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Titlebook: Probabilistic Risk Analysis and Bayesian Decision Theory; Marcel van Oijen,Mark Brewer Book 2022 The Author(s), under exclusive license to

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发表于 2025-3-21 18:31:07 | 显示全部楼层 |阅读模式
书目名称Probabilistic Risk Analysis and Bayesian Decision Theory
编辑Marcel van Oijen,Mark Brewer
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概述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
丛书名称SpringerBriefs in Statistics
图书封面Titlebook: Probabilistic Risk Analysis and Bayesian Decision Theory;  Marcel van Oijen,Mark Brewer Book 2022 The Author(s), under exclusive license to
描述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.
出版日期Book 2022
关键词Bayesian Methods; Decision Theory; Hazards; Probability Theory; Risk Analysis; System Vulnerability; Uncer
版次1
doihttps://doi.org/10.1007/978-3-031-16333-3
isbn_softcover978-3-031-16332-6
isbn_ebook978-3-031-16333-3Series ISSN 2191-544X Series E-ISSN 2191-5458
issn_series 2191-544X
copyrightThe Author(s), under exclusive license to Springer Nature Switzerland AG 2022
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发表于 2025-3-22 01:23:37 | 显示全部楼层
PRA vs. BDT in the Spatial Example,use irrigation in those locations where it increases the expectation for utility .[.], calculated from the 19 years of data. We aim to show that locations where irrigation increases .[.] are also the locations where it decreases the ... that we defined in Chap. ..
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Sampling-Based Single-Threshold PRA,es .[.] are then replaced by normalised frequencies, but we shall denote those with .[.] too. Say the total number of (., .) observations is . of which .. have .-values that are below a threshold .. We then write, as before, .[. < .] = .[.] and estimate this as ..∕..
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Sampling-Based Single-Threshold PRA: Uncertainty Quantification (UQ),Uncertainty in sampling-based expectations may be quantified as the standard deviations of the sample means, see Eq. (4.1).
发表于 2025-3-23 02:25:44 | 显示全部楼层
Density Estimation to Move from Sampling- to Distribution-Based PRA,Our approach to sampling-based single-threshold PRA with UQ in Chap. . was to take a collection of . data pairs (., .), define a hazardous region ., and estimate .[.], .  and . as, respectively, .∕.., . and .. The approach was completed with UQ using Eqs. (.)–(.).
发表于 2025-3-23 08:10:56 | 显示全部楼层
Bayesian Model-Based PRA,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.
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