Parmigiani / Inoue Decision Theory

Principles and Approaches
1. Auflage 2009
ISBN: 978-0-470-74667-7
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 402 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

Decision theory provides a formal framework for making logicalchoices in the face of uncertainty. Given a set of alternatives, aset 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 andoutcomes of rational decision making under uncertainty,highlighting the implications for statistical practice.
The authors have developed a series of self contained chaptersfocusing on bridging the gaps between the different fields thathave contributed to rational decision making and presenting ideasin a unified framework and notation while respecting andhighlighting the different and sometimes conflictingperspectives.
This book:
* Provides a rich collection of techniques and procedures.
* Discusses the foundational aspects and modern daypractice.
* Links foundations to practical applications in biostatistics,computer science, engineering and economics.
* Presents different perspectives and controversies to encouragereaders to form their own opinion of decision making andstatistics.
Decision Theory is fundamental to all scientific disciplines,including biostatistics, computer science, economics andengineering. Anyone interested in the whys and wherefores ofstatistical science will find much to enjoy in this book.

Autoren/Hrsg.

Parmigiani, Giovanni

Inoue, Lurdes

Inhaltsverzeichnis

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 representationtheorem.
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 alpha level across studies withdifferent 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.