Foundations of the Theory of Probability

Second English Edition

Author: A.N. Kolmogorov

Publisher: Courier Dover Publications

ISBN: 0486829790

Category: Mathematics

Page: 96

View: 2016

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.
Posted in Mathematics

Foundations of Probability

Author: Alfred Renyi

Publisher: Courier Corporation

ISBN: 0486462617

Category: Mathematics

Page: 366

View: 6457

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.
Posted in Mathematics

Theories of Probability

An Examination of Foundations

Author: Terrence L. Fine

Publisher: Academic Press

ISBN: 1483263894

Category: Mathematics

Page: 276

View: 5230

Theories of Probability: An Examination of Foundations reviews the theoretical foundations of probability, with emphasis on concepts that are important for the modeling of random phenomena and the design of information processing systems. Topics covered range from axiomatic comparative and quantitative probability to the role of relative frequency in the measurement of probability. Computational complexity and random sequences are also discussed. Comprised of nine chapters, this book begins with an introduction to different types of probability theories, followed by a detailed account of axiomatic formalizations of comparative and quantitative probability and the relations between them. Subsequent chapters focus on the Kolmogorov formalization of quantitative probability; the common interpretation of probability as a limit of the relative frequency of the number of occurrences of an event in repeated, unlinked trials of a random experiment; an improved theory for repeated random experiments; and the classical theory of probability. The book also examines the origin of subjective probability as a by-product of the development of individual judgments into decisions. Finally, it suggests that none of the known theories of probability covers the whole domain of engineering and scientific practice. This monograph will appeal to students and practitioners in the fields of mathematics and statistics as well as engineering and the physical and social sciences.
Posted in Mathematics

Foundations of Modern Probability

Author: Olav Kallenberg

Publisher: Springer Science & Business Media

ISBN: 0387227040

Category: Mathematics

Page: 523

View: 6305

Unique for its broad and yet comprehensive coverage of modern probability theory, ranging from first principles and standard textbook material to more advanced topics. In spite of the economical exposition, careful proofs are provided for all main results. After a detailed discussion of classical limit theorems, martingales, Markov chains, random walks, and stationary processes, the author moves on to a modern treatment of Brownian motion, L=82vy processes, weak convergence, It=93 calculus, Feller processes, and SDEs. The more advanced parts include material on local time, excursions, and additive functionals, diffusion processes, PDEs and potential theory, predictable processes, and general semimartingales. Though primarily intended as a general reference for researchers and graduate students in probability theory and related areas of analysis, the book is also suitable as a text for graduate and seminar courses on all levels, from elementary to advanced. Numerous easy to more challenging exercises are provided, especially for the early chapters. From the author of "Random Measures".
Posted in Mathematics

Good Thinking

The Foundations of Probability and Its Applications

Author: Irving John Good

Publisher: U of Minnesota Press

ISBN: 1452910146

Category: Mathematics

Page: 332

View: 393

Good Thinking was first published in 1983.Good Thinking is a representative sampling of I. J. Good's writing on a wide range of questions about the foundations of statistical inference, especially where induction intersects with philosophy. Good believes that clear reasoning about many important practical and philosophical questions is impossible except in terms of probability. This book collects from various published sources 23 of Good's articles with an emphasis on more philosophical than mathematical.He covers such topics as rational decisions, randomness, operational research, measurement of knowledge, mathematical discovery, artificial intelligence, cognitive psychology, chess, and the nature of probability itself. In spite of the wide variety of topics covered, Good Thinking is based on a unified philosophy which makes it more than the sum of its parts. The papers are organized into five sections: Bayesian Rationality; Probability; Corroboration, Hypothesis Testing, and Simplicity; Information and Surprise; and Causality and Explanation. The numerous references, an extensive index, and a bibliography guide the reader to related modern and historic literature.This collection makes available to a wide audience, for the first time, the most accessible work of a very creative thinker. Philosophers of science, mathematicians, scientists, and, in Good's words, anyone who wants “to understand understanding, to reason about reasoning, to explain explanation, to think about thought, and to decide how to decide” will find Good Thinking a stimulating and provocative look at probability.
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Rethinking the Foundations of Statistics

Author: Joseph B. Kadane,Mark J. Schervish,Teddy Seidenfeld

Publisher: Cambridge University Press

ISBN: 9780521649759

Category: Mathematics

Page: 388

View: 9780

This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists.
Posted in Mathematics

The Logic of Chance

An Essay on the Foundations and Province of the Theory of Probability, with Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science

Author: John Venn

Publisher: N.A

ISBN: N.A

Category: Chance

Page: 488

View: 5133

Posted in Chance

Proceedings of the Conference Foundations of Probability and Physics

Vaxjo, Sweden, 25 November-1 December 2000

Author: A. Khrennikov

Publisher: World Scientific

ISBN: 9789812810809

Category: Electronic books

Page: 377

View: 1811

In this volume, leading experts in experimental as well as theoretical physics (both classical and quantum) and probability theory give their views on many intriguing (and still mysterious) problems regarding the probabilistic foundations of physics. The problems discussed during the conference include EinsteinOCoPodolskyOCoRosen paradox, Bell's inequality, realism, nonlocality, role of Kolmogorov model of probability theory in quantum physics, von Mises frequency theory, quantum information, computation, OC quantum effectsOCO in classical physics. Contents: Locality and Bell's Inequality (L Accardi & M Regoli); Refutation of Bell's Theorem (G Adenier); Forcing Discretization and Determination in Quantum History Theories (B Coecke); Some Remarks on Hardy Functions Associated with Dirichlet Series (W Ehm); Ensemble Probabilistic Equilibrium and Non-Equilibrium Thermodynamics without the Thermodynamic Limit (D H E Gross); An Approach to Quantum Probability (S Gudder); Innovation Approach to Stochastic Processes and Quantum Dynamics (T Hida); Origin of Quantum Probabilities (A Khrennikov); OC ComplementarityOCO or Schizophrenia: Is Probability in Quantum Mechanics Information or Onta? (A F Kracklauer); A Probabilistic Inequality for the KochenOCoSpecker Paradox (J-A Larsson); Quantum Stochastics. The New Approach to the Description of Quantum Measurements (E Loubenets); Is Random Event a Core Question? Some Remarks and a Proposal (P Rocchi); Quantum Cryptography in Space and Bell's Theorem (I Volovich); and other papers. Readership: Graduate students and researchers in quantum physics, mathematical physics, theoretical physics, stochastic processes, and probability & statistics."
Posted in Electronic books

Foundations of Stochastic Analysis

Author: M. M. Rao

Publisher: Courier Corporation

ISBN: 0486296539

Category: Mathematics

Page: 320

View: 7808

This volume considers fundamental theories and contrasts the natural interplay between real and abstract methods. No prior knowledge of probability is assumed. Numerous problems, most with hints. 1981 edition.
Posted in Mathematics

The Foundations of Statistics

Author: Leonard J. Savage

Publisher: Courier Corporation

ISBN: 0486137104

Category: Mathematics

Page: 352

View: 432

Classic analysis of the foundations of statistics and development of personal probability, one of the greatest controversies in modern statistical thought. Revised edition. Calculus, probability, statistics, and Boolean algebra are recommended.
Posted in Mathematics

Probabilistic Foundations of Statistical Network Analysis

Author: Harry Crane

Publisher: CRC Press

ISBN: 1351807331

Category: Business & Economics

Page: 236

View: 6930

Probabilistic Foundations of Statistical Network Analysis presents a fresh and insightful perspective on the fundamental tenets and major challenges of modern network analysis. Its lucid exposition provides necessary background for understanding the essential ideas behind exchangeable and dynamic network models, network sampling, and network statistics such as sparsity and power law, all of which play a central role in contemporary data science and machine learning applications. The book rewards readers with a clear and intuitive understanding of the subtle interplay between basic principles of statistical inference, empirical properties of network data, and technical concepts from probability theory. Its mathematically rigorous, yet non-technical, exposition makes the book accessible to professional data scientists, statisticians, and computer scientists as well as practitioners and researchers in substantive fields. Newcomers and non-quantitative researchers will find its conceptual approach invaluable for developing intuition about technical ideas from statistics and probability, while experts and graduate students will find the book a handy reference for a wide range of new topics, including edge exchangeability, relative exchangeability, graphon and graphex models, and graph-valued Levy process and rewiring models for dynamic networks. The author’s incisive commentary supplements these core concepts, challenging the reader to push beyond the current limitations of this emerging discipline. With an approachable exposition and more than 50 open research problems and exercises with solutions, this book is ideal for advanced undergraduate and graduate students interested in modern network analysis, data science, machine learning, and statistics. Harry Crane is Associate Professor and Co-Director of the Graduate Program in Statistics and Biostatistics and an Associate Member of the Graduate Faculty in Philosophy at Rutgers University. Professor Crane’s research interests cover a range of mathematical and applied topics in network science, probability theory, statistical inference, and mathematical logic. In addition to his technical work on edge and relational exchangeability, relative exchangeability, and graph-valued Markov processes, Prof. Crane’s methods have been applied to domain-specific cybersecurity and counterterrorism problems at the Foreign Policy Research Institute and RAND’s Project AIR FORCE. ? ? ? ? ? ?
Posted in Business & Economics

The Foundations of Causal Decision Theory

Author: James M. Joyce

Publisher: Cambridge University Press

ISBN: 9780521641647

Category: Computers

Page: 268

View: 2417

The early chapters of the book introduce the nonspecialist to the rudiments of expected utility theory.
Posted in Computers

Theories of Probability

An Examination of Logical and Qualitative Foundations

Author: Louis Narens

Publisher: World Scientific

ISBN: 9812708014

Category: Mathematics

Page: 219

View: 9498

Standard probability theory has been an enormously successful contribution to modern science. However, from many perspectives it is too narrow as a general theory of uncertainty, particularly for issues involving subjective uncertainty. This first-of-its-kind book is primarily based on qualitative approaches to probabilistic-like uncertainty, and includes qualitative theories for the standard theory as well as several of its generalizations.One of these generalizations produces a belief function composed of two functions: a probability function that measures the probabilistic strength of an uncertain event, and another function that measures the amount of ambiguity or vagueness of the event. Another unique approach of the book is to change the event space from a boolean algebra, which is closely linked to classical propositional logic, to a different event algebra that is closely linked to a well-studied generalization of classical propositional logic known as intuitionistic logic. Together, these new qualitative theories succeed where the standard probability theory fails by accounting for a number of puzzling empirical findings in the psychology of human probability judgments and decision making.
Posted in Mathematics

Probability Theory

The Logic of Science

Author: E. T. Jaynes

Publisher: Cambridge University Press

ISBN: 1139435167

Category: Science

Page: N.A

View: 1345

The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.
Posted in Science

Mathematical Foundations of Information Theory

Author: Aleksandr I?Akovlevich Khinchin

Publisher: Courier Corporation

ISBN: 0486604349

Category: Mathematics

Page: 120

View: 3762

First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.
Posted in Mathematics

The Theory of Probability

Author: Harold Jeffreys

Publisher: OUP Oxford

ISBN: 0191589675

Category: Mathematics

Page: 470

View: 2515

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.
Posted in Mathematics

Probability Foundations of Economic Theory

Author: Charles McCann

Publisher: Routledge

ISBN: 113483912X

Category: Business & Economics

Page: 188

View: 7492

First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.
Posted in Business & Economics

Probability Theory

Author: Alfred Renyi

Publisher: Courier Corporation

ISBN: 0486458679

Category: Mathematics

Page: 666

View: 1973

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.
Posted in Mathematics