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Author: John Winsor Pratt
Publisher:
ISBN:
Category : Statistical Decision
Languages : en
Pages : 875
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Book Description
Author: John Winsor Pratt
Publisher:
ISBN:
Category : Statistical Decision
Languages : en
Pages : 875
Get Book Here
Book Description
Author: Silvia Bacci
Publisher: CRC Press
ISBN: 1351621386
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Introduction to Statistical Decision Theory: Utility Theory and Causal Analysis provides the theoretical background to approach decision theory from a statistical perspective. It covers both traditional approaches, in terms of value theory and expected utility theory, and recent developments, in terms of causal inference. The book is specifically designed to appeal to students and researchers that intend to acquire a knowledge of statistical science based on decision theory. Features Covers approaches for making decisions under certainty, risk, and uncertainty Illustrates expected utility theory and its extensions Describes approaches to elicit the utility function Reviews classical and Bayesian approaches to statistical inference based on decision theory Discusses the role of causal analysis in statistical decision theory
Author: James O. Berger
Publisher: Springer Science & Business Media
ISBN: 147574286X
Category : Mathematics
Languages : en
Pages : 633
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Book Description
In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.
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: Michael Zabarankin
Publisher: Springer Science & Business Media
ISBN: 1461484715
Category : Business & Economics
Languages : en
Pages : 254
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Book Description
Statistical Decision Problems presents a quick and concise introduction into the theory of risk, deviation and error measures that play a key role in statistical decision problems. It introduces state-of-the-art practical decision making through twenty-one case studies from real-life applications. The case studies cover a broad area of topics and the authors include links with source code and data, a very helpful tool for the reader. In its core, the text demonstrates how to use different factors to formulate statistical decision problems arising in various risk management applications, such as optimal hedging, portfolio optimization, cash flow matching, classification, and more. The presentation is organized into three parts: selected concepts of statistical decision theory, statistical decision problems, and case studies with portfolio safeguard. The text is primarily aimed at practitioners in the areas of risk management, decision making, and statistics. However, the inclusion of a fair bit of mathematical rigor renders this monograph an excellent introduction to the theory of general error, deviation, and risk measures for graduate students. It can be used as supplementary reading for graduate courses including statistical analysis, data mining, stochastic programming, financial engineering, to name a few. The high level of detail may serve useful to applied mathematicians, engineers, and statisticians interested in modeling and managing risk in various applications.
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: 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: John Winsor Pratt
Publisher: MIT Press
ISBN: 9780262161442
Category : Business & Economics
Languages : en
Pages : 906
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Book Description
They then examine the Bernoulli, Poisson, and Normal (univariate and multivariate) data generating processes.
Author: David Middleton
Publisher: Wiley-IEEE Press
ISBN:
Category : Mathematics
Languages : en
Pages : 1192
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Book Description
This IEEE Classic Reissue provides at an advanced level, a uniquely fundamental exposition of the applications of Statistical Communication Theory to a vast spectrum of important physical problems. Included are general analysis of signal detection, estimation, measurement, and related topics involving information transfer. Using the statistical Bayesian viewpoint, renowned author David Middleton employs statistical decision theory specifically tailored for the general tasks of signal processing. Dr. Middleton also provides a special focus on physical modeling of the canonical channel with real-world examples relating to radar, sonar, and general telecommunications. This book offers a detailed treatment and an array of problems and results spanning an exceptionally broad range of technical subjects in the communications field. Complete with special functions, integrals, solutions of integral equations, and an extensive, updated bibliography by chapter, An Introduction to Statistical Communication Theory is a seminal reference, particularly for anyone working in the field of communications, as well as in other areas of statistical physics. (Originally published in 1960.)
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.
