Modelling Under Risk and Uncertainty

Preface xv Acknowledgements xvii Introduction and reading guide xix Notation xxxiii Acronyms and abbreviations xxxvii 1 Applications and practices of modelling, risk and uncertainty 1 1.1 Protection against natural risk 1 1.2 Engineering design, safety and structural reliability analysis (SRA) 7 1.3 Industrial safety, system reliability and probabilistic risk assessment (PRA) 12 1.4 Modelling under uncertainty in metrology, environmental/sanitary assessment and numerical analysis 20 1.5 Forecast and time-based modelling in weather, operations research, economics or finance 27 1.6 Conclusion: The scope for generic modelling under risk and uncertainty 28 References 31 2 A generic modelling framework 34 2.1 The system under uncertainty 34 2.2 Decisional quantities and goals of modelling under risk and uncertainty 37 2.3 Modelling under uncertainty: Building separate system and uncertainty models 41 2.4 Modelling under uncertainty - the general case 50 2.5 Combining probabilistic and deterministic settings 60 2.6 Computing an appropriate risk measure or quantity of interest and associated sensitivity indices 64 2.7 Summary: Main steps of the studies and later issues 73 Exercises 74 References 75 3 A generic tutorial example: Natural risk in an industrial installation 77 3.1 Phenomenology and motivation of the example 77 3.2 A short introduction to gradual illustrative modelling steps 86 3.3 Summary of the example 99 Exercises 101 References 101 4 Understanding natures of uncertainty, risk margins and time bases for probabilistic decision-making 102 4.1 Natures of uncertainty: Theoretical debates and practical implementation 103 4.2 Understanding the impact on margins of deterministic vs. probabilistic formulations 110 4.3 Handling time-cumulated risk measures through frequencies and probabilities 121 4.4 Choosing an adequate risk measure - decision-theory aspects 135 Exercises 140 References 141 5 Direct statistical estimation techniques 143 5.1 The general issue 143 5.2 Introducing estimation techniques on independent samples 147 5.3 Modelling dependence 165 5.4 Controlling epistemic uncertainty through classical or Bayesian estimators 175 5.5 Understanding rare probabilities and extreme value statistical modelling 194 Exercises 203 References 204 6 Combined model estimation through inverse techniques 206 6.1 Introducing inverse techniques 206 6.2 One-dimensional introduction of the gradual inverse algorithms 216 6.3 The general structure of inverse algorithms: Residuals, identifiability, estimators, sensitivity and epistemic uncertainty 233 6.4 Specificities for parameter identification, calibration or data assimilation algorithms 251 6.5 Intrinsic variability identification 260 6.6 Conclusion: The modelling process and open statistical and computing challenges 267 Exercises 267 References 268 7 Computational methods for risk and uncertainty propagation 271 7.1 Classifying the risk measure computational issues 272 7.2 The generic Monte-Carlo simulation method and associated error control 283 7.3 Classical alternatives to direct Monte-Carlo sampling 299 7.4 Monotony, regularity and robust risk measure computation 317 7.5 Sensitivity analysis and importance ranking 330 7.6 Numerical challenges, distributed computing and use of direct or adjoint differentiation of codes 342 Exercises 342 References 343 8 Optimising under uncertainty: Economics and computational challenges 347 8.1 Getting the costs inside risk modelling - from engineering economics to financial modelling 347 8.2 The role of time - cash flows and associated risk measures 358 8.3 Computational challenges associated to optimisation 366 8.4 The promise of high performance computing 369 Exercises 372 References 372 9 Conclusion: Perspectives of modelling in the context of risk and uncertainty and further research 374 9.1 Open scientific challenges 374 9.2 Challenges involved by the dissemination of advanced modelling in the context of risk and uncertainty 377 References 377 10 Annexes 378 10.1 Annex 1 - refresher on probabilities and statistical modelling of uncertainty 378 10.2 Annex 2 - comments about the probabilistic foundations of the uncertainty models 386 10.3 Annex 3 - introductory reflections on the sources of macroscopic uncertainty 394 10.4 Annex 4 - details about the pedagogical example 397 10.5 Annex 5 - detailed mathematical demonstrations 414 References 426 Epilogue 427 Index 429