Pierre-Simon Laplace Philosophical Essay on Probabilities

Translated from the fifth French edition of 1825 With Notes by the Translator

Author: Pierre-Simon Laplace

Publisher: Springer Science & Business Media

ISBN: 9780387943497

Category: Mathematics

Page: 270

View: 1806

Pierre-Simon Laplace (1749-1827) is remembered amoung probabilitists today particularly for his "Theorie analytique des probabilites", published in 1812. This is a thorough and modern translation based on the recent re-issue, with its voluminous notes, of the fifth edition of 1826, with preface by Rene Thom and postscript by Bernard Bru. In the second part of the book, the reader is provided with an extensive commentary by the translator including valuable histographical and mathematical remarks and various proofs.

Measures and Probabilities

Author: Michel Simonnet

Publisher: Springer Science & Business Media

ISBN: 9780387946443

Category: Mathematics

Page: 510

View: 4539

Integration theory holds a prime position, whether in pure mathematics or in various fields of applied mathematics. It plays a central role in analysis; it is the basis of probability theory and provides an indispensable tool in mathe matical physics, in particular in quantum mechanics and statistical mechanics. Therefore, many textbooks devoted to integration theory are already avail able. The present book by Michel Simonnet differs from the previous texts in many respects, and, for that reason, it is to be particularly recommended. When dealing with integration theory, some authors choose, as a starting point, the notion of a measure on a family of subsets of a set; this approach is especially well suited to applications in probability theory. Other authors prefer to start with the notion of Radon measure (a continuous linear func tional on the space of continuous functions with compact support on a locally compact space) because it plays an important role in analysis and prepares for the study of distribution theory. Starting off with the notion of Daniell measure, Mr. Simonnet provides a unified treatment of these two approaches.

Probability For Dummies

Author: Deborah J. Rumsey

Publisher: John Wiley & Sons

ISBN: 9780470043639

Category: Mathematics

Page: 384

View: 6060

Packed with practical tips and techniques for solving probability problems Increase your chances of acing that probability exam -- or winning at the casino! Whether you're hitting the books for a probability or statistics course or hitting the tables at a casino, working out probabilities can be problematic. This book helps you even the odds. Using easy-to-understand explanations and examples, it demystifies probability -- and even offers savvy tips to boost your chances of gambling success! Discover how to * Conquer combinations and permutations * Understand probability models from binomial to exponential * Make good decisions using probability * Play the odds in poker, roulette, and other games

A Philosophical Essay on Probabilities

Author: Pierre-Simon Laplace

Publisher: Courier Corporation

ISBN: 0486170349

Category: Mathematics

Page: 224

View: 5677

Without the use of higher mathematics, this classic demonstrates the application of probability to games of chance, physics, reliability of witnesses, astronomy, insurance, democratic government, and many other areas.

Interpretations of Probability

Author: Andrei Khrennikov

Publisher: Walter de Gruyter

ISBN: 3110213192

Category: Mathematics

Page: 237

View: 7119

This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.

Fundamentals-Based Estimation of Default Probabilities: A Survey

Author: Jorge A. Chan-Lau

Publisher: International Monetary Fund


Category: Corporations

Page: 20

View: 1023

This survey reviews a number of different fundamentals-based models for estimating default probabilities for firms and/or industries, and illustrates them with real applications by practitioners and policy making institutions. The models are especially useful when the firms analyzed do not have publicly traded securities or secondary market prices are unreliable because of low liquidity.

The Doctrine of Chances

Or, a Method of Calculating the Probabilities of Events in Play. The Third Edition, Fuller, Clearer, and More Correct Than the Former. By A. de Moivre, ...

Author: Abraham de Moivre

Publisher: N.A


Category: Electronic books

Page: 348

View: 7424

Market-Based Estimation of Default Probabilities and Its Application to Financial Market Surveillance

Author: Jorge A. Chan-Lau

Publisher: International Monetary Fund


Category: Capital market

Page: 19

View: 4121

This paper reviews a number of different techniques for estimating default probabilities from the prices of publicly traded securities. These techniques are useful for assessing credit exposure, systemic risk, and stress testing financial systems. The choice of techniques was guided by their ease of implementation and their applicability to a wide cross-section of countries and markets. Simple one-period cases are studied to sharpen the reader's intuition, and the usefulness of each technique for enhancing financial surveillance is illustrated with real applications.

Probability Theory

Author: A A Borovkov

Publisher: CRC Press

ISBN: 9789056990466

Category: Mathematics

Page: 484

View: 1324

Probability theory forms the basis of mathematical statistics, and has applications in many related areas. This comprehensive book tackles the principal problems and advanced questions of probability theory in 21 self-contained chapters, which are presented in logical order, but are also easy to deal with individually. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results. Probability theory is currently an extremely active area of research internationally, and the importance of the Russian school in the development of the subject has long been recognized. The frequent references to Russian literature throughout this work lend a fresh dimension to the book, and make it an invaluable source of reference for Western researchers and advanced students in probability related subjects.

Philosophical Theories of Probability

Author: Donald Gillies

Publisher: Routledge

ISBN: 1134672454

Category: Philosophy

Page: 240

View: 947

The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

Fuzzy Probabilities and Fuzzy Sets for Web Planning

Author: James J. Buckley

Publisher: Springer Science & Business Media

ISBN: 9783540004738

Category: Mathematics

Page: 190

View: 2832

1.1 Introduction This book is written in five major divisions. The first part is the introduc tory chapters consisting of Chapters 1-3. In part two, Chapters 4-10, we use fuzzy probabilities to model a fuzzy queuing system . We switch to employ ing fuzzy arrival rates and fuzzy service rates to model the fuzzy queuing system in part three in Chapters 11 and 12. Optimization models comprise part four in Chapters 13-17. The final part has a brief summary and sug gestions for future research in Chapter 18, and a summary of our numerical methods for calculating fuzzy probabilities, values of objective functions in fuzzy optimization, etc., is in Chapter 19. First we need to be familiar with fuzzy sets. All you need to know about fuzzy sets for this book comprises Chapter 2. Two other items relating to fuzzy sets, needed in Chapters 13-17, are also in Chapter 2: (1) how we plan to handle the maximum/minimum of a fuzzy set; and (2) how we will rank a finite collection of fuzzy numbers from smallest to largest.


The Little Numbers That Rule Our Lives

Author: Peter Olofsson

Publisher: John Wiley & Sons

ISBN: 1118898907

Category: Education

Page: 328

View: 6887

What are the chances? Find out in this entertaining exploration of probabilities in our everyday lives "If there is anything you want to know, or remind yourself, about probabilities, then look no further than this comprehensive, yet wittily written and enjoyable, compendium of how to apply probability calculations in real-world situations."--Keith Devlin, Stanford University, National Public Radio's "Math Guy" and author of The Math Gene and The Math Instinct. "A delightful guide to the sometimes counterintuitive discipline of probability. Olofsson points out major ideas here, explains classic puzzles there, and everywhere makes free use of witty vignettes to instruct and amuse."--John Allen Paulos, Temple University, author of Innumeracy and A Mathematician Reads the Newspaper. "Beautifully written, with fascinating examples and tidbits of information. Olofsson gently and persuasively shows us how to think clearly about the uncertainty that governs our lives."--John Haigh, University of Sussex, author of Taking Chances: Winning with Probability. From probable improbabilities to regular irregularities, Probabilities: The Little Numbers That Rule Our Lives investigates the often-surprising effects of risk and chance in our everyday lives. With examples ranging from WWII espionage to the O.J. Simpson trial, from bridge to blackjack, from Julius Caesar to Jerry Seinfeld, the reader is taught how to think straight in a world of randomness and uncertainty. Throughout the book, readers learn: -Why it is not that surprising for someone to win the lottery twice -How a faulty probability calculation forced an innocent woman to spend three years in prison -How to place bets if you absolutely insist on gambling -How a newspaper turned an opinion poll into one of the greatest election blunders in history. Educational, eloquent, and entertaining, Probabilities: The Little Numbers That Rule Our Lives is the ideal companion for anyone who wants to obtain a better understanding of the mathematics of chance.

Invariant Probabilities of Transition Functions

Author: Radu Zaharopol

Publisher: Springer

ISBN: 3319057235

Category: Mathematics

Page: 389

View: 8951

The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizations of the supports of various types of invariant probability measures and the use of these to obtain criteria for unique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will be of interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also find this book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, general topology, measure theory, the Bochner integral and some of its applications.