An Introduction to Decision Theory

An Introduction to Decision Theory
Author: Martin Peterson
Publisher: Cambridge University Press
Total Pages: 351
Release: 2017-03-30
Genre: Business & Economics
ISBN: 1107151597

A comprehensive and accessible introduction to all aspects of decision theory, now with new and updated discussions and over 140 exercises.

Decision Theory

Decision Theory
Author: Giovanni Parmigiani
Publisher: John Wiley & Sons
Total Pages: 416
Release: 2009-05-26
Genre: Business & Economics
ISBN:

Decision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice. The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives. This book: * Provides a rich collection of techniques and procedures. * Discusses the foundational aspects and modern day practice. * Links foundations to practical applications in biostatistics, computer science, engineering and economics. * Presents different perspectives and controversies to encourage readers to form their own opinion of decision making and statistics. Decision Theory is fundamental to all scientific disciplines, including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book.

Decision Theory with a Human Face

Decision Theory with a Human Face
Author: Richard Bradley
Publisher: Cambridge University Press
Total Pages: 351
Release: 2017-10-26
Genre: Business & Economics
ISBN: 1107003210

Explores how decision-makers can manage uncertainty that varies in both kind and severity by extending and supplementing Bayesian decision theory.

Elementary Decision Theory

Elementary Decision Theory
Author: Herman Chernoff
Publisher: Courier Corporation
Total Pages: 386
Release: 1986-01-01
Genre: Mathematics
ISBN: 9780486652184

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.

Statistical Decision Theory and Bayesian Analysis

Statistical Decision Theory and Bayesian Analysis
Author: James O. Berger
Publisher: Springer Science & Business Media
Total Pages: 633
Release: 2013-03-14
Genre: Mathematics
ISBN: 147574286X

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.

Theory of Games and Statistical Decisions

Theory of Games and Statistical Decisions
Author: David A. Blackwell
Publisher: Courier Corporation
Total Pages: 388
Release: 2012-06-14
Genre: Mathematics
ISBN: 0486150895

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.

Theory of Decision Under Uncertainty

Theory of Decision Under Uncertainty
Author: Itzhak Gilboa
Publisher: Cambridge University Press
Total Pages: 216
Release: 2009-03-16
Genre: Business & Economics
ISBN: 052151732X

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.

Decision Theory as Philosophy

Decision Theory as Philosophy
Author: Mark Kaplan
Publisher: Cambridge University Press
Total Pages: 250
Release: 1996
Genre: Philosophy
ISBN: 9780521624961

Kaplan presents an accessible new variant on Bayesian decision theory.

Statistical Decision Theory

Statistical Decision Theory
Author: F. Liese
Publisher: Springer Science & Business Media
Total Pages: 696
Release: 2008-12-30
Genre: Mathematics
ISBN: 0387731946

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.