Probabilistic Risk Analysis and Bayesian Decision Theory

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction to Probabilistic Risk Analysis (PRA)

   • Marcel van Oijen, Mark Brewer

   Pages 1-7

3. Distribution-Based Single-Threshold PRA

   • Marcel van Oijen, Mark Brewer

   Pages 9-14

4. Sampling-Based Single-Threshold PRA

   • Marcel van Oijen, Mark Brewer

   Pages 15-18

5. Sampling-Based Single-Threshold PRA: Uncertainty Quantification (UQ)

   • Marcel van Oijen, Mark Brewer

   Pages 19-28

6. Density Estimation to Move from Sampling- to Distribution-Based PRA

   • Marcel van Oijen, Mark Brewer

   Pages 29-30

7. Copulas for Distribution-Based PRA

   • Marcel van Oijen, Mark Brewer

   Pages 31-37

8. Bayesian Model-Based PRA

   • Marcel van Oijen, Mark Brewer

   Pages 39-43

9. Sampling-Based Multi-Threshold PRA: Gaussian Linear Example

   • Marcel van Oijen, Mark Brewer

   Pages 45-47

10. Distribution-Based Continuous PRA: Gaussian Linear Example

    • Marcel van Oijen, Mark Brewer

    Pages 49-50

11. Categorical PRA with Other Splits than for Threshold-Levels: Spatio-Temporal Example

    • Marcel van Oijen, Mark Brewer

    Pages 51-56

12. Three-Component PRA

    • Marcel van Oijen, Mark Brewer

    Pages 57-59

13. Introduction to Bayesian Decision Theory (BDT)

    • Marcel van Oijen, Mark Brewer

    Pages 61-65

14. Implementation of BDT Using Bayesian Networks

    • Marcel van Oijen, Mark Brewer

    Pages 67-76

15. A Spatial Example: Forestry in Scotland

    • Marcel van Oijen, Mark Brewer

    Pages 77-83

16. Spatial BDT Using Model and Emulator

    • Marcel van Oijen, Mark Brewer

    Pages 85-87

17. Linkages Between PRA and BDT

    • Marcel van Oijen, Mark Brewer

    Pages 89-93

18. PRA vs. BDT in the Spatial Example

    • Marcel van Oijen, Mark Brewer

    Pages 95-98

19. Three-Component PRA in the Spatial Example

    • Marcel van Oijen, Mark Brewer

    Pages 99-100

20. Discussion

    • Marcel van Oijen, Mark Brewer

    Pages 101-106

The book shows how risk, defined as the statistical expectation of loss, can be formally decomposed as the product of two terms: hazard probability and system vulnerability. This requires a specific definition of vulnerability that replaces the many fuzzy definitions abounding in the literature. The approach is expanded to more complex risk analysis with three components rather than two, and with various definitions of hazard. Equations are derived to quantify the uncertainty of each risk component and show how the approach relates to Bayesian decision theory. Intended for statisticians, environmental scientists and risk analysts interested in the theory and application of risk analysis, this book provides precise definitions, new theory, and many examples with full computer code. The approach is based on straightforward use of probability theory which brings rigour and clarity. Only a moderate knowledge and understanding of probability theory is expected from the reader.

• Bayesian Methods
• Decision Theory
• Hazards
• Probability Theory
• Risk Analysis
• System Vulnerability
• Uncertainty Quantification
• Utility

• Edinburgh, UK

  Marcel van Oijen

• BioSS Office, The James Hutton Institute, Aberdeen, UK

  Mark Brewer

​Marcel van Oijen studied mathematical biology at the University of Utrecht, graduating cum laude in 1985. He completed his PhD in plant disease epidemiology at Wageningen University, where he then worked on modelling the impacts of environmental change on crops. In 1999, he moved to Edinburgh where he was a senior scientist for the UK’s Natural Environment Research Council, focusing on the use of Bayesian methods in the modelling of ecosystem services provided by grasslands, forests and agroforestry systems. He is now an independent researcher and this is his second book, following the publication in 2020 of ‘Bayesian Compendium’, an introductory guide to the universality of Bayesian methods. 

Mark Brewer is director of BioSS (Biomathematics and Statistics Scotland). His first degree was in Probability and Statistics from the University of Sheffield, and Mark subsequently studied for a PhD in statistics - specialising in MCMC and graphical models - at the University of Edinburgh. After three years working in statistical consultancy at the University of Aberdeen and five years as a lecturer in statistics at the University of Exeter, in 2001 Mark moved to BioSS as a senior statistician. He has worked mainly in ecological and environmental applications, conducting research in spatio-temporal and Bayesian modelling. He became head of BioSS in 2018, and has seen the organisation increase both its funding and staffing complement since that time. Mark acted as co-Editor for Biometrics (2019-2021) and was previously on the Executive Board of the International Biometric Society (2017-2020).