Introduction To Imprecise Probabilities
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Introduction To Imprecise Probabilities
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Author : Thomas Augustin
language : en
Publisher: John Wiley & Sons
Release Date : 2014-04-11
Introduction To Imprecise Probabilities written by Thomas Augustin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-11 with Mathematics categories.
In recent years, the theory has become widely accepted and has beenfurther developed, but a detailed introduction is needed in orderto make the material available and accessible to a wide audience.This will be the first book providing such an introduction,covering core theory and recent developments which can be appliedto many application areas. All authors of individual chapters areleading researchers on the specific topics, assuring high qualityand up-to-date contents. An Introduction to Imprecise Probabilities provides acomprehensive introduction to imprecise probabilities, includingtheory and applications reflecting the current state if the art.Each chapter is written by experts on the respective topics,including: Sets of desirable gambles; Coherent lower (conditional)previsions; Special cases and links to literature; Decision making;Graphical models; Classification; Reliability and risk assessment;Statistical inference; Structural judgments; Aspects ofimplementation (including elicitation and computation); Models infinance; Game-theoretic probability; Stochastic processes(including Markov chains); Engineering applications. Essential reading for researchers in academia, researchinstitutes and other organizations, as well as practitionersengaged in areas such as risk analysis and engineering.
Introduction To Imprecise Probabilities
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Author : Thomas Augustin
language : en
Publisher: John Wiley & Sons
Release Date : 2014-06-03
Introduction To Imprecise Probabilities written by Thomas Augustin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-03 with Mathematics categories.
In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state if the art. Each chapter is written by experts on the respective topics, including: Sets of desirable gambles; Coherent lower (conditional) previsions; Special cases and links to literature; Decision making; Graphical models; Classification; Reliability and risk assessment; Statistical inference; Structural judgments; Aspects of implementation (including elicitation and computation); Models in finance; Game-theoretic probability; Stochastic processes (including Markov chains); Engineering applications. Essential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering.
Uncertainty In Engineering
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Author : Louis J. M. Aslett
language : en
Publisher: Springer Nature
Release Date : 2021-12-09
Uncertainty In Engineering written by Louis J. M. Aslett and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-09 with Mathematics categories.
This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.
Statistical Reasoning With Imprecise Probabilities
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Author : Peter Walley
language : en
Publisher: Springer
Release Date :
Statistical Reasoning With Imprecise Probabilities written by Peter Walley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
When I started writing this book, my mind was full of ignorance and uncertainty, particularly about how best to deal with ignorance and uncertainty. Much of the ignorance and uncertainty remains, now that the book is finished, but it is organized more coherently. I see that as progress. As the title indicates, the book is about methods of reasoning and statistical inference using imprecise probabilities. The methods are based on a behavioural interpretation of probability and principles of coherence. The idea for such a book originated in 1982, after I had written two long reports on the mathematics and elicitation of upper and lower probabilities. My experience in teaching and applying the existing theories of statistical inference had convinced me that each of them was inadequate. The Bayesian theory is inadequate, despite its great virtues of coherence, because it requires all probability assessments to be precise yet gives little guidance on how to make them. It seemed natural to investigate whether the Bayesian theory could be modified by admitting imprecise probabilities as models for partial ignorance. Is it possible to reconcile imprecision with coherence, vagueness with rationality? Fortunately the ans wer is yes! The basic ideas of the book appeared in the two technical reports (1981, 1982). The coherence principles for conditional probabilities and statistical models were worked out in New Zealand, in 1983.
Game Theoretic Foundations For Probability And Finance
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Author : Glenn Shafer
language : en
Publisher: John Wiley & Sons
Release Date : 2019-03-21
Game Theoretic Foundations For Probability And Finance written by Glenn Shafer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-21 with Business & Economics categories.
Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University
The Geometry Of Uncertainty
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Author : Fabio Cuzzolin
language : en
Publisher: Springer Nature
Release Date : 2020-12-17
The Geometry Of Uncertainty written by Fabio Cuzzolin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Computers categories.
The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.
Fuzzy Probabilities
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Author : James J. Buckley
language : en
Publisher: Physica
Release Date : 2012-12-06
Fuzzy Probabilities written by James J. Buckley and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.
Optimization Under Uncertainty With Applications To Aerospace Engineering
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Author : Massimiliano Vasile
language : en
Publisher: Springer Nature
Release Date : 2021-02-15
Optimization Under Uncertainty With Applications To Aerospace Engineering written by Massimiliano Vasile and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-15 with Science categories.
In an expanding world with limited resources, optimization and uncertainty quantification have become a necessity when handling complex systems and processes. This book provides the foundational material necessary for those who wish to embark on advanced research at the limits of computability, collecting together lecture material from leading experts across the topics of optimization, uncertainty quantification and aerospace engineering. The aerospace sector in particular has stringent performance requirements on highly complex systems, for which solutions are expected to be optimal and reliable at the same time. The text covers a wide range of techniques and methods, from polynomial chaos expansions for uncertainty quantification to Bayesian and Imprecise Probability theories, and from Markov chains to surrogate models based on Gaussian processes. The book will serve as a valuable tool for practitioners, researchers and PhD students.
Uncertainty Theory
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Author : Baoding Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-14
Uncertainty Theory written by Baoding Liu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-14 with Business & Economics categories.
This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. For this new edition the entire text has been totally rewritten. The chapters on chance theory and uncertainty theory are completely new. Mathematicians, researchers, engineers, designers, and students will find this work a stimulating and useful reference.
Uncertainty Based Information
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Author : George J. Klir
language : en
Publisher: Physica
Release Date : 2013-06-05
Uncertainty Based Information written by George J. Klir and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.
Information is precious. It reduces our uncertainty in making decisions. Knowledge about the outcome of an uncertain event gives the possessor an advantage. It changes the course of lives, nations, and history itself. Information is the food of Maxwell's demon. His power comes from know ing which particles are hot and which particles are cold. His existence was paradoxical to classical physics and only the realization that information too was a source of power led to his taming. Information has recently become a commodity, traded and sold like or ange juice or hog bellies. Colleges give degrees in information science and information management. Technology of the computer age has provided access to information in overwhelming quantity. Information has become something worth studying in its own right. The purpose of this volume is to introduce key developments and results in the area of generalized information theory, a theory that deals with uncertainty-based information within mathematical frameworks that are broader than classical set theory and probability theory. The volume is organized as follows.