Estimation of rare event probabilities in complex aerospace and other systems : a practical approach / / Jérôme Morio and Mathieu Balesdent

• Record Nr.: UNINA9910815465303321
• Autore: Morio Jérôme
• Pubbl/distr/stampa: Waltham, MA : , : Elsevier, , [2016]; ©2016
• ISBN: 0-08-100111-8; 0-08-100091-X
• Edizione: [First edition.]
• Descrizione fisica: 1 online resource (217 p.)
• Collana: Woodhead Publishing in mechanical engineering ; ; number 720
• Soggetti: Probabilities; Industrial engineering - Statistical methods; Probabilitats; Enginyeria industrial - Mètodes estadístics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di contenuto: Front Cover; Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach; Copyright; Dedication; Contents; Preface; Foreword; Biography of the external contributors to this book; Abbreviations; Chapter 1: Introduction to rare event probability estimation; 1.1 The book purposes; 1.2 What are the events of interest considered in this book?; 1.3 The book organization; References; Part One: Essential Background in Mathematics and System Analysis; Chapter 2: Basics of probability and statistics; 2.1 Probability theory operators; 2.1.1 Elements of vocabulary; 2.1.2 Notion of dependence of random events andconditional probabilities 2.1.3 Continuous random variables; 2.1.3.1 Definitions; 2.1.3.2 Parameters of continuous random variables; 2.1.4 Continuous multivariate random variables; 2.1.4.1 Definitions and theorems; 2.1.4.2 Dependence of multivariate random variables ; 2.1.5 Point estimation ; 2.2 Random variable modeling; 2.2.1 Overview of common probability distributions; 2.2.1.1 Univariate distributions; Uniform distribution; Exponential distribution; Gaussian distribution; Truncated ; Gaussian distribution; Log-normal distribution; Cauchy distributionChi-squared distribution; Gamma and beta distributions; Laplace distribution; Some properties of univariate distributions; 2.2.1.2 Multivariate distributions; Multivariate normal distribution; 2.2.2 Kernel-based laws; 2.3 Convergence theorems and sampling algorithms; 2.3.1 Strong law of large numbers ; 2.3.2 Central limit theorem ; 2.3.3 Simulation of complex laws using the Metropolis-Hastings algorithm; 2.3.3.1 Markov chain; 2.3.3.2 Some properties of transition kernels; 2.3.3.3 The Metropolis-Hastings algorithm ; 2.3.3.4 Transformation of random variables; References; Chapter 3: The formalism of rare event probability estimation in complex systems3.1 Input-output system; 3.1.1 Description; 3.1.2 Formalism; 3.2 Time-variant system; 3.2.1 Description; 3.2.2 Formalism; 3.3 Characterization of a probability estimation; References; Part Two: Practical Overview of the Main Rare Event EstimationTechniques; Chapter 4: Introduction; 4.1 Categories of estimation methods; 4.2 General notations; 4.3 Description of the toy cases; 4.3.1 Identity function; 4.3.2 Polynomial square root function; 4.3.3 Four-branch system; 4.3.4 Polynomial product function; References; Chapter 5: Simulation techniques5.1 Crude Monte Carlo; 5.1.1 Principle; 5.1.2 Application on a toy case; Four-branch system; 5.1.3 Conclusion; 5.2 Simple variance reduction techniques; 5.2.1 Quasi-Monte Carlo; 5.2.2 Conditional Monte Carlo; 5.2.2.1 Principle; 5.2.2.2 Conclusion; 5.2.3 Control variates; 5.2.3.1 Principle; 5.2.3.2 Application on a toy case; Four-branch system; 5.2.3.3 Conclusion; 5.2.4 Antithetic variates; 5.2.4.1 Principle; 5.2.4.2 Application to a toy case; Identity function; 5.2.4.3 Conclusion; 5.3 Importance sampling; 5.3.1 Principle of importance sampling; 5.3.2 Nonadaptive importance sampling