Giovanni Parmigiani, Lurdes Inoue

Decision Theory

Principles and Approaches

• Gebundenes Buch

Produktbeschreibung

Decision Theory: Principles and Approaches offers a rich collection of techniques and procedures to reveal preferences and to introduce them into models of decision. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. It is fundamental to all scientific disciplines, including biostatistics, computer science, economics and engineering.

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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.

Produktdetails

• Verlag: John Wiley & Sons / Wiley
• Seitenzahl: 408
• Erscheinungstermin: 1. Juni 2009
• Englisch
• Abmessung: 235mm x 157mm x 26mm
• Gewicht: 736g
• ISBN-13: 9780471496571
• ISBN-10: 047149657X
• Artikelnr.: 26172295

Autorenporträt

Giovanni Parmigiani is the author of Decision Theory: Principles and Approaches, published by Wiley. Lurdes Yoshiko Tani Inoue is a Brazilian-born statistician of Japanese descent, who specializes in Bayesian inference. She works as a professor of biostatistics in the University of Washington School of Public Health.

Inhaltsangabe

Preface. Acknowledgments. 1 Introduction. 1.1 Controversies. 1.2 A guided
tour of decision theory. Part One: Foundations. 2 Coherence. 2.1 The "Dutch
Book" theorem. 2.2 Temporal coherence. 2.3 Scoring rules and the axioms of
probabilities. 2.4 Exercises. 3 Utility. 3.1 St. Petersburg paradox. 3.2
Expected utility theory and the theory of means. 3.3 The expected utility
principle. 3.4 The von Neumann-Morgenstern representation theorem. 3.5
Allais' criticism. 3.6 Extensions. 3.7 Exercises. 4 Utility in action. 4.1
The "standard gamble". 4.2 Utility of money. 4.3 Utility functions for
medical decisions. 4.4 Exercises. 5 Ramsey and Savage. 5.1 Ramsey's theory.
5.2 Savage's theory. 5.3 Allais revisited. 5.4 Ellsberg paradox. 5.5
Exercises. 6 State independence. 6.1 Horse lotteries. 6.2 State-dependent
utilities. 6.3 State-independent utilities. 6.4 Anscombe-Aumann
representation theorem. 6.5 Exercises. Part Two Statistical Decision
Theory. 7 Decision functions. 7.1 Basic concepts. 7.2 Data-based decisions.
7.3 The travel insurance example. 7.4 Randomized decision rules. 7.5
Classification and hypothesis tests. 7.6 Estimation. 7.7 Minimax-Bayes
connections. 7.8 Exercises. 8 Admissibility. 8.1 Admissibility and
completeness. 8.2 Admissibility and minimax. 8.3 Admissibility and Bayes.
8.4 Complete classes. 8.5 Using the same ± level across studies with
different sample sizes is inadmissible. 8.6 Exercises. 9 Shrinkage. 9.1 The
Stein effect. 9.2 Geometric and empirical Bayes heuristics. 9.3 General
shrinkage functions. 9.4 Shrinkage with different likelihood and losses.
9.5 Exercises. 10 Scoring rules. 10.1 Betting and forecasting. 10.2 Scoring
rules. 10.3 Local scoring rules. 10.4 Calibration and refinement. 10.5
Exercises. 11 Choosing models. 11.1 The "true model" perspective. 11.2
Model elaborations. 11.3 Exercises. Part Three Optimal Design. 12 Dynamic
programming. 12.1 History. 12.2 The travel insurance example revisited.
12.3 Dynamic programming. 12.4 Trading off immediate gains and information.
12.5 Sequential clinical trials. 12.6 Variable selection in multiple
regression. 12.7 Computing. 12.8 Exercises. 13 Changes in utility as
information. 13.1 Measuring the value of information. 13.2 Examples. 13.3
Lindley information. 13.4 Minimax and the value of information. 13.5
Exercises. 14 Sample size. 14.1 Decision-theoretic approaches to sample
size. 14.2 Computing. 14.3 Examples. 14.4 Exercises. 15 Stopping. 15.1
Historical note. 15.2 A motivating example. 15.3 Bayesian optimal stopping.
15.4 Examples. 15.5 Sequential sampling to reduce uncertainty. 15.6 The
stopping rule principle. 15.7 Exercises. Appendix. A.1 Notation. A.2
Relations. A.3 Probability (density) functions of some distributions. A.4
Conjugate updating. References. Index.