Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods -- Contents -- Preface -- Acknowledgements -- Introduction and reading guide -- Notation -- Acronyms and abbreviations -- 1 Applications and practices of modelling, risk and uncertainty -- 1.1 Protection against natural risk -- 1.1.1 The popular 'initiator/frequency approach' -- 1.1.2 Recent developments towards an 'extended frequency approach' -- 1.2 Engineering design, safety and structural reliability analysis (SRA) -- 1.2.1 The domain of structural reliability -- 1.2.2 Deterministic safety margins and partial safety factors -- 1.2.3 Probabilistic structural reliability analysis -- 1.2.4 Links and differences with natural risk studies -- 1.3 Industrial safety, system reliability and probabilistic risk assessment (PRA) -- 1.3.1 The context of systems analysis -- 1.3.2 Links and differences with structural reliability analysis -- 1.3.3 The case of elaborate PRA (multi-state, dynamic) -- 1.3.4 Integrated probabilistic risk assessment (IPRA) -- 1.4 Modelling under uncertainty in metrology, environmental/sanitary assessment and numerical analysis -- 1.4.1 Uncertainty and sensitivity analysis (UASA) -- 1.4.2 Specificities in metrology/industrial quality control -- 1.4.3 Specificities in environmental/health impact assessment -- 1.4.4 Numerical code qualification (NCQ), calibration and data assimilation -- 1.5 Forecast and time-based modelling in weather, operations research, economics or finance -- 1.6 Conclusion: The scope for generic modelling under risk and uncertainty -- 1.6.1 Similar and dissimilar features in modelling, risk and uncertainty studies -- 1.6.2 Limitations and challenges motivating a unified framework -- References -- 2 A generic modelling framework -- 2.1 The system under uncertainty.

2.2 Decisional quantities and goals of modelling under risk and uncertainty -- 2.2.1 The key concept of risk measure or quantity of interest -- 2.2.2 Salient goals of risk/uncertainty studies and decision-making -- 2.3 Modelling under uncertainty: Building separate system and uncertainty models -- 2.3.1 The need to go beyond direct statistics -- 2.3.2 Basic system models -- 2.3.3 Building a direct uncertainty model on variable inputs -- 2.3.4 Developing the underlying epistemic/aleatory structure -- 2.3.5 Summary -- 2.4 Modelling under uncertainty - the general case -- 2.4.1 Phenomenological models under uncertainty and residual model error -- 2.4.2 The model building process -- 2.4.3 Combining system and uncertainty models into an integrated statistical estimation problem -- 2.4.4 The combination of system and uncertainty models: A key information choice -- 2.4.5 The predictive model combining system and uncertainty components -- 2.5 Combining probabilistic and deterministic settings -- 2.5.1 Preliminary comments about the interpretations of probabilistic uncertainty models -- 2.5.2 Mixed deterministic-probabilistic contexts -- 2.6 Computing an appropriate risk measure or quantity of interest and associated sensitivity indices -- 2.6.1 Standard risk measures or q.i. (single-probabilistic) -- 2.6.2 A fundamental case: The conditional expected utility -- 2.6.3 Relationship between risk measures, uncertainty model and actions -- 2.6.4 Double probabilistic risk measures -- 2.6.5 The delicate issue of propagation/numerical uncertainty -- 2.6.6 Importance ranking and sensitivity analysis -- 2.7 Summary: Main steps of the studies and later issues -- Exercises -- References -- 3 A generic tutorial example: Natural risk in an industrial installation -- 3.1 Phenomenology and motivation of the example -- 3.1.1 The hydro component.

3.1.2 The system's reliability component -- 3.1.3 The economic component -- 3.1.4 Uncertain inputs, data and expertise available -- 3.2 A short introduction to gradual illustrative modelling steps -- 3.2.1 Step one: Natural risk standard statistics -- 3.2.2 Step two: Mixing statistics and a QRA model -- 3.2.3 Step three: Uncertainty treatment of a physical/engineering model (SRA) -- 3.2.4 Step four: Mixing SRA and QRA -- 3.2.5 Step five: Level-2 uncertainty study on mixed SRA-QRA model -- 3.2.6 Step six: Calibration of the hydro component and updating of risk measure -- 3.2.7 Step seven: Economic assessment and optimisation under risk and/or uncertainty -- 3.3 Summary of the example -- Exercises -- References -- 4 Understanding natures of uncertainty, risk margins and time bases for probabilistic decision-making -- 4.1 Natures of uncertainty: Theoretical debates and practical implementation -- 4.1.1 Defining uncertainty - ambiguity about the reference -- 4.1.2 Risk vs. uncertainty - an impractical distinction -- 4.1.3 The aleatory/epistemic distinction and the issue of reducibility -- 4.1.4 Variability or uncertainty - the need for careful system specification -- 4.1.5 Other distinctions -- 4.2 Understanding the impact on margins of deterministic vs. probabilistic formulations -- 4.2.1 Understanding probabilistic averaging, dependence issues and deterministic maximisation and in the linear case -- 4.2.2 Understanding safety factors and quantiles in the monotonous case -- 4.2.3 Probability limitations, paradoxes of the maximal entropy principle -- 4.2.4 Deterministic settings and interval computation - uses and limitations -- 4.2.5 Conclusive comments on the use of probabilistic and deterministic risk measures -- 4.3 Handling time-cumulated risk measures through frequencies and probabilities.

4.3.1 The underlying time basis of the state of the system -- 4.3.2 Understanding frequency vs. probability -- 4.3.3 Fundamental risk measures defined over a period of interest -- 4.3.4 Handling a time process and associated simplifications -- 4.3.5 Modelling rare events through extreme value theory -- 4.4 Choosing an adequate risk measure - decision-theory aspects -- 4.4.1 The salient goal involved -- 4.4.2 Theoretical debate and interpretations about the risk measure when selecting between risky alternatives (or controlling compliance with a risk target) -- 4.4.3 The choice of financial risk measures -- 4.4.4 The challenges associated with using double-probabilistic or conditional probabilistic risk measures -- 4.4.5 Summary recommendations -- Exercises -- References -- 5 Direct statistical estimation techniques -- 5.1 The general issue -- 5.2 Introducing estimation techniques on independent samples -- 5.2.1 Estimation basics -- 5.2.2 Goodness-of-fit and model selection techniques -- 5.2.3 A non-parametric method: Kernel modelling -- 5.2.4 Estimating physical variables in the flood example -- 5.2.5 Discrete events and time-based statistical models (frequencies, reliability models, time series) -- 5.2.6 Encoding phenomenological knowledge and physical constraints inside the choice of input distributions -- 5.3 Modelling dependence -- 5.3.1 Linear correlations -- 5.3.2 Rank correlations -- 5.3.3 Copula model -- 5.3.4 Multi-dimensional non-parametric modelling -- 5.3.5 Physical dependence modelling and concluding comments -- 5.4 Controlling epistemic uncertainty through classical or Bayesian estimators -- 5.4.1 Epistemic uncertainty in the classical approach -- 5.4.2 Classical approach for Gaussian uncertainty models (small samples) -- 5.4.3 Asymptotic covariance for large samples -- 5.4.4 Bootstrap and resampling techniques.

5.4.5 Bayesian-physical settings (small samples with expert judgement) -- 5.5 Understanding rare probabilities and extreme value statistical modelling -- 5.5.1 The issue of extrapolating beyond data - advantages and limitations of the extreme value theory -- 5.5.2 The significance of extremely low probabilities -- Exercises -- References -- 6 Combined model estimation through inverse techniques -- 6.1 Introducing inverse techniques -- 6.1.1 Handling calibration data -- 6.1.2 Motivations for inverse modelling and associated literature -- 6.1.3 Key distinctions between the algorithms: The representation of time and uncertainty -- 6.2 One-dimensional introduction of the gradual inverse algorithms -- 6.2.1 Direct least square calibration with two alternative interpretations -- 6.2.2 Bayesian updating, identification and calibration -- 6.2.3 An alternative identification model with intrinsic uncertainty -- 6.2.4 Comparison of the algorithms -- 6.2.5 Illustrations in the flood example -- 6.3 The general structure of inverse algorithms: Residuals, identifiability, estimators, sensitivity and epistemic uncertainty -- 6.3.1 The general estimation problem -- 6.3.2 Relationship between observational data and predictive outputs for decision-making -- 6.3.3 Common features to the distributions and estimation problems associated to the general structure -- 6.3.4 Handling residuals and the issue of model uncertainty -- 6.3.5 Additional comments on the model-building process -- 6.3.6 Identifiability -- 6.3.7 Importance factors and estimation accuracy -- 6.4 Specificities for parameter identification, calibration or data assimilation algorithms -- 6.4.1 The BLUE algorithm for linear Gaussian parameter identification -- 6.4.2 An extension with unknown variance: Multidimensional model calibration -- 6.4.3 Generalisations to non-linear calibration.

6.4.4 Bayesian multidimensional model updating.

Modelling has permeated virtually all areas of industrial, environmental, economic, bio-medical or civil engineering: yet the use of models for decision-making raises a number of issues to which this book is dedicated: How uncertain is my model ? Is it truly valuable to support decision-making ? What kind of decision can be truly supported and how can I handle residual uncertainty ? How much refined should the mathematical description be, given the true data limitations ? Could the uncertainty be reduced through more data, increased modeling investment or computational budget ? Should it be reduced now or later ? How robust is the analysis or the computational methods involved ? Should / could those methods be more robust ? Does it make sense to handle uncertainty, risk, lack of knowledge, variability or errors altogether ? How reasonable is the choice of probabilistic modeling for rare events ? How rare are the events to be considered ? How far does it make sense to handle extreme events and elaborate confidence figures ? Can I take advantage of expert / phenomenological knowledge to tighten the probabilistic figures ? Are there connex domains that could provide models or inspiration for my problem ? Written by a leader at the crossroads of industry, academia and engineering, and based on decades of multi-disciplinary field experience, Modelling Under Risk and Uncertainty gives a self-consistent introduction to the methods involved by any type of modeling development acknowledging the inevitable uncertainty and associated risks. It goes beyond the "black-box" view that some analysts, modelers, risk experts or statisticians develop on the underlying phenomenology of the environmental or industrial processes, without valuing enough their physical properties and inner modelling potential nor challenging the practical plausibility of

mathematical hypotheses; conversely it is also to attract environmental or engineering modellers to better handle model confidence issues through finer statistical and risk analysis material taking advantage of advanced scientific computing, to face new regulations departing from deterministic design or support robust decision-making. Modelling Under Risk and Uncertainty: Addresses a concern of growing interest for large industries, environmentalists or analysts: robust modeling for decision-making in complex systems. Gives new insights into the peculiar mathematical and computational challenges generated by recent industrial safety or environmental control analysis for rare events. Implements decision theory choices differentiating or aggregating the dimensions of risk/aleatory and epistemic uncertainty through a consistent multi-disciplinary set of statistical estimation, physical modelling, robust computation and risk analysis. Provides an original review of the advanced inverse probabilistic approaches for model identification, calibration or data assimilation, key to digest fast-growing multi-physical data acquisition. Illustrated with one favourite pedagogical example crossing natural risk, engineering and economics, developed throughout the book to facilitate the reading and understanding. Supports Master/PhD-level course as well as advanced tutorials for professional training Analysts and researchers in numerical modeling, applied statistics, scientific computing, reliability, advanced engineering, natural risk or environmental science will benefit from this book.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.