STA 226 - Statistical Decision Theory Duke University, Spring 2001

Tentative Course Plan - to be updated throughout the semester:

Jan 10 - 1. Introductory example. Overview of the course.

Foundations

Jan 17 - 2. Basic concepts, notation and definitions. Principles of choice (minimax,

expected utility).

Jan 22 - 3. Coherence and the axioms of probability. Dutch Book Theorem. Called-off

bets and conditional probability.

Jan 24 - 4. Proper scoring rules and subjective probability. Characterization of proper local

scoring rules. Application: assessing model adequacy on validation samples.

Jan 29 - 5. History. Bernoulli: St. Petersburg Paradox. Certainty equivalents.

von-Neumann and Morggenstern utility theory.

Jan 31 - 6. Anscombe-Aumann model, axioms and characterization.

Feb 5 - 7. Overview of Savage's Theory

Feb 7 - 8. Criticisms of expected utility theory. Allais. Ellsberg.

Decision Making

Feb 12 - 9. Eliciting utility for money

Feb 14 - 10. Eliciting utility for health states

Feb 19 - 11. Two-stage sequential decision problems. Folding back decision trees.

Feb 21 - 12. Decision analysis of axillary lymph node dissection in breast cancer.

Feb 26 - 13. Multistage decisions, dynamic programming.

Feb 28 - 14. Cost-effectiveness and cost-utility analysis.

Mar 5 - 15. a) The decision tree for statistical analsyes. The value of observation.

b) Lindley's measure of the information contained in an experiment

Mar 7 - 16. Optimal fixed sample size problems: Estimation and Testing

Mar 19 - 17. a) Optimal Stopping

b) (optional) Optimal Stoppin in testing simple vs. simple hypotheses with

binary data.

Mar 21 - 18. Admissibility. Rao-Blackwell theorem. Admissibility of Bayes rules.

Admissibility ofin estimating the mean of a normal.

Mar 26 - no class. (ENAR)

Mar 28 - no class (ENAR)

April 2 - 19. a) Inadmissibility of in multidemensional normal problems.

b) More on Stein estimation. Empirical bayes interpretation. Extensions.

April 4 - 20. Minimax estimation. Basics. Game Theory. Minimax Theorem.

Least Favorable Priors. Minimax and shrinkage estimators

April 9, 11, 16, 18 - Student presentations. (your choice of article)