A Modern Approach to Probability Theory
A Modern Approach to Probability Theory

Author: Bert E. Fristedt

Publisher: Springer Science & Business Media

Published: 1996-12-23

Total Pages: 780

ISBN-13: 9780817638078

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Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

A Modern Introduction to Probability and Statistics
A Modern Introduction to Probability and Statistics

Author: F.M. Dekking

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 485

ISBN-13: 1846281687

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Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

A Modern Approach to Probability Theory
A Modern Approach to Probability Theory

Author: Bert E. Fristedt

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 775

ISBN-13: 1489928375

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Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

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.

Basic Probability Theory
Basic Probability Theory

Author: Robert B. Ash

Publisher: Courier Corporation

Published: 2008-06-26

Total Pages: 354

ISBN-13: 0486466280

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This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus. Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.

The Theory of Probability
The Theory of Probability

Author: Santosh S. Venkatesh

Publisher: Cambridge University Press

Published: 2013

Total Pages: 830

ISBN-13: 1107024471

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From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.

Creating Modern Probability
Creating Modern Probability

Author: Jan von Plato

Publisher: Cambridge University Press

Published: 1998-01-12

Total Pages: 336

ISBN-13: 9780521597357

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In this book the author charts the history and development of modern probability theory.

Introduction to Probability
Introduction to Probability

Author: David F. Anderson

Publisher: Cambridge University Press

Published: 2017-11-02

Total Pages: 447

ISBN-13: 110824498X

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This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

Essentials of Probability Theory for Statisticians
Essentials of Probability Theory for Statisticians

Author: Michael A. Proschan

Publisher: CRC Press

Published: 2016-03-23

Total Pages: 334

ISBN-13: 1498704204

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Essentials of Probability Theory for Statisticians provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes based on accumulating data. The authors explain different methods of proofs and show how they are useful for establishing classic probability results. After building a foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic. This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.