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Probabilistic Risk Analysis and Bayesian Decision Theory

  • Book
  • © 2022

Overview

Authors:
  1. Marcel van Oijen

    1. Edinburgh, UK

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    You can also search for this author in PubMed   Google Scholar

  2. Mark Brewer

    1. BioSS Office, The James Hutton Institute, Aberdeen, UK

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    You can also search for this author in PubMed   Google Scholar

  • Introduces a new theory of probabilistic risk analysis that is rigorous and versatile
  • Explains how risk analysis is related to Bayesian decision theory
  • Provides many examples, all with R-code

Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter 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
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Keywords

About this book

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.

Authors and Affiliations

  • Edinburgh, UK

    Marcel van Oijen

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

    Mark Brewer

About the authors

​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).

Bibliographic Information

  • Book Title: Probabilistic Risk Analysis and Bayesian Decision Theory

  • Authors: Marcel van Oijen, Mark Brewer

  • Series Title: SpringerBriefs in Statistics

  • DOI: https://doi.org/10.1007/978-3-031-16333-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Softcover ISBN: 978-3-031-16332-6Published: 24 November 2022

  • eBook ISBN: 978-3-031-16333-3Published: 23 November 2022

  • Series ISSN: 2191-544X

  • Series E-ISSN: 2191-5458

  • Edition Number: 1

  • Number of Pages: XIII, 114

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Statistical Theory and Methods, Biostatistics, Bayesian Inference

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