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Probabilistic Risk Analysis and Bayesian Decision Theory

Part of the SpringerBriefs in Statistics Book Series

DOI: 10.1007/978-3-031-16333-3

ISBN: 978-3-031-16332-6

Publisher: Springer International Publishing - Springer Journals

Aug 31, 2022

1 - 10 of 19 Chapters

LitStream

Chapter 1Introduction to Probabilistic Risk Analysis (PRA)

van Oijen, Marcel; Brewer, Mark

Pages: 1 –7

[In this book, we use the common definition of risk as the expectation of loss or damage due to some hazard (UN, Internationally agreed glossary of basic terms related to disaster management. Department of Humanitarian Affairs, Geneva, 1992). Risk analysis seeks to decompose a risk into its...
LitStream

Chapter 2Distribution-Based Single-Threshold PRA

van Oijen, Marcel; Brewer, Mark

Pages: 9 –14

[Equation (1.3) shows that the key probability distributions for basic PRA are p[z|x < thr] and p[z|x ≥ thr].]
LitStream

Chapter 3Sampling-Based Single-Threshold PRA

van Oijen, Marcel; Brewer, Mark

Pages: 15 –18

[In applications, we do not have a pre-specified joint distribution for x and z, but we have a sample of observations as in the left panel of Fig. 3.1. So we cannot use the functions defined above for the distribution-based PRA. Instead, we must estimate the PRA-integrals by sampling. The...
LitStream

Chapter 4Sampling-Based Single-Threshold PRA: Uncertainty Quantification (UQ)

van Oijen, Marcel; Brewer, Mark

Pages: 19 –28

[Uncertainty in sampling-based expectations may be quantified as the standard deviations of the sample means, see Eq. (4.1).]
LitStream

Chapter 5Density Estimation to Move from Sampling- to Distribution-Based PRA

van Oijen, Marcel; Brewer, Mark

Pages: 29 –30

[Our approach to sampling-based single-threshold PRA with UQ in Chap. 4 was to take a collection of n data pairs (x, z), define a hazardous region H, and estimate p[H], V and R as, respectively, n∕nH, z¬H¯−zH¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}...
LitStream

Chapter 6Copulas for Distribution-Based PRA

van Oijen, Marcel; Brewer, Mark

Pages: 31 –37

[Our development of probabilistic risk analysis in this book centers on the joint probability distribution for an environmental variable x and a system variable z. This joint distribution, together with a decision on what values of x constitute hazardous conditions, is all the information we need...
LitStream

Chapter 7Bayesian Model-Based PRA

van Oijen, Marcel; Brewer, Mark

Pages: 39 –43

[In practice, given a particular data set we will want to model the relationship between outcome/response variables and associated explanatory variables. We can then use this model to conduct our PRA. We will illustrate this using the existing linear (bivariate Gaussian) and nonlinear examples.]
LitStream

Chapter 8Sampling-Based Multi-Threshold PRA: Gaussian Linear Example

van Oijen, Marcel; Brewer, Mark

Pages: 45 –47

[In this section, we carry out multi-threshold PRA which distinguishes multiple levels of hazard, such that H is the union of H1, ..Hn. The relevant Eqs. (1.4) and (1.5) were already shown in Chap. 1.]
LitStream

Chapter 9Distribution-Based Continuous PRA: Gaussian Linear Example

van Oijen, Marcel; Brewer, Mark

Pages: 49 –50

[We now turn to continuous PRA, which can be viewed as the limit of multi-threshold PRA when the number of thresholds goes to infinity. We already showed the equations for continuous PRA above (Eqs. (1.6) and (1.7)), and implement this form of PRA now for the same bivariate Gaussian that we...
LitStream

Chapter 10Categorical PRA with Other Splits than for Threshold-Levels: Spatio-Temporal Example

van Oijen, Marcel; Brewer, Mark

Pages: 51 –56

[In multi-threshold PRA, we split up the hazardous region H (defined by some highest threshold-value) into a range of intervals for the environmental variable x. But other ways of splitting up H can be envisaged too. We may for example think of how lag-effects and cumulative effects of hazards...

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