. Certify a safety criterion. Understand and rank sources of uncertainties with respect to failure threshold exceedance. Select design to optimize the complete cost. Generally a standard probabilistic, possibly with a.

Generally a mixed deterministic-probabilistic setting.

Risk and uncertainty separated or not in a double or single-level probabilistic or mixed setting. Acceptability of deterministic vs. Computational and mathematical complexity in handling rare probabilities. Scarcity of data to control extreme event distributions. Complexity to handle double probabilistic criteria. These should be seen as applying both to industrial or environmental fields within which there is already some experience in uncertainty treatment, as nuclear safety or waste management think of the Yucca Mountain nuclear waste facility, for which the performance assessment involves more considerable effort to represent uncertainty , or to fields where practice is more recent.

Climate change may be seen as a frontier case in that respect, for which each of the three challenges discussed hereafter, mobilizing information on uncertainty sources, numerically treating uncertainty, and building acceptable representations along a precautionary principle, will take acute dimensions. Needless to say, the relevance and significance of the entire uncertainty study relies upon the quality of such an input uncertainty model. Key difficulties arise with the highly-limited sampling information directly available on uncertain input variables in real-world industrial cases: Nevertheless, most publications poorly detail the underlying process or openly acknowledge deliberate decisions such as: Indeed, flood monitoring generates data on maximal water elevations or velocities rather than on uncertain friction coefficient or riverbed topology.

Run-off coefficients, and Strickler or Manning friction coefficients are typical examples in the hydrological or hydraulic domain of uncertain inputs for which no direct data is made available, although rainfall-flow, stage-discharge or stage line curves could provide indirect data to be calibrated against. This approach, which involves the inversion of a physical model to transform the indirect information, is intimately connected to classical data assimilation, parameter identification model calibration or updating techniques, although inverse uncertainty identification has some distinctive features: However such an estimation uncertainty happens to be purely epistemic or reducible which is not satisfactory in the case of intrinsically uncertain or variable physical systems, i.

We have seen how, in a strong deterministic paradigm, the maximisation of the response for uncertain domains implies numerous optimisation calculations; in a simple probabilistic paradigm, even with accelerated methods, several dozens or hundreds of calculations are necessary at least.

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In the former case, computational greediness is associated to the need of nesting a maximisation by intervals for the deterministic components with, for each point, a conditional probabilistic calculation for the probabilised variables. In the latter two cases, nesting optimization algorithms with propagation by sampling is required in the general non-linear, non-Gaussian case, generating a large computational cost. Aside from the internal optimisation of the code solvers themselves and their parallelisation, the numerical challenges posed by large-scale uncertainty treatment, depending on the propagation methods adopted, may indeed benefit from massively distributed computing.

Beyond simple Monte-Carlo, accelerated sampling e. Everything nevertheless depends on the quantity of interest fixed for the study, the paradigm chosen, for example "mixed deterministic-probabilistic", and the more or less probabilistic treatment devoted to the different sources of uncertainty, i. Step A in the framework. More generally, a decision rule with non-linear probability that is to say, based on the subjective transformation of probabilities by the agents equally constitutes a generalised representation of the risk aversion involved Quiggin, In the case of probabilities judged to be imprecise, this transformation can be interpreted as an aversion to uncertainty on the distribution of probabilities.

While the calculation of the criterion c Z is more sophisticated, because the functional on the measure of Z is more complex, that does not structurally change the global framework defined above. The mode of treatment of uncertainties is in effect a subject for discussion, depending on the level of subjective uncertainty or cognitive uncertainty, when the consequences are long term or serious, for example when it is a question of the storage of wastes with a long life, or climate change.

Accepting a probabilistic treatment when the uncertain occurrence will only occur once, and in a manner that is not observable ex ante for the deciders, is a delicate matter: This progression leads to the examination of methods and selection of the most relevant, those which closely associate the applied mathematics involved and the analysis of the physical system, with the emphasis on the problem to be resolved, which itself depends on the type of regulation concerned or the decision criterion chosen Step A , and not on the specific industrial or phenomenological domain. Furthermore, while this global approach shows that other mathematical paradigms are possible, the mixed deterministic-probabilistic framework appears to play a central role in current industrial applications, giving rise to numerous problems of statistical modeling and of scientific computing.

This suggests that, in preference to the implementation of a single research field, applications should be oriented towards capitalizing on all the various numerical and statistical algorithms available, made transparent in order to increase public accountability on the key uncertainty and risk issues, which is the whole object of the development of open source initiatives. Beyond, several directions for research remain to be explored. This is especially so when it is linked to the delicate but promising area of the evaluation of expert judgment, or the question of modeling dependences also in Step B.

Over and above efforts to provide cross-cultural training, the question rapidly becomes one of the acceptability, precaution and legibility associated with regulatory criteria, a debate lying at the heart of the society's attitude to risk. These questions remain open, in particular as regards the delicate choices of differentiation and aggregation of uncertainties according to natures, joined with the global conceptual apprehension of risks when considering issues of such public significance as industrial safety, natural risk or environmental impact.

At the very least, recent applied research and industrial experience leads us to think that by systematically encouraging people to question hypotheses in step B and to test numerous alternative calculations in step C , a study of uncertainties , even if its ambition appears presumptuous, will always be more reliable than a straightforward deterministic approach whose justification resides in the impossibility of giving complete confidence to quantitative uncertainty modeling.

The distinction between aleatory and epistemic uncertainties is important; an example from the inclusion of aging effects in the PSA.

A Review of the Analysis of Uncertainty, Wat. Upper and lower probabilities induced by a multi-valued mapping, Annals of Math. Environmental Monitoring and Assessment ;32 2: Nuclear Safety ;22 1: Japan , 75, A multidisciplinary journal devoted to the study of interactions between environment and society. Contents - Previous document - Next document.

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Abstract Uncertainty is ubiquitous in modern decision-making supported by quantitative modeling. A debate on the natures of uncertainty and associated quantification methods. A Generic methodological framework in the industrial world. Industrial system models considered. The central concept of the quantity of interest or risk measure. Generic goals of uncertainty studies. Generic conceptual framework and key steps in any uncertainty study.

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Metrology of environmental emissions. Structural reliability and design margins of a mechanical structure. An educational example — flood risk. Uncertainty quantification, acceptability and precautionary principle.

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Editor's notes The article has been reviewed by Enrico Zio, Roger Flague and a third anonymous referee. Full text PDF 1. Introduction 1 Uncertainty and associated risk assessment is rapidly developing on large-scale industrial or environmental systems along with the dissemination of advanced quantitative modeling in support of decision-making, the increased public awareness or appetite for questioning expertise and the enforcement of tighter safety or environmental control standards.

Zoom Original jpeg, 56k. Figure 3 — generic conceptual framework Zoom Original jpeg, k. Figure 4 — Thermal power plant emissions left and metrological steps right Zoom Original jpeg, 44k. Figure 5 — Flood risk model Zoom Original jpeg, 24k. Various possible approaches to uncertainty treatment of flood levels Zoom Original jpeg, k. Dupuy Dupuy, on the fact that at a certain stage uncertainty is n List of illustrations Title Figure 1: Various possible approaches to uncertainty treatment of flood levels URL http: References Electronic reference E.

About the author E. Copyright Licence Creative Commons Top of page. Browse Index Authors Keywords Sections. Full text issues 8.

An elementary approach to thinking under uncertainty in SearchWorks catalog

A multidisciplinary journal devoted to the study of interactions between environment and society Publisher: Metrological errors Variability of operating conditions. Variability of material properties Randomness of accidental transients Lack of knowledge of fracture mechanical features. Flow Randomness and epistemic uncertainty in the extreme value distribution Lack of knowledge and natural variability of river bed and friction conditions.

Accredit measurement result and comply with metrological criterion Understand and reduce main sources of uncertainty. We will contact you if necessary. To learn more about Copies Direct watch this short online video. How do I find a book?

An Elementary Approach To Thinking Under Uncertainty

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