Introduction To Imprecise Probabilities

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Introduction to Imprecise Probabilities

Author : Thomas Augustin
Publisher : John Wiley & Sons
ISBN 13 : 1118763149
Total Pages : 448 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Introduction to Imprecise Probabilities by : Thomas Augustin

Download or read book Introduction to Imprecise Probabilities written by Thomas Augustin and published by John Wiley & Sons. This book was released on 2014-04-11 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Uncertainty in Engineering

Author : Louis J. M. Aslett
Publisher : Springer Nature
ISBN 13 : 3030836401
Total Pages : 148 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Uncertainty in Engineering by : Louis J. M. Aslett

Download or read book Uncertainty in Engineering written by Louis J. M. Aslett and published by Springer Nature. This book was released on 2022 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Game-Theoretic Foundations for Probability and Finance

Author : Glenn Shafer
Publisher : John Wiley & Sons
ISBN 13 : 1118547934
Total Pages : 480 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Game-Theoretic Foundations for Probability and Finance by : Glenn Shafer

Download or read book Game-Theoretic Foundations for Probability and Finance written by Glenn Shafer and published by John Wiley & Sons. This book was released on 2019-03-21 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Fabio Cuzzolin
Publisher : Springer Nature
ISBN 13 : 3030631532
Total Pages : 850 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis The Geometry of Uncertainty by : Fabio Cuzzolin

Download or read book The Geometry of Uncertainty written by Fabio Cuzzolin and published by Springer Nature. This book was released on 2020-12-17 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Probability and Statistics

Author : Vijay K. Rohatgi
Publisher : John Wiley & Sons
ISBN 13 : 1118799658
Total Pages : 728 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis An Introduction to Probability and Statistics by : Vijay K. Rohatgi

Download or read book An Introduction to Probability and Statistics written by Vijay K. Rohatgi and published by John Wiley & Sons. This book was released on 2015-09-01 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well-balanced introduction to probability theory and mathematical statistics Featuring updated material, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided intothree parts, the Third Edition begins by presenting the fundamentals and foundationsof probability. The second part addresses statistical inference, and the remainingchapters focus on special topics. An Introduction to Probability and Statistics, Third Edition includes: A new section on regression analysis to include multiple regression, logistic regression, and Poisson regression A reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics Additional topical coverage on bootstrapping, estimation procedures, and resampling Discussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals Over 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarks Numerous figures to further illustrate examples and proofs throughout An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.

Introduction to Probability

Author : Narayanaswamy Balakrishnan
Publisher : John Wiley & Sons
ISBN 13 : 1118548558
Total Pages : 548 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Introduction to Probability by : Narayanaswamy Balakrishnan

Download or read book Introduction to Probability written by Narayanaswamy Balakrishnan and published by John Wiley & Sons. This book was released on 2021-11-24 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: INTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: Includes classroom-tested problems and solutions to probability exercises Highlights real-world exercises designed to make clear the concepts presented Uses Mathematica software to illustrate the text’s computer exercises Features applications representing worldwide situations and processes Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.

Optimization Under Uncertainty with Applications to Aerospace Engineering

Author : Massimiliano Vasile
Publisher : Springer Nature
ISBN 13 : 3030601668
Total Pages : 573 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Optimization Under Uncertainty with Applications to Aerospace Engineering by : Massimiliano Vasile

Download or read book Optimization Under Uncertainty with Applications to Aerospace Engineering written by Massimiliano Vasile and published by Springer Nature. This book was released on 2021-02-15 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Probability Theory and Its Applications, Volume 1

Author : William Feller
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 538 pages
Book Rating : 4.:/5 ( download)

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Book Synopsis An Introduction to Probability Theory and Its Applications, Volume 1 by : William Feller

Download or read book An Introduction to Probability Theory and Its Applications, Volume 1 written by William Feller and published by John Wiley & Sons. This book was released on 1968-01-15 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nature of probability theory. The sample space. Elements of combinatorial analysis. Fluctuations in coin tossing and random walks. Combination of events. Conditional probability, stochastic independence. The binomial and the Poisson distributions. The Normal approximation to the binomial distribution. Unlimited sequences of Bernoulli trials. Random variables, expectation. Laws of large numbers. Integral valued variables, generating functions. Compound distributions. Branching processes. Recurrent events. Renewal theory. Random walk and ruin problems. Markov chains. Algebraic treatment of finite Markov chains. The simplest time-dependent stochastic processes. Answer to problems. Index.

Theory of Probability

Author : Bruno de Finetti
Publisher : John Wiley & Sons
ISBN 13 : 1119286379
Total Pages : 611 pages
Book Rating : 4.1/5 (192 download)

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Book Synopsis Theory of Probability by : Bruno de Finetti

Download or read book Theory of Probability written by Bruno de Finetti and published by John Wiley & Sons. This book was released on 2017-04-17 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics. De Finetti's theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something will happen and that that probability does not exist outside the mind. It is the rate at which a person is willing to bet on something happening. This view is directly opposed to the classicist/ frequentist view of the likelihood of a particular outcome of an event, which assumes that the same event could be identically repeated many times over, and the 'probability' of a particular outcome has to do with the fraction of the time that outcome results from the repeated trials.

Statistical Reasoning with Imprecise Probabilities

Author : Peter Walley
Publisher : Chapman and Hall/CRC
ISBN 13 :
Total Pages : 728 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Statistical Reasoning with Imprecise Probabilities by : Peter Walley

Download or read book Statistical Reasoning with Imprecise Probabilities written by Peter Walley and published by Chapman and Hall/CRC. This book was released on 1991 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

Probability: A Very Short Introduction

Author : John Haigh
Publisher : OUP Oxford
ISBN 13 : 0191636835
Total Pages : 144 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Probability: A Very Short Introduction by : John Haigh

Download or read book Probability: A Very Short Introduction written by John Haigh and published by OUP Oxford. This book was released on 2012-04-26 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making good decisions under conditions of uncertainty - which is the norm - requires a sound appreciation of the way random chance works. As analysis and modelling of most aspects of the world, and all measurement, are necessarily imprecise and involve uncertainties of varying degrees, the understanding and management of probabilities is central to much work in the sciences and economics. In this Very Short Introduction, John Haigh introduces the ideas of probability and different philosophical approaches to probability, and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions, and goes on to discuss a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Probability

Author : Robert P. Dobrow
Publisher : John Wiley & Sons
ISBN 13 : 1118589440
Total Pages : 366 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Probability by : Robert P. Dobrow

Download or read book Probability written by Robert P. Dobrow and published by John Wiley & Sons. This book was released on 2013-10-16 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to probability at the undergraduate level Chance and randomness are encountered on a daily basis. Authored by a highly qualified professor in the field, Probability: With Applications and R delves into the theories and applications essential to obtaining a thorough understanding of probability. With real-life examples and thoughtful exercises from fields as diverse as biology, computer science, cryptology, ecology, public health, and sports, the book is accessible for a variety of readers. The book’s emphasis on simulation through the use of the popular R software language clarifies and illustrates key computational and theoretical results. Probability: With Applications and R helps readers develop problem-solving skills and delivers an appropriate mix of theory and application. The book includes: Chapters covering first principles, conditional probability, independent trials, random variables, discrete distributions, continuous probability, continuous distributions, conditional distribution, and limits An early introduction to random variables and Monte Carlo simulation and an emphasis on conditional probability, conditioning, and developing probabilistic intuition An R tutorial with example script files Many classic and historical problems of probability as well as nontraditional material, such as Benford’s law, power-law distributions, and Bayesian statistics A topics section with suitable material for projects and explorations, such as random walk on graphs, Markov chains, and Markov chain Monte Carlo Chapter-by-chapter summaries and hundreds of practical exercises Probability: With Applications and R is an ideal text for a beginning course in probability at the undergraduate level.

Rational Choice Using Imprecise Probabilities and Utilities

Author : Paul Weirich
Publisher : Cambridge University Press
ISBN 13 : 1108604781
Total Pages : 139 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Rational Choice Using Imprecise Probabilities and Utilities by : Paul Weirich

Download or read book Rational Choice Using Imprecise Probabilities and Utilities written by Paul Weirich and published by Cambridge University Press. This book was released on 2021-02-25 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement.

Probability-Based Structural Fire Load

Author : Leo Razdolsky
Publisher : Cambridge University Press
ISBN 13 : 110703874X
Total Pages : 353 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Probability-Based Structural Fire Load by : Leo Razdolsky

Download or read book Probability-Based Structural Fire Load written by Leo Razdolsky and published by Cambridge University Press. This book was released on 2014-08-25 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the subject of probabilistic analysis to engineers and can be used as a reference in applying this technology.

Fuzzy Probabilities

Author : James J. Buckley
Publisher : Physica
ISBN 13 : 3642867863
Total Pages : 168 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Fuzzy Probabilities by : James J. Buckley

Download or read book Fuzzy Probabilities written by James J. Buckley and published by Physica. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Probability Tutoring Book

Author : Carol Ash
Publisher : Wiley-IEEE Press
ISBN 13 : 9780780310513
Total Pages : 0 pages
Book Rating : 4.3/5 (15 download)

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Book Synopsis The Probability Tutoring Book by : Carol Ash

Download or read book The Probability Tutoring Book written by Carol Ash and published by Wiley-IEEE Press. This book was released on 1996-11-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-study guide for practicing engineers, scientists, and students, this book offers practical, worked-out examples on continuous and discrete probability for problem-solving courses. It is filled with handy diagrams, examples, and solutions that greatly aid in the comprehension of a variety of probability problems.

Probability and Statistics with Reliability, Queuing, and Computer Science Applications

Author : Kishor S. Trivedi
Publisher : John Wiley & Sons
ISBN 13 : 1119314208
Total Pages : 880 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Probability and Statistics with Reliability, Queuing, and Computer Science Applications by : Kishor S. Trivedi

Download or read book Probability and Statistics with Reliability, Queuing, and Computer Science Applications written by Kishor S. Trivedi and published by John Wiley & Sons. This book was released on 2016-06-30 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications Second edition now also available in Paperback. This updated and revised edition of the popular classic first edition relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance. This edition features an entirely new section on stochastic Petri nets—as well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section. Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.