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001451499 020__ $$a9783031163333$$q(electronic bk.)
001451499 020__ $$a3031163338$$q(electronic bk.)
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001451499 0247_ $$a10.1007/978-3-031-16333-3$$2doi
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001451499 1001_ $$aVan Oijen, Marcel,$$eauthor.
001451499 24510 $$aProbabilistic risk analysis and Bayesian decision theory /$$cMarcel van Oijen, Mark Brewer.
001451499 264_1 $$aCham :$$bSpringer,$$c[2022]
001451499 264_4 $$c©2022
001451499 300__ $$a1 online resource (118 pages) :$$billustrations.
001451499 336__ $$atext$$btxt$$2rdacontent
001451499 337__ $$acomputer$$bc$$2rdamedia
001451499 338__ $$aonline resource$$bcr$$2rdacarrier
001451499 4901_ $$aSpringerBriefs in statistics
001451499 504__ $$aIncludes bibliographical references and index.
001451499 5050_ $$aIntro -- Preface -- Why This Book? -- Who Is this Book for? -- Notation -- Outline of Chapters -- Acknowledgements -- Contents -- 1 Introduction to Probabilistic Risk Analysis (PRA) -- 1.1 From Risk Matrices to PRA -- 1.2 Basic Equations for PRA -- 1.3 Decomposition of Risk: 2 or 3 Components -- 1.4 Resolution of PRA: Single-Threshold, Multi-Threshold, Categorical, Continuous -- 1.4.1 Single-Threshold PRA -- 1.4.2 Multi-Threshold PRA -- 1.4.3 Categorical PRA -- 1.4.4 Continuous PRA -- 1.5 Implementation of PRA: Distribution-Based, Sampling-Based, Model-Based -- 2 Distribution-Based Single-Threshold PRA -- 2.1 Conditional Distributions for z -- 2.1.1 Conditions for V Being Constant -- 2.2 Example of Distribution-Based PRA: Gaussian p[x,z] -- 2.2.1 Hazard Probability and Conditional Distributions -- 2.2.2 Conditional Expectations and PRA -- 2.3 Approximation Formulas for the Conditional Bivariate Gaussian Expectations -- 3 Sampling-Based Single-Threshold PRA -- 3.1 Example of Sampling-Based PRA: Linear Relationship -- 3.1.1 Varying the Threshold -- 3.2 Example of Sampling-Based PRA: Nonlinear Relationship -- 4 Sampling-Based Single-Threshold PRA: Uncertainty Quantification (UQ) -- 4.1 Uncertainty in p[H] -- 4.2 Uncertainty in V -- 4.3 Uncertainty in R -- 4.4 Extension of R-Code for PRA: Adding the UQ -- 4.5 PRA with UQ on the Nonlinear Data Set -- 4.6 Verification of the UQ by Simulating Multiple Data Sets -- 4.6.1 UQ-Verification: Nonlinear Relationship -- 4.6.2 UQ-Verification: Linear Relationship -- 4.7 Approximation Formulas for the Conditional Bivariate Gaussian Variances -- 5 Density Estimation to Move from Sampling- to Distribution-Based PRA -- 6 Copulas for Distribution-Based PRA -- 6.1 Sampling from Copulas and Carrying out PRA -- 6.2 Copula Selection -- 6.3 Using Copulas in PRA -- 7 Bayesian Model-Based PRA.
001451499 5058_ $$a7.1 Linear Example: Full Bayesian PRA with Uncertainty -- 7.1.1 Checking the MCMC -- 7.1.2 PRA -- 7.2 Nonlinear Example: Full Bayesian PRA with Uncertainty -- 7.3 Advantages of the Bayesian Modelling Approach -- 8 Sampling-Based Multi-Threshold PRA:Gaussian Linear Example -- 9 Distribution-Based Continuous PRA: Gaussian Linear Example -- 10 Categorical PRA with Other Splits than for Threshold-Levels: Spatio-Temporal Example -- 10.1 Spatio-Temporal Environmental Data: x(s,t) -- 10.2 Spatio-Temporal System Data: z(s,t) -- 10.3 Single-Category Single-Threshold PRA for the Spatio-Temporal Data -- 10.4 Two-Category Single-Threshold PRA for Spatio-Temporal Data -- 11 Three-Component PRA -- 11.1 Three-Component PRA for Spatio-Temporal Data -- 11.2 Country-Wide Application of Three-Component PRA -- 11.3 UQ for Three-Component PRA -- 12 Introduction to Bayesian Decision Theory (BDT) -- 12.1 Example of BDT in Action -- 13 Implementation of BDT Using Bayesian Networks -- 13.1 Three Ways to Specify a Multivariate Gaussian -- 13.1.1 Switching Between the Three Different Specifications of the Multivariate Gaussian -- 13.2 Sampling from a GBN and Bayesian Updating -- 13.2.1 Updating a GBN When Information About Nodes Becomes Available -- 13.3 A Linear BDT Example Implemented as a GBN -- 13.4 A Linear BDT Example Implemented Using \texttt{Nimble} -- 13.4.1 Varying IRRIG to Identify the Value for Which E[U] Is Maximized -- 13.5 A Nonlinear BDT Example Implemented Using \texttt{Nimble} -- 14 A Spatial Example: Forestry in Scotland -- 14.1 A Decision Problem: Forest Irrigation in Scotland -- 14.2 Computational Demand of BDT and Emulation -- 14.3 Data -- 14.4 A Simple Model for Forest Yield Class (YC) -- 14.5 Emulation -- 14.6 Application of the Emulator -- 15 Spatial BDT Using Model and Emulator -- 15.1 Multiple Action Levels -- 16 Linkages Between PRA and BDT.
001451499 5058_ $$a16.1 Risk Management -- 16.2 The Relationship Between Utility Maximisation in BDT and Risk Assessment in PRA: R_c -- 16.3 Simplified Accounting for Both Benefits and Costs of the Action: R_b -- 16.4 Only Correcting for Costs: R_a -- 17 PRA vs. BDT in the Spatial Example -- 18 Three-Component PRA in the Spatial Example -- 19 Discussion -- 19.1 PRA and Its Application -- 19.2 Data and Computational Demand of PRA -- 19.3 BDT -- 19.4 Computational Demand of BDT -- 19.5 PRA as a Tool for Simplifying and Elucidating BDT -- 19.6 Parameter and Model Uncertainties -- 19.7 Modelling and Decision-Support for Forest Response to Hazards -- 19.8 Spatial Statistics -- References -- Index.
001451499 506__ $$aAccess limited to authorized users.
001451499 520__ $$aThe 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.
001451499 588__ $$aDescription based upon print version of record.
001451499 650_0 $$aBayesian statistical decision theory.
001451499 650_0 $$aProbabilities.
001451499 650_0 $$aRisk assessment$$xStatistical methods.
001451499 655_0 $$aElectronic books.
001451499 7001_ $$aBrewer, Mark,$$eauthor.
001451499 77608 $$iPrint version:$$avan Oijen, Marcel$$tProbabilistic Risk Analysis and Bayesian Decision Theory$$dCham : Springer International Publishing AG,c2022$$z9783031163326
001451499 830_0 $$aSpringerBriefs in statistics.
001451499 852__ $$bebk
001451499 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-16333-3$$zOnline Access$$91397441.1
001451499 909CO $$ooai:library.usi.edu:1451499$$pGLOBAL_SET
001451499 980__ $$aBIB
001451499 980__ $$aEBOOK
001451499 982__ $$aEbook
001451499 983__ $$aOnline
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