Elementary Decision Theory PDF Download
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Author: Herman Chernoff
Publisher: Courier Corporation
ISBN: 9780486652184
Category : Mathematics
Languages : en
Pages : 386
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Book Description
This well-respected introduction to statistics and statistical theory covers data processing, probability and random variables, utility and descriptive statistics, computation of Bayes strategies, models, testing hypotheses, and much more. 1959 edition.
Author: Herman Chernoff
Publisher: Courier Corporation
ISBN: 9780486652184
Category : Mathematics
Languages : en
Pages : 386
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Book Description
This well-respected introduction to statistics and statistical theory covers data processing, probability and random variables, utility and descriptive statistics, computation of Bayes strategies, models, testing hypotheses, and much more. 1959 edition.
Author: Martin Peterson
Publisher: Cambridge University Press
ISBN: 1107151597
Category : Business & Economics
Languages : en
Pages : 351
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Book Description
A comprehensive and accessible introduction to all aspects of decision theory, now with new and updated discussions and over 140 exercises.
Author: Peter C. Fishburn
Publisher:
ISBN:
Category : Decision-making
Languages : en
Pages : 120
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Book Description
Author: David A. Blackwell
Publisher: Courier Corporation
ISBN: 0486150895
Category : Mathematics
Languages : en
Pages : 388
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Book Description
Evaluating statistical procedures through decision and game theory, as first proposed by Neyman and Pearson and extended by Wald, is the goal of this problem-oriented text in mathematical statistics. First-year graduate students in statistics and other students with a background in statistical theory and advanced calculus will find a rigorous, thorough presentation of statistical decision theory treated as a special case of game theory. The work of Borel, von Neumann, and Morgenstern in game theory, of prime importance to decision theory, is covered in its relevant aspects: reduction of games to normal forms, the minimax theorem, and the utility theorem. With this introduction, Blackwell and Professor Girshick look at: Values and Optimal Strategies in Games; General Structure of Statistical Games; Utility and Principles of Choice; Classes of Optimal Strategies; Fixed Sample-Size Games with Finite Ω and with Finite A; Sufficient Statistics and the Invariance Principle; Sequential Games; Bayes and Minimax Sequential Procedures; Estimation; and Comparison of Experiments. A few topics not directly applicable to statistics, such as perfect information theory, are also discussed. Prerequisites for full understanding of the procedures in this book include knowledge of elementary analysis, and some familiarity with matrices, determinants, and linear dependence. For purposes of formal development, only discrete distributions are used, though continuous distributions are employed as illustrations. The number and variety of problems presented will be welcomed by all students, computer experts, and others using statistics and game theory. This comprehensive and sophisticated introduction remains one of the strongest and most useful approaches to a field which today touches areas as diverse as gambling and particle physics.
Author: Thomas S. Ferguson
Publisher: Academic Press
ISBN: 1483221237
Category : Mathematics
Languages : en
Pages : 409
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Book Description
Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in mathematics.
Author: James Berger
Publisher: Springer Science & Business Media
ISBN: 147571727X
Category : Mathematics
Languages : en
Pages : 440
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Book Description
Decision theory is generally taught in one of two very different ways. When of opti taught by theoretical statisticians, it tends to be presented as a set of mathematical techniques mality principles, together with a collection of various statistical procedures. When useful in establishing the optimality taught by applied decision theorists, it is usually a course in Bayesian analysis, showing how this one decision principle can be applied in various practical situations. The original goal I had in writing this book was to find some middle ground. I wanted a book which discussed the more theoretical ideas and techniques of decision theory, but in a manner that was constantly oriented towards solving statistical problems. In particular, it seemed crucial to include a discussion of when and why the various decision prin ciples should be used, and indeed why decision theory is needed at all. This original goal seemed indicated by my philosophical position at the time, which can best be described as basically neutral. I felt that no one approach to decision theory (or statistics) was clearly superior to the others, and so planned a rather low key and impartial presentation of the competing ideas. In the course of writing the book, however, I turned into a rabid Bayesian. There was no single cause for this conversion; just a gradual realization that things seemed to ultimately make sense only when looked at from the Bayesian viewpoint.
Author: F. Liese
Publisher: Springer Science & Business Media
ISBN: 0387731946
Category : Mathematics
Languages : en
Pages : 696
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Book Description
For advanced graduate students, this book is a one-stop shop that presents the main ideas of decision theory in an organized, balanced, and mathematically rigorous manner, while observing statistical relevance. All of the major topics are introduced at an elementary level, then developed incrementally to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. With its broad coverage of decision theory, this book fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory.
Author: Simon French
Publisher: Prentice Hall
ISBN: 9780132010139
Category : Science
Languages : en
Pages : 448
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Book Description
Author: Itzhak Gilboa
Publisher: Cambridge University Press
ISBN: 052151732X
Category : Business & Economics
Languages : en
Pages : 216
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Book Description
This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques.
Author: T. W. Körner
Publisher: Cambridge University Press
ISBN: 1139473565
Category : Mathematics
Languages : en
Pages : 375
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Book Description
How should one choose the best restaurant to eat in? Can one really make money at gambling? Or predict the future? Naive Decision Making presents the mathematical basis for making decisions where the outcome may be uncertain or the interests of others have to taken into consideration. Professor Körner takes the reader on an enjoyable journey through many aspects of mathematical decision making, with pithy observations, anecdotes and quotations. Topics include probability, statistics, Arrow's theorem, Game Theory and Nash equilibrium. Readers will also gain a great deal of insight into mathematics in general and the role it can play within society. Intended for those with elementary calculus, this book is ideal as a supplementary text for undergraduate courses in probability, game theory and decision making. Engaging and intriguing, it will also appeal to all those of a mathematical mind. To aid understanding, many exercises are included, with solutions available online.
