STATISTICAL DECISION THEORY

Instructor:

Feng Liang : feng@stat.duke.edu
Office : 217 Old Chem

Class Time:

Mon & Fri, 10:30 - 11:45am
Class begins on Jan 9, 2004

Office Hour:

Mon, 1:30 - 3:30pm

Class Location:

Old Chem 025

Text:

• (JB) Jim Berger, "Statistical Decision Theory and Bayesian Analysis"
• (CR) Christian Robert, "The Bayesian Choice"

Books are reserved at Perkins library. You can borrow them out for at most 3 consecutive nights.

Final Project

Lectures:

• Jan 9 : Basic concepts, notation and definitions. Principles of choice (minimax, Bayes risk).
  Reading: JB chap 1, CR chap 2.4
  
  
• Jan 12 : Coherence and the axioms of probability. Dutch Book Theorem. Called-off bets and conditional probability.
  
  
• Jan 16 : More on Dutch Book Theorem. Utility.
  Reading: JB chap 2, CR chap 2.2-2.3
  
  
• Jan 19 : Martin Luther King, Jr. Day
  
  
• Jan 23, 30 : Minimax theorem for finite games.
  Reading: JB chap 5
  HW : [hw1.ps] [hw1.pdf]
  
  
• Feb 2 : (Minimal) Complete class, essentially complete class, complete class theorem.
  Reading: JB chap 8.1-8.2
  
  
• Feb 6 : Methods to find minimax rules. Simple hypothesis as a finite game.
  Reading: JB chap 5.3
  
  
• Feb 9 : Bayes rule for simple hypothesis. The Neyman-Pearson lemma. Bayes factor.
  Reading: JB chap 4.3.3
  
  
• Feb 13 : Review on classical hypothesis testing.
  HW : [hw2.ps] [hw2.pdf]
  
  
• Feb 16 : p-values and posterior probabilities of hypotheses. False discovery rate.
  Reading:
  
  • Berger, J. and Sellke, T. (1987). Testing of a point null hypothesis: The irreconcilability of a significance levels and evidence. Journal of the American Statistical Association, 82, 112-139.
  • Casella, G. and Berger, R. (1987). Reconciling Bayesian and frequentist evidence in the one-sided testing problem. Journal of the American Statistical Association, 82, 106-111.
  
  
• Feb 20, 23 : False discovery rate (FDR). Positive false discovery rate (pFDR).
  Reading:
  
  • Benjamini Y. and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, B, 57, 289-300.
  • Storey, J.D. (2003). The positive false discovery rate: A Bayesian interpretation and the q-value. The Annals of Statistics, 1-23.
  
  
• Feb 27, Mar 1 : Point estimation. Sampling models.
  Reading : CR chap 4.1-4.3
  HW : [hw3.ps] [hw3.pdf]
  
  
• Mar 5, 15 : The Normal case.
  Reading : CR chap 8.1-8.3
  
  
• Mar 19, 22, 26, 29 : Nonparametric function estimation and Gaussian sequence model. Minimax risk in restricted space such as hyperrectangles and Ellipsoid.
  Reading :
  
  • Iain Johnstone's monograph, Function Estimation in Gaussian Noise: Sequence Models, chap 1-3.
  • Donoho, D.L., Liu, R.C. and MacGibbon, B. (1990). Minimax risk over hyperrectangles, and implications. The Annals of Statistics, 1416-1437.
  
  
• Apr 2, 5 : Invariance.
  Reading : JB chap 6 or CR ahp 9.
  HW : [hw4.ps] [hw4.pdf]
  
  
• Apr 9 : No class.
  
• Apr 12, 16, 19 : Student Presentation.