Probabilistic Risk Analysis and Bayesian Decision Theory / / by Marcel van Oijen, Mark Brewer

• Autore: van Oijen Marcel
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
• Edizione: 1st ed. 2022.
• Descrizione fisica: 1 online resource (118 pages)
• Disciplina: 810
• Soggetto topico: Statistics; Biometry; Statistical Theory and Methods; Biostatistics; Bayesian Inference; Estadística bayesiana; Probabilitats; Avaluació del risc
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): BrewerMark
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- 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. ; 7.1 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. ; 16.1 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Probabilistic risk analysis and Bayesian decision theory
• ISBN: 9783031163333; 3031163338
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910632480803321
• Lo trovi qui: Univ. Federico II
• Serie: SpringerBriefs in Statistics, . 2191-5458