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| Preface | |
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| Acknowledgements | |
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| Introduction and reading guide | |
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| Notation | |
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| Acronyms and abbreviations | |
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| Applications and practices of modelling, risk and uncertainty | |
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| Protection against natural risk | |
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| The popular 'initiator/frequency approach' | |
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| Recent developments towards an 'extended frequency approach' | |
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| Engineering design, safety and structural reliability analysis (SRA) | |
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| The domain of structural reliability | |
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| Deterministic safety margins and partial safety factors | |
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| Probabilistic structural reliability analysis | |
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| Links and differences with natural risk studies | |
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| Industrial safety, system reliability and probabilistic risk assessment (PRA) | |
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| The context of systems analysis | |
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| Links and differences with structural reliability analysis | |
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| The case of elaborate PRA (multi-state, dynamic) | |
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| Integrated probabilistic risk assessment (IPRA) | |
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| Modelling under uncertainty in metrology, environmental/sanitary assessment and numerical analysis | |
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| Uncertainty and sensitivity analysis (UASA) | |
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| Specificities in metrology/industrial quality control | |
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| Specificities in environmental/health impact assessment | |
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| Numerical code qualification (NCQ), calibration and data assimilation | |
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| Forecast and time-based modelling in weather, operations research, economics or finance | |
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| Conclusion: The scope for generic modelling under risk and uncertainty | |
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| Similar and dissimilar features in modelling, risk and uncertainty studies | |
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| Limitations and challenges motivating a unified framework | |
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| References | |
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| A generic modelling framework | |
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| The system under uncertainty | |
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| Decisional quantities and goals of modelling under risk and uncertainty | |
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| The key concept of risk measure or quantity of interest | |
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| Salient goals of risk/uncertainty studies and decision-making | |
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| Modelling under uncertainty: Building separate system and uncertainty models | |
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| The need to go beyond direct statistics | |
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| Basic system models | |
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| Building a direct uncertainty model on variable inputs | |
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| Developing the underlying epistemic/aleatory structure | |
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| Summary | |
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| Modelling under uncertainty - the general case | |
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| Phenomenological models under uncertainty and residual model error | |
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| The model building process | |
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| Combining system and uncertainty models into an integrated statistical estimation problem | |
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| The combination of system and uncertainty models: A key information choice | |
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| The predictive model combining system and uncertainty components | |
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| Combining probabilistic and deterministic settings | |
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| Preliminary comments about the interpretations of probabilistic uncertainty models | |
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| Mixed deterministic-probabilistic contexts | |
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| Computing an appropriate risk measure or quantity of interest and associated sensitivity indices | |
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| Standard risk measures or q.i. (single-probabilistic) | |
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| A fundamental case: The conditional expected utility | |
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| Relationship between risk measures, uncertainty model and actions | |
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| Double probabilistic risk measures | |
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| The delicate issue of propagation/numerical uncertainty' | |
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| Importance ranking and sensitivity analysis | |
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| Summary: Main steps of the studies and later issues | |
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| Exercises | |
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| References | |
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| A generic tutorial example: Natural risk in an industrial installation | |
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| Phenomenology and motivation of the example | |
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| The hydro component | |
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| The system's reliability component | |
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| The economic component | |
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| Uncertain inputs, data and expertise available | |
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| A short introduction to gradual illustrative modelling steps | |
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| Step one: Natural risk standard statistics | |
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| Step two: Mixing statistics and a QRA model | |
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| Step three: Uncertainty treatment of a physical/engineering model (SRA) | |
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| Step four: Mixing SRA and QRA | |
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| Step five: Level-2 uncertainty study on mixed SRA-QRA model | |
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| Step six: Calibration of the hydro component and updating of risk measure | |
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| Step seven: Economic assessment and optimisation under risk and/or uncertainty | |
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| Summary of the example | |
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| Exercises | |
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| References | |
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| Understanding natures of uncertainty, risk margins and time bases for probabilistic decision-making | |
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| Natures of uncertainty: Theoretical debates and practical implementation | |
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| Defining uncertainty - ambiguity about the reference | |
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| Risk vs. uncertainty - an impractical distinction | |
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| The aleatory/epistemic distinction and the issue of reducibility | |
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| Variability or uncertainty - the need for careful system specification | |
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| Other distinctions | |
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| Understanding the impact on margins of deterministic vs. probabilistic formulations | |
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| Understanding probabilistic averaging, dependence issues and deterministic maximisation and in the linear case | |
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| Understanding safety factors and quantiles in the monotonous case | |
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| Probability limitations, paradoxes of the maximal entropy principle | |
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| Deterministic settings and interval computation � uses and limitations | |
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| Conclusive comments on the use of probabilistic and deterministic risk measures | |
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| Handling time-cumulated risk measures through frequencies and probabilities | |
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| The underlying time basis of the state of the system | |
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| Understanding frequency vs. probability | |
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| Fundamental risk measures defined over a period of interest | |
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| Handling a time process and associated simplifications | |
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| Modelling rare events through extreme value theory | |
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| Choosing an adequate risk measure - decision-theory aspects | |
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| The salient goal involved | |
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| Theoretical debate and interpretations about the risk measure when selecting between risky alternatives (or controlling compliance with a risk target) | |
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| The choice of financial risk measures | |
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| The challenges associated with using double-probabilistic or conditional probabilistic risk measures | |
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| Summary recommendations | |
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| Exercises | |
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| References | |
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| Direct statistical estimation techniques | |
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| The general issue | |
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| Introducing estimation techniques on independent samples | |
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| Estimation basics | |
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| Goodness-of-fit and model selection techniques | |
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| A non-parametric method: Kernel modelling | |
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| Estimating physical variables in the flood example | |
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| Discrete events and time-based statistical models (frequencies, reliability models, time series) | |
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| Encoding phenomenological knowledge and physical constraints inside the choice of input distributions | |
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| Modelling dependence | |
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| Linear correlations | |
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| Rank correlations | |
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| Copula model | |
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| Multi-dimensional non-parametric modelling | |
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| Physical dependence modelling and concluding comments | |
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| Controlling epistemic uncertainty through classical or Bayesian estimators | |
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| Epistemic uncertainty in the classical approach | |
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| Classical approach for Gaussian uncertainty models (small samples) | |
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| Asymptotic covariance for large samples | |
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| Bootstrap and resampling techniques | |
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| Bayesian-physical settings (small samples with expert judgement) | |
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| Understanding rare probabilities and extreme value statistical modelling | |
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| The issue of extrapolating beyond data � advantages and limitations of the extreme value theory | |
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| The significance of extremely low probabilities | |
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| Exercises | |
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| References | |
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| Combined model estimation through inverse techniques | |
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| Introducing inverse techniques | |
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| Handling calibration data | |
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| Motivations for inverse modelling and associated literature | |
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| Key distinctions between the algorithms: The representation of time and uncertainty | |
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| One-dimensional introduction of the gradual inverse algorithms | |
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| Direct least square calibration with two alternative interpretations | |
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| Bayesian updating, identification and calibration | |
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| An alternative identification model with intrinsic uncertainty | |
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| Comparison of the algorithms | |
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| Illustrations in the flood example | |
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| The general structure of inverse algorithms: Residuals, identifiability, estimators, sensitivity and epistemic uncertainty | |
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| The general estimation problem | |
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| Relationship between observational data and predictive outputs for decision-making | |
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| Common features to the distributions and estimation problems associated to the general structure | |
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| Handling residuals and the issue of model uncertainty | |
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| Additional comments on the model-building process | |
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| Identifiability | |
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| Importance factors and estimation accuracy | |
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| Specificities for parameter identification, calibration or data assimilation algorithms | |
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| The BLUE algorithm for linear Gaussian parameter identification | |
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| An extension with unknown variance: Multidimensional model calibration | |
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| Generalisations to non-linear calibration | |
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| Bayesian multidimensional model updating | |
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| Dynamic data assimilation | |
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| Intrinsic variability identification | |
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| A general formulation | |
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| Linearised Gaussian case | |
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| Non-linear Gaussian extensions | |
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| Moment methods | |
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| Recent algorithms and research fields | |
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| Conclusion: The modelling process and open statistical and computing challenges | |
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| Exercises | |
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| References | |
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| Computational methods for risk and uncertainty propagation | |
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| Classifying the risk measure computational issues | |
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| Risk measures in relation to conditional and combined uncertainty distributions | |
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| Expectation-based single probabilistic risk measures | |
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| Simplified integration of sub-parts with discrete inputs | |
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| Non-expectation based single probabilistic risk measures | |
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| Other risk measures (double probabilistic, mixed deterministic-probabilistic) | |
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| The generic Monte-Carlo simulation method and associated error control | |
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| Undertaking Monte-Carlo simulation on a computer | |
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| Dual interpretation and probabilistic properties of Monte-Carlo simulation | |
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| Control of propagation uncertainty: Asymptotic results | |
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| Control of propagation uncertainty: Robust results for quantiles (Wilks formula) | |
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| Sampling double-probabilistic risk measures | |
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| Sampling mixed deterministic-probabilistic measures | |
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| Classical alternatives to direct Monte-Carlo sampling | |
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| Overview of the computation alternatives to MCS | |
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| Taylor approximation (linear or polynomial system models) | |
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| Numerical integration | |
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| Accelerated sampling (or variance reduction) | |
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| Reliability methods (FORM-SORM and derived methods) | |
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| Polynomial chaos and stochastic developments | |
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| Response surface or meta-models | |
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| Monotony, regularity and robust risk measure computation | |
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| Simple examples of monotonous behaviours | |
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| Direct consequences of monotony for computing the risk measure | |
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| Robust computation of exceedance probability in the monotonous case | |
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| Use of other forms of system model regularity | |
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| Sensitivity analysis and importance ranking | |
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| Elementary indices and importance measures and then-equivalence in linear system models | |
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| Sobol sensitivity indices | |
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| Specificities of Boolean input/output events � importance measures in risk assessment | |
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| Concluding remarks and further research | |
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| Numerical challenges, distributed computing and use of direct or adjoint differentiation of codes | |
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| Exercises | |
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| References | |
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| Optimising under uncertainty: Economics and computational challenges | |
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| Getting the costs inside risk modelling - from engineering economics to financial modelling | |
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| Moving to costs as output variables of interest � elementary engineering economics | |
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| Costs of uncertainty and the value of information | |
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| The expected utility approach for risk aversion | |
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| Non-linear transformations | |
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| Robust design and alternatives mixing cost expectation and variance inside the optimisation procedure | |
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| The role of time - cash flows and associated risk measures | |
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| Costs over a time period - the cash flow model | |
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| The issue of discounting | |
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| Valuing time flexibility of decision-making and stochastic optimisation | |
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| Computational challenges associated to optimisation | |
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| Static optimisation (utility-based) | |
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| Stochastic dynamic programming | |
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| Computation and robustness challenges | |
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| The promise of high performance computing | |
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| The computational load of risk and uncertainty modelling | |
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| The potential of high-performance computing | |
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| Exercises | |
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| References | |
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| Conclusion: Perspectives of modelling in the context of risk and uncertainty and further research | |
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| Open scientific challenges | |
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| Challenges involved by the dissemination of advanced modelling in the context of risk and uncertainty | |
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| References | |
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| Annexes | |
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| Annex 1 - refresher on probabilities and statistical modelling of uncertainty | |
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| Modelling through a random variable | |
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| The impact of data and the estimation uncertainty | |
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| Continuous probabilistic distributions | |
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| Dependence and stationarity | |
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| Non-statistical approach of probabilistic modelling | |
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| Annex 2 - comments about the probabilistic foundations of the uncertainty models | |
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| The overall space of system states and the output space | |
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| Correspondence to the Kaplan/Garrick risk analysis triplets | |
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| The model and model input space | |
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| Estimating the uncertainty model through direct data | |
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| Model calibration and estimation through indirect data and inversion techniques | |
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| Annex 3 - introductory reflections on the sources of macroscopic uncertainty | |
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| Annex 4 - details about the pedagogical example | |
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| Data samples | |
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| Reference probabilistic model for the hydro component | |
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| Systems reliability component - expert information on elementary failure probabilities | |
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| Economic component - cost functions and probabilistic model | |
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| Detailed results on various steps | |
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| Annex 5 - detailed mathematical demonstrations | |
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| Basic results about vector random variables and matrices | |
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| Differentiation results and solutions of quadratic likelihood maximisation | |
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| Proof of the Wilks formula | |
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| Complements on the definition and chaining of monotony | |
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| Proofs on level-2 quantiles of monotonous system models | |
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| Proofs on the estimator of adaptive Monte-Carlo under monotony (section 7.4.3) | |
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| References | |
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| Epilogue | |
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| Index | |