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

Book Description

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.

Table of Contents

  1. Cover
  2. Wiley Series in Probability and Statistics
  3. Title Page
  4. Copyright
  5. Dedication
  6. Preface
  7. Acknowledgements
  8. Introduction and Reading Guide
    1. 1 The Scope of Risk and Uncertainty Considered
    2. 2 A Journey Through an Uncertain Reality
    3. 3 The Generic Methodological Approach of the Book
    4. 4 Book Positioning and Related Literature
    5. 5 A Reading Guide Through the Chapters
    6. References
  9. Notation
  10. Acronyms and Abbreviations
  11. Chapter 1: Applications and Practices of Modelling, Risk and Uncertainty
    1. 1.1 Protection Against Natural Risk
    2. 1.2 Engineering Design, Safety and Structural Reliability Analysis (SRA)
    3. 1.3 Industrial Safety, System Reliability and Probabilistic Risk Assessment (PRA)
    4. 1.4 Modelling Under Uncertainty in Metrology, Environmental/Sanitary Assessment and Numerical Analysis
    5. 1.5 Forecast and Time-Based Modelling in Weather, Operations Research, Economics or Finance
    6. 1.6 Conclusion: The Scope for Generic Modelling Under Risk and Uncertainty
    7. References
  12. Chapter 2: A Generic Modelling Framework
    1. 2.1 The System Under Uncertainty
    2. 2.2 Decisional Quantities and Goals of Modelling Under Risk and Uncertainty
    3. 2.3 Modelling Under Uncertainty: Building Separate System and Uncertainty Models
    4. 2.4 Modelling Under Uncertainty – The General Case
    5. 2.5 Combining Probabilistic and Deterministic Settings
    6. 2.6 Computing an Appropriate Risk Measure or Quantity of Interest and Associated Sensitivity Indices
    7. 2.7 Summary: Main Steps of the Studies and Later Issues
    8. References
  13. Chapter 3: A Generic Tutorial Example: Natural Risk in an Industrial Installation
    1. 3.1 Phenomenology and Motivation of the Example
    2. 3.2 A Short Introduction to Gradual Illustrative Modelling Steps
    3. 3.3 Summary of the Example
    4. References
  14. Chapter 4: Understanding Natures of Uncertainty, Risk Margins and Time Bases for Probabilistic Decision-Making
    1. 4.1 Natures of Uncertainty: Theoretical Debates and Practical Implementation
    2. 4.2 Understanding the Impact on Margins of Deterministic vs. Probabilistic Formulations
    3. 4.3 Handling Time-Cumulated Risk Measures Through Frequencies and Probabilities
    4. 4.4 Choosing an Adequate Risk Measure – Decision-Theory Aspects
    5. References
  15. Chapter 5: Direct Statistical Estimation Techniques
    1. 5.1 The General Issue
    2. 5.2 Introducing Estimation Techniques on Independent Samples
    3. 5.3 Modelling Dependence
    4. 5.4 Controlling Epistemic Uncertainty Through Classical or Bayesian Estimators
    5. 5.5 Understanding Rare Probabilities and Extreme Value Statistical Modelling
    6. References
  16. Chapter 6: Combined Model Estimation Through Inverse Techniques
    1. 6.1 Introducing Inverse Techniques
    2. 6.2 One-Dimensional Introduction of the Gradual Inverse Algorithms
    3. 6.3 The General Structure of Inverse Algorithms: Residuals, Identifiability, Estimators, Sensitivity and Epistemic Uncertainty
    4. 6.4 Specificities for Parameter Identification, Calibration or Data Assimilation Algorithms
    5. 6.5 Intrinsic Variability Identification
    6. 6.6 Conclusion: The Modelling Process and Open Statistical and Computing Challenges
    7. References
  17. Chapter 7: Computational Methods for Risk and Uncertainty Propagation
    1. 7.1 Classifying the Risk Measure Computational Issues
    2. 7.2 The Generic Monte-Carlo Simulation Method and Associated Error Control
    3. 7.3 Classical Alternatives to Direct Monte-Carlo sampling
    4. 7.4 Monotony, Regularity and Robust Risk Measure Computation
    5. 7.5 Sensitivity Analysis and Importance Ranking
    6. 7.6 Numerical Challenges, Distributed Computing and use of Direct or Adjoint Differentiation of Codes
    7. References
  18. Chapter 8: Optimising under Uncertainty: Economics and Computational Challenges
    1. 8.1 Getting the Costs Inside Risk Modelling – from Engineering Economics to Financial Modelling
    2. 8.2 The Role of Time – Cash Flows and Associated Risk Measures
    3. 8.3 Computational Challenges Associated to Optimisation
    4. 8.4 The Promise of High Performance Computing
    5. Exercises
    6. References
  19. Chapter 9: Conclusion: Perspectives of Modelling in the Context of Risk and Uncertainty and Further Research
    1. 9.1 Open Scientific Challenges
    2. 9.2 Challenges Involved by the Dissemination of Advanced Modelling in the Context of Risk and Uncertainty
    3. References
  20. Chapter 10: Annexes
    1. 10.1 Annex 1 – Refresher on Probabilities and Statistical Modelling of Uncertainty
    2. 10.2 Annex 2 – Comments About the Probabilistic Foundations of the Uncertainty Models
    3. 10.3 Annex 3 – Introductory Reflections on the Sources of Macroscopic Uncertainty
    4. 10.4 Annex 4 – Details about the Pedagogical Example
    5. 10.5 Annex 5 – Detailed Mathematical Demonstrations
    6. References
  21. Epilogue
  22. Index