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Modelling under Risk and Uncertainty An Introduction to Statistical, Phenomenological and Computational Methods

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ISBN-10: 0470695145

ISBN-13: 9780470695142

Edition: 2012

Authors: Etienne de Rocquigny

List price: $79.50
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Description:

There is a growing demand from institutional bodies for the justification of industrial methodologies and practices (e.g., safety criteria, environmental protection and control, maintenance, and design optimization). Previous books in this area have either been too theoretical, or too specific in their scope. This book aims to provide a practical reference on uncertainty treatment for all types of industry, enabling the adoption of universal practices. The text is built upon a wide range of examples taken from within relevant industries, including nuclear technology, aeronautics, civil structures, and mechanical engineering.
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Book details

List price: $79.50
Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 4/19/2012
Binding: Hardcover
Pages: 484
Size: 6.75" wide x 10.00" long x 1.25" tall
Weight: 1.892
Language: English

#60;b#62;Shahra Razavi#60;/b#62; is Senior Researcher at the United Nations Research Institute for Social Development (UNRISD). She specializes in the gender dimensions of social development, with a particular focus on livelihoods and social policy. Her recent books include #60;i#62;The Gendered Impacts of Liberalization: Towards "Embedded Liberalism"?#60;/i#62; (2009) and #60;i#62;Gender and Social Policy in a Global Context: Uncovering the Gendered Structure of 'the Social'#60;/i#62;, edited with Shireen Hassim (2006).#60;p#62;

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