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Books on the topic 'Rare event probability'

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Author: Grafiati

Published: 7 July 2024

Last updated: 7 July 2024

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1

1955-, Rubino Gerardo, and Tuffin Bruno, eds. Rare event simulation using Monte Carlo methods. Hoboken, N.J: Wiley, 2009.

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2

Falk, Michael. Laws of Small Numbers: Extremes and Rare Events. Basel: Springer Basel AG, 2011.

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3

Kalashnikov, Vladimir Vi͡acheslavovich. Geometric sums, bounds for rare events with applications: Risk analysis, reliability, queueing. Dordrecht: Kluwer Academic, 1997.

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4

Falk, Michael. Laws of small numbers: Extremes and rare events. 2nd ed. Basel: Birkhauser Verlag, 2004.

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5

Falk, Michael. Laws of small numbers: Extremes and rare events. Basel: Birkhäuser Verlag, 1994.

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6

Kalashnikov, Vladimir. Geometric Sums: Bounds for Rare Events with Applications: Risk Analysis, Reliability, Queueing. Dordrecht: Springer Netherlands, 1997.

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7

Schneider, Jörg, and Ton Vrouwenvelder. Introduction to safety and reliability of structures. 3rd ed. Zurich, Switzerland: International Association for Bridge and Structural Engineering (IABSE), 1997. http://dx.doi.org/10.2749/sed005.

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<p>Society expects that buildings and other structures are safe for the people who use them or who are near them. The failure of a building or structure is expected to be an extremely rare event. Thus, society implicitly relies on the expertise of the professionals involved in the planning, design, construction, operation and maintenance of the structures it uses.<p>Structural engineers devote all their effort to meeting society’s expectations effi ciently. Engineers and scientists work together to develop solutions to structural problems. Given that nothing is absolutely and eternally safe, the goal is to attain an acceptably small probability of failure for a structure, a facility, or a situation. Reliability analysis is part of the science and practice of engineering today, not only with respect to the safety of structures, but also for questions of serviceability and other requirements of technical systems that might be impacted by some probability.<p>The present volume takes a rather broad approach to safety and reliability in Structural Engineering. It treats the underlying concepts of safety, reliability and risk and introduces the reader in a ﬁ rst chapter to the main concepts and strategies for dealing with hazards. The next chapter is devoted to the processing of data into information that is relevant for applying reliability theory. Two following chapters deal with the modelling of structures and with methods of reliability analysis. Another chapter focuses on problems related to establishing target reliabilities, assessing existing structures, and on effective strategies against human error. The last chapter presents an outlook to more advanced applications. The Appendix supports the application of the methods proposed and refers readers to a number of related computer programs.<p>This book is aimed at both students and practicing engineers. It presents the concepts and procedures of reliability analysis in a straightforward, understandable way, making use of simple examples, rather than extended theoretical discussion. It is hoped that this approach serves to advance the application of safety and reliability analysis in engineering practice.<p>The book is amended with a free access to an educational version of a Variables Processor computer program. FreeVaP can be downloaded free of charge and supports the understanding of the subjects treated in this book.

8

1969-, Lee-Treweek Geraldine, and Linkogle Stephanie, eds. Danger in the field: Risk and ethics in social research. London: Routledge, 2000.

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9

Clark, James S., Dave Bell, Michael Dietze, Michelle Hersh, Ines Ibanez, Shannon LaDeau, Sean McMahon, et al. Assessing the probability of rare climate events. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.16.

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This article focuses on the use of Bayesian methods in assessing the probability of rare climate events, and more specifically the potential collapse of the meridional overturning circulation (MOC) in the Atlantic Ocean. It first provides an overview of climate models and their use to perform climate simulations, drawing attention to uncertainty in climate simulators and the role of data in climate prediction, before describing an experiment that simulates the evolution of the MOC through the twenty-first century. MOC collapse is predicted by the GENIE-1 (Grid Enabled Integrated Earth system model) for some values of the model inputs, and Bayesian emulation is used for collapse probability analysis. Data comprising a sparse time series of five measurements of the MOC from 1957 to 2004 are analysed. The results demonstrate the utility of Bayesian analysis in dealing with uncertainty in complex models, and in particular in quantifying the risk of extreme outcomes.

10

Hüsler, Jürg, Rolf-Dieter Reiss, and Michael Falk. Laws of Small Numbers: Extremes and Rare Events. Birkhauser Verlag, 2013.

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11

Husler, Jurg, R. D. Reiss, and Michael Falk. Laws Of Small Numbers: Extremes And Rare Events. Birkhauser, 2005.

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12

Hüsler, Jürg, Rolf-Dieter Reiss, and Michael Falk. Laws of Small Numbers: Extremes and Rare Events (Oberwolfach Seminars). 2nd ed. Birkhäuser Basel, 2005.

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13

Ben-Haim, Yakov. Uncertainty, Ignorance, Surprise—The Endless Frontier. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822233.003.0003.

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Some things happen by chance. Chance has diverse interpretations, but probability theory is relevant if there is some regularity of events. Probability also has limitations, especially when considering very rare events that we can only vaguely imagine. There are endless unknown possibilities, and the totality of rare events is massive. Hence it is hard to estimate probabilities of events that are individually rare but collectively not so rare. The rareness illusion is the impression of rareness arising from ignorance of the unknown. The rareness illusion results from our inability to assess probabilities of rare events. Non-probabilistic Knightian uncertainty extends our understanding of the unknown, and Shackle–Popper indeterminism provides a logical foundation. We illustrate these ideas by discussing the vagueness of human language, the impossibility of one unified theory of uncertainty, and the paradox that science is possible because science could someday come to an end.

14

Hand, D. J. The improbability principle: Why coincidences, miracles, and rare events happen every day. 2014.

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15

Kravtsov, Vladimir. Heavy-tailed random matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.13.

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This article considers non-Gaussian random matrices consisting of random variables with heavy-tailed probability distributions. In probability theory heavy tails of distributions describe rare but violent events which usually have a dominant influence on the statistics. Furthermore, they completely change the universal properties of eigenvalues and eigenvectors of random matrices. This article focuses on the universal macroscopic properties of Wigner matrices belonging to the Lévy basin of attraction, matrices representing stable free random variables, and a class of heavy-tailed matrices obtained by parametric deformations of standard ensembles. It first examines the properties of heavy-tailed symmetric matrices known as Wigner–Lévy matrices before discussing free random variables and free Lévy matrices as well as heavy-tailed deformations. In particular, it describes random matrix ensembles obtained from standard ensembles by a reweighting of the probability measure. It also analyses several matrix models belonging to heavy-tailed random matrices and presents methods for integrating them.

16

Draganov, Alexandr. Mathematical Tools for Real-World Applications. The MIT Press, 2022. http://dx.doi.org/10.7551/mitpress/14218.001.0001.

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Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found in textbooks: they are messier, take longer to solve, and standard solution recipes might not apply. This book fills the gap between what is taught in the typical college curriculum and what a practicing engineer or scientist needs to know. It presents six powerful tools for analysis, research, and problem solving in the real world: dimensional analysis, limiting cases, symmetry, scaling, making order of magnitude estimates, and the method of successive approximations. The book does not focus on formulaic manipulations of equations, but emphasizes analysis and explores connections between the equations and the application. Each chapter introduces a set of ideas and techniques and then shows how these techniques apply to a series of problems. (Knowledge of algebra and trigonometry, but not calculus, is required.) The final two chapters tie all six techniques together and apply them to two real-world problems: computing the probability of a rare, catastrophic event, and tracking a satellite with a GPS receiver. Readers will learn how to analyze, dissect, and gain insight into the results by using all the techniques presented in earlier chapters—and discover how analysis tools work on problems not concocted for a textbook. The appendix provides solutions to many of the problems found throughout the book. Alexandr Draganov was born and raised in Kyiv, Ukraine; in light of the current war in Ukraine he will donate 100% of his royalties for the first year to support medical and humanitarian efforts there.

17

Hardy, Thomas. Desperate Remedies. Edited by Patricia Ingham. Oxford University Press, 2009. http://dx.doi.org/10.1093/owc/9780199554829.001.0001.

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She was swayed into emotional opinions concerning the strange man before her; new impulses of thought…entered into her with a gnawing thrill.' Hardy's first published work, Desperate Remedies moves the sensation novel into new territory. The anti-hero, Aeneas Manston, as physically alluring as he is evil, even fascinates the innocent Cytherea, though she is in love with another man. When he cannot seduce her, Manston resorts to deception, blackmail, bigamy, murder, and rape. Yet this compelling story also raises the great questions underlying Hardy's major novels, which relate to the injustice of the class system, the treatment of women, probability and causality. This edition shows for the first time that the sensation novel was always Hardy's natural medium.

18

Jappelli, Tullio, and Luigi Pistaferri. Lifetime Uncertainty. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199383146.003.0011.

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Lifetime uncertainty represents an additional risk that affects intertemporal choice, because consumers may live longer than expected and run the risk of exhausting the resources accumulated for retirement. Lifetime uncertainty introduces an incentive to consume earlier in life because consumers discount future utility at a higher rate. Second, since in each period there is some positive probability that the consumer will not survive to the next period, the terminal condition on wealth corresponds effectively to a liquidity constraint. Third, with lifetime uncertainty, the decumulation of wealth by the elderly is slower than predicted by the life-cycle model. Finally, the model with lifetime uncertainty generates transfers of wealth across generations even without an express bequest motive, through what we can term involuntary or accidental bequests. The chapter highlights the necessity of accounting for lifetime uncertainty when interpreting empirical age-wealth profiles estimated from microeconomic data.

19

Lee-Treweek, Geraldine, and Stephanie Linkogle. Danger in the Field: Ethics and Risk in Social Research. Taylor & Francis Group, 2002.

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20

Lee-Treweek, Geraldine, and Stephanie Linkogle. Danger in the Field: Ethics and Risk in Social Research. Taylor & Francis Group, 2002.

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21

Lee-Treweek, Geraldine, and Stephanie Linkogle. Danger in the Field: Ethics and Risk in Social Research. Taylor & Francis Group, 2002.

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22

Lee-Treweek, Geraldine, and Stephanie Linkogle. Danger in the Field: Ethics and Risk in Social Research. Taylor & Francis Group, 2002.

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23

Lee-Treweek, Geraldine, and Stephanie Linkogle. Danger in the Field: Risk and Ethics in Social Research. Routledge, 2000.

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24

Lee-Treweek, Geraldine, and Stephanie Linkogle. Danger in the Field. Routledge, 2002.

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