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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. show more (1)
this text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. a detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. this well-organized treatment supplements its rigor with intuitive ideas. starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, lagrangians, and gauge invariance; lagrange's equation for particle fields; and the inhomogeneous field equation. additional topics include free dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. the text concludes with references, a selected bibliography, an index of notation, and a general index. show more (1)

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1 图书 Gauge Theory and Variational Principles
责任者 David Bleecker

出版信息 Dover Publications, Inc. ,2005

ISBN 978-0-48644-546-5

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David Bleecker.Gauge Theory and Variational Principles.Dover Publications, Inc.,2005.
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Gauge Theory and Variational Principles

David Bleecker.Dover Publications, Inc.,2005.
2 图书 Theory of Games and Statistical Decisions
责任者 Blackwell, David A ; Girshick, M A

出版信息 Dover Publications, Inc. ,1979

ISBN 978-0-48663-831-7

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Blackwell, David A ; Girshick, M A.Theory of Games and Statistical Decisions.Dover Publications, Inc.,1979.
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Theory of Games and Statistical Decisions

Blackwell, David A ; Girshick, M A.Dover Publications, Inc.,1979.

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