Foundations of the Theory of Probability

Second English Edition

Author: A.N. Kolmogorov

Publisher: Courier Dover Publications

ISBN: 0486829790

Category: Mathematics

Page: 96

View: 3218

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.

Foundations of Probability

Author: Alfred Renyi

Publisher: Courier Corporation

ISBN: 0486462617

Category: Mathematics

Page: 366

View: 6376

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.

Theories of Probability

An Examination of Foundations

Author: Terrence L. Fine

Publisher: Academic Press

ISBN: 1483263894

Category: Mathematics

Page: 276

View: 1034

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.

Foundations of Modern Probability

Author: Olav Kallenberg

Publisher: Springer Science & Business Media

ISBN: 0387227040

Category: Mathematics

Page: 523

View: 2455

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".

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


Category: Chance

Page: 488

View: 5959

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: 9824

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.

The Foundations of Causal Decision Theory

Author: James M. Joyce

Publisher: Cambridge University Press

ISBN: 1139471384

Category: Science

Page: N.A

View: 5001

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available.

Theories of Probability

An Examination of Logical and Qualitative Foundations

Author: Louis Narens

Publisher: World Scientific

ISBN: 9812708014

Category: Mathematics

Page: 219

View: 3942

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.

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: 8643

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."

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: 5653

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.

Mathematical Foundations of Statistical Mechanics

Author: Aleksandr I?Akovlevich Khinchin

Publisher: Courier Corporation

ISBN: 9780486601472

Category: Mathematics

Page: 179

View: 797

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.

The Foundations of Statistics

Author: Leonard J. Savage

Publisher: Courier Corporation

ISBN: 0486137104

Category: Mathematics

Page: 352

View: 7488

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.

Probability Theory

Author: Alfred Renyi

Publisher: Courier Corporation

ISBN: 0486458679

Category: Mathematics

Page: 666

View: 923

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 Stochastic Analysis

Author: M. M. Rao

Publisher: Courier Corporation

ISBN: 0486296539

Category: Mathematics

Page: 320

View: 7297

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.

Probability Theory

A Historical Sketch

Author: L. E. Maistrov

Publisher: Academic Press

ISBN: 1483218635

Category: Mathematics

Page: 292

View: 7569

Probability Theory: A Historical Sketch covers the probability theory, mainly axiomatization problems. The book discusses the prehistory of the probability theory; the first stage in the development of probability theory; and the development of probability theory to the middle of the 19th century. The text also describes the probability theory in the second half of the 19th century; and the axiomatic foundations of the probability theory. Historians and mathematicians will find the book invaluable.

The Theory of Probability

An Inquiry Into the Logical and Mathematical Foundations of the Calculus of Probability

Author: Hans Reichenbach

Publisher: Univ of California Press

ISBN: 9780520019294

Category: Logic, Symbolic and mathematical

Page: 492

View: 3862

The Theory of Probability

Author: Harold Jeffreys

Publisher: OUP Oxford

ISBN: 0191589675

Category: Mathematics

Page: 470

View: 7051

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.

Lady Luck

The Theory of Probability

Author: Warren Weaver

Publisher: Courier Corporation

ISBN: 0486150917

Category: Mathematics

Page: 400

View: 9149

This witty, nontechnical introduction to probability elucidates such concepts as permutations, independent events, mathematical expectation, the law of averages and more. No advanced math required. 49 drawings.

Nomic Probability and the Foundations of Induction

Author: John L. Pollock

Publisher: Oxford University Press

ISBN: 9780195345216

Category: Mathematics

Page: 368

View: 4720

In this book Pollock deals with the subject of probabilistic reasoning, making general philosophical sense of objective probabilities and exploring their relationship to the problem of induction. He argues that probability is fundamental not only to physical science, but to induction, epistemology, the philosophy of science and much of the reasoning relevant to artificial intelligence. Pollock's main claim is that the fundamental notion of probability is nomic--that is, it involves the notion of natural law, valid across possible worlds. The various epistemic and statistical conceptions of probability, he demonstrates, are derived from this nomic notion. He goes on to provide a theory of statistical induction, an account of computational principles allowing some probabilities to be derived from others, an account of acceptance rules, and a theory of direct inference.