Author: William Eckhardt
Publisher: Springer Science & Business Media
ISBN: 9400751400
Category : Mathematics
Languages : en
Pages : 85
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Book Description
Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.
Author: Gábor J. Székely
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 272
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Book Description
It isn't that they can't see the solution. Approach your problems from the right end and begin with the answers. It is that they can't see the problem. Then one day, perhaps you will find G. K. Chesterton. The Scandal of the final question. Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (nontrivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowski lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experi mental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Author: Michael A. Proschan
Publisher: CRC Press
ISBN: 1498704204
Category : Mathematics
Languages : en
Pages : 334
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Book Description
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.
Author: Charles Miller Grinstead
Publisher: American Mathematical Soc.
ISBN: 0821894145
Category : Mathematics
Languages : en
Pages : 530
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Book Description
This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject.
Author: Eric Sowey
Publisher: John Wiley & Sons
ISBN: 1119075823
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Dieses Buch nimmt den Leser mit auf eine anregende Reise rund um die Welt der Statistik. Auf eine ganz andere Art werden Theorie und Praxis Dozenten, Studenten und Praktikern nahe gebracht. Auf jeder Etappe dieser Reise untersuchen die Autoren ungewöhnliche und skurille Aspekte der Statistik, stellen historische, biographische und philosophische Dimensionen heraus. Die einzelnen Kapitel beginnen mit einem Ausblick auf das Thema, oftmals aus unterschiedlichen Blickwinkeln. Darauf folgen fünf Fragen, die zum Nachdenken anregen. Ziel ist es, die Kenntnisse der Leser zu erweitern und zu vertiefen. Zu den Fragen gibt es auch immer wieder unterhaltsame Rätsel, mit denen spannende Paradoxa aufgelöst werden. Die Leser können ihre eigenen Entdeckungen in der Welt der Statistik mit den ausführlichen Antworten der Autoren auf die jeweiligen Fragen vergleichen.
Author: Mark Chang
Publisher: CRC Press
ISBN: 1466509864
Category : Computers
Languages : en
Pages : 294
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Book Description
Paradoxes are poems of science and philosophy that collectively allow us to address broad multidisciplinary issues within a microcosm. A true paradox is a source of creativity and a concise expression that delivers a profound idea and provokes a wild and endless imagination. The study of paradoxes leads to ultimate clarity and, at the same time, indisputably challenges your mind. Paradoxes in Scientific Inference analyzes paradoxes from many different perspectives: statistics, mathematics, philosophy, science, artificial intelligence, and more. The book elaborates on findings and reaches new and exciting conclusions. It challenges your knowledge, intuition, and conventional wisdom, compelling you to adjust your way of thinking. Ultimately, you will learn effective scientific inference through studying the paradoxes.
Author: Raymond S. Nickerson
Publisher: Psychology Press
ISBN: 113561461X
Category : Business & Economics
Languages : en
Pages : 798
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Book Description
Lack of ability to think probabilistically makes one prone to a variety of irrational fears and vulnerable to scams designed to exploit probabilistic naiveté, impairs decision making under uncertainty, facilitates the misinterpretation of statistical information, and precludes critical evaluation of likelihood claims. Cognition and Chance presents an overview of the information needed to avoid such pitfalls and to assess and respond to probabilistic situations in a rational way. Dr. Nickerson investigates such questions as how good individuals are at thinking probabilistically and how consistent their reasoning under uncertainty is with principles of mathematical statistics and probability theory. He reviews evidence that has been produced in researchers' attempts to investigate these and similar types of questions. Seven conceptual chapters address such topics as probability, chance, randomness, coincidences, inverse probability, paradoxes, dilemmas, and statistics. The remaining five chapters focus on empirical studies of individuals' abilities and limitations as probabilistic thinkers. Topics include estimation and prediction, perception of covariation, choice under uncertainty, and people as intuitive probabilists. Cognition and Chance is intended to appeal to researchers and students in the areas of probability, statistics, psychology, business, economics, decision theory, and social dilemmas.
Author: Y. Rozanov
Publisher: Springer Science & Business Media
ISBN: 9401104492
Category : Mathematics
Languages : en
Pages : 267
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Book Description
Probability Theory, Theory of Random Processes and Mathematical Statistics are important areas of modern mathematics and its applications. They develop rigorous models for a proper treatment for various 'random' phenomena which we encounter in the real world. They provide us with numerous tools for an analysis, prediction and, ultimately, control of random phenomena. Statistics itself helps with choice of a proper mathematical model (e.g., by estimation of unknown parameters) on the basis of statistical data collected by observations. This volume is intended to be a concise textbook for a graduate level course, with carefully selected topics representing the most important areas of modern Probability, Random Processes and Statistics. The first part (Ch. 1-3) can serve as a self-contained, elementary introduction to Probability, Random Processes and Statistics. It contains a number of relatively sim ple and typical examples of random phenomena which allow a natural introduction of general structures and methods. Only knowledge of elements of real/complex analysis, linear algebra and ordinary differential equations is required here. The second part (Ch. 4-6) provides a foundation of Stochastic Analysis, gives information on basic models of random processes and tools to study them. Here a familiarity with elements of functional analysis is necessary. Our intention to make this course fast-moving made it necessary to present important material in a form of examples.
Author: Mark Chang
Publisher: CRC Press
ISBN: 1466509872
Category : Computers
Languages : en
Pages : 284
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Book Description
Paradoxes are poems of science and philosophy that collectively allow us to address broad multidisciplinary issues within a microcosm. A true paradox is a source of creativity and a concise expression that delivers a profound idea and provokes a wild and endless imagination. The study of paradoxes leads to ultimate clarity and, at the same time, in
Author:
Publisher: Allied Publishers
ISBN: 9788177644517
Category :
Languages : en
Pages : 436
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Book Description
Probability theory
