Stat 583

Advanced Theory of Statistical Inference

• Instructor: Peter Hoff
• Lectures: MWF, 10:30-11:20, CMU 226
• Office hours: T Th 12:30-1:30 and by appointment, PDL C-319

• Homework assigned by Wednesday is due the following Monday.
• There will be a midterm (4/30/12) and final (6/4/12) exam.
• The homework, midterm and final will count as 25%, 30% and 45% of the course grade, respectively.
• The final is 8:30-10:20 AM, Monday June 4 in CMU 226.

• Week 1:
  • Reading: LR 3.1-3.4.
  • Do the 581 final exam, to be turned in Monday, 4/2.
  • Do supplementary exercises 1 and 2, LR 3.9 and LR 3.18, to be turned in Monday, 4/9.
• Week 2:
  • No class on Monday 4/2.
  • Do LR 3.29, 3.34, to be turned in Monday, 4/9.
• Week 3:
  • Reading: LR 3.7, 4.1-4.3.
  • Homework: LR 4.1, 4.3 and supplementary exercises 3, 4 and 5.
• Week 4:
  • Reading: LR 4.4, 4.5, 5.1.
  • Homework: LR 4.4, 4.8, 4.18, 4.25, and supplementary exercises 6 and 7.
• Week 5:
  • Reading: LR 5.1-5.5.
  • Homework: LR 5.5, 5.6, 5.7, 5.15 and supplementary exercise 8.
• Week 6:
  • Reading: LR 3.5, 5.5.
  • Homework: Supplementary exercises 9,10,11,12, due Monday 5/14.
• Week 7:
  • Reading: LR 3.5, 5.5, 6.1.
  • Homework: Supplementary exercises 13 and 14, due Monday 5/14.
• Week 8:
  • Reading: LR 6.1-6.3.
  • Homework: Supplementary exercises 15, 16, 17 and 18, due Monday 5/21.
• Week 9:
  • Reading: LR 6.5, 6.6, 7.1, 7.2.
  • Homework: LR 6.11, 6.12, 6.18, 6.19, due Wednesday 5/30. Note the typo in 6.11, and for 6.12, describe how to (approximately) implement this test in practice, assuming you have a 1-d numerical integrator and can simulate from f0.
• Week 10:
  • W: Bayesian confidence intervals.
  • F: Model selection, Laplace's approximation and the BIC

1. UMP Testing (LR Chapter 3)
   1. NP Lemma
   2. Montone likelihood ratio
2. UMPU Testing (LR Chapters 4 and 5)
   1. One-parameter exponential families
   2. Similarity and completeness
   3. Multiparameter exponential families
   4. UMPU tests for normal models
3. UMPI Testing (LR Chapters 6 and 7)
   1. Invariance
   2. Maximal invariants
   3. UMPI tests for normal models
4. Bayesian Methods
   1. Confidence intervals
   2. BIC