Foundations of Modern Probability

Foundations of Modern Probability

Author: Olav Kallenberg

Publisher: Springer Science & Business Media

Published: 2002-01-08

Total Pages: 670

ISBN-13: 9780387953137

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The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.


Foundations of Probability

Foundations of Probability

Author: Alfred Renyi

Publisher: Courier Corporation

Published: 2007-01-01

Total Pages: 386

ISBN-13: 0486462617

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Introducing many innovations in content and methods, this book involves the foundations, basic concepts, and fundamental results of probability theory. Geared toward readers seeking a firm basis for study of mathematical statistics or information theory, it also covers the mathematical notions of experiments and independence. 1970 edition.


Philosophical Foundations of Probability Theory

Philosophical Foundations of Probability Theory

Author: Roy Weatherford

Publisher: Taylor & Francis

Published: 2022-06-01

Total Pages: 220

ISBN-13: 1000626091

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First published in 1982, Philosophical Foundations of Probability Theory starts with the uses we make of the concept in everyday life and then examines the rival theories that seek to account for these applications. It offers a critical exposition of the major philosophical theories of probability, with special attention given to the metaphysical and epistemological assumptions and implications of each. The Classical Theory suggests probability is simply the ratio of favorable cases to all equi-possible cases: it is this theory that is relied on by gamblers and by most non-specialists. The A Priori Theory, on the other hand, describes probability as a logical relation between statements based on evidence. The Relative Frequency theories locate it not in logic but among empirical rates of occurrence in the real world, while the Subjectivist Theory identifies probability with the degree of a person’s belief in a proposition. Each of these types of theory is examined in turn, and the treatment is unified by the use of running examples and parallel analyses of each theory. The final chapter includes a summary and the author’s conclusions. This book is an essential read for scholars and researchers of Philosophy.


Probability Theory

Probability Theory

Author: Alfred Renyi

Publisher: Courier Corporation

Published: 2007-05-11

Total Pages: 674

ISBN-13: 0486458679

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The founder of Hungary's Probability Theory School, A. Rényi made significant contributions to virtually every area of mathematics. This introductory text is the product of his extensive teaching experience and is geared toward readers who wish to learn the basics of probability theory, as well as those who wish to attain a thorough knowledge in the field. Based on the author's lectures at the University of Budapest, this text requires no preliminary knowledge of probability theory. Readers should, however, be familiar with other branches of mathematics, including a thorough understanding of the elements of the differential and integral calculus and the theory of real and complex functions. These well-chosen problems and exercises illustrate the algebras of events, discrete random variables, characteristic functions, and limit theorems. The text concludes with an extensive appendix that introduces information theory.


Foundations of the Theory of Probability

Foundations of the Theory of Probability

Author: A.N. Kolmogorov

Publisher: Courier Dover Publications

Published: 2018-03-19

Total Pages: 97

ISBN-13: 0486829790

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This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.


The Theory of Probability

The Theory of Probability

Author: Harold Jeffreys

Publisher: OUP Oxford

Published: 1998-08-06

Total Pages: 474

ISBN-13: 0191589675

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Another title in the reissued Oxford Classic Texts in the Physical Sciences series, Jeffrey's Theory of Probability, first published in 1939, was the first to develop a fundamental theory of scientific inference based on the ideas of Bayesian statistics. His ideas were way ahead of their time and it is only in the past ten years that the subject of Bayes' factors has been significantly developed and extended. Until recently the two schools of statistics (Bayesian and Frequentist) were distinctly different and set apart. Recent work (aided by increased computer power and availability) has changed all that and today's graduate students and researchers all require an understanding of Bayesian ideas. This book is their starting point.


Concepts of Probability Theory

Concepts of Probability Theory

Author: Paul E. Pfeiffer

Publisher: Courier Corporation

Published: 2013-05-13

Total Pages: 418

ISBN-13: 0486165663

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Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.


Probability, Statistics, and Truth

Probability, Statistics, and Truth

Author: Richard Von Mises

Publisher: Courier Corporation

Published: 1981-01-01

Total Pages: 273

ISBN-13: 0486242145

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This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.


An Elementary Introduction to the Theory of Probability

An Elementary Introduction to the Theory of Probability

Author: Boris Vladimirovich Gnedenko

Publisher: Courier Corporation

Published: 1962-01-01

Total Pages: 162

ISBN-13: 0486601552

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This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself. After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics. The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.