Foundations of Statistical Inference II was taught Spring 2020 at Rice/GSBS by James Long. This website is no longer maintained but is available for reference purposes.

Instructor Contact

• name: James Long
• email: jplong followed by @mdanderson.org
• office: FCT 4.6082 (Pickens Academic Tower), email me to schedule meeting

Course Information and Syllabus

Description: This is a PhD level course in mathematical statistics, covering hypothesis testing, construction of confidence sets, and multiple testing.

• Course textbooks:
  • Mathematical Statistics by Shao Second Edition. Chapters 6 and 7.
  • Large Scale Inference by Efron Selections from Chapters 1–5 with an emphasis on theory.
• Syllabus

Course Schedule

Unless otherwise specified, all reading is from “Mathematical Statistics” Second Edition by Shao.

• January 14: Hypothesis Test Definitions, Randomized Tests
  • Suggested Reading: Section 2.4.2 and Beginning Chapter 6 through end of 6.1.1
• January 16: Neyman-Pearson Lemma, p-values
  • Suggested Reading: Examples 6.1 and 6.2, Definition of p-values in Section 2.4.2
• January 21: Monotone Likelihood Ratios, 1-sided UMP tests
  • Suggested Reading: Section 6.1.2
• January 23: Likelihood Ratio Tests
  • Suggested Reading: Section 6.4.1
• January 28: Wald and Score Tests
  • Suggested Reading: Section 6.4.2
• January 30: Chi-squared Tests and Multinomial Data
  • Suggested Reading: Section 6.4.3
• February 4: Goodness-of-fit and Bayesian Testing
  • Suggested Reading: Section 6.4.4
• February 6: Bayes Factors and p-values
  • Finish Bayesian testing (6.4.4), review

• February 11: Midterm 1 covering topics through February 6 lecture

• February 18: Confidence Set Introduction, Pivotal Quantities
  • Suggested Reading: Section 2.4.3 and Section 7.1.1
• February 20: Inverting Acceptance Regions
  • Suggested Reading: Sections 7.1.2 and 7.1.3
• February 27: Confidence Set Lengths and Asymptotic Sets
  • Suggested Reading: Sections 7.2.1 and 7.3.1
• March 3: Confidence Sets Based on Likelihoods
  • Suggested Reading: Sections 7.3.2
• March 5: Edgeworth Expansions and Asymptotic Accuracy
  • Suggested Reading: Sections 1.5.6 and 7.3.4
  • Edgeworth Simulation
• March 7 and 12: Second Order Accurate Bounds
  • Classes Cancelled This Week
  • Lecture Notes
• March 24: Midterm 2
  • Take home exam emailed to students
• March 26: Introduction to Multiple Testing, FWER
  • Suggested Reading: Section 2.1 and 3.1,3.2 in Efron “Large Scale Inference”
  • Lecture Notes
  • R
• March 31: False Discovery Rate
  • Suggested Reading: Section 4.1 and 4.2 of Efron
  • Lecture Notes, R
• April 2: Empirical Bayes False Discovery Rate
  • Suggested Reading: Section 2.2–2.5 of Efron
  • Lecture Notes, R
• April 9: Empirical Bayes Interpretation of BH FDR Control Procedure
  • Suggested Reading: Section 4.3
  • Lecture Notes, R
• April 14: Estimating Proportion True Nulls
  • Suggested Reading: Section 4.5 Estimation of pi0
  • Lecture Notes, R
• April 16: Local Fdr
  • Suggested Reading: Sections 5.1-5.3
  • Lecture Notes, R
• April 21: Estimating the Null Distribution
  • Suggested Reading: Chapter 6
  • Lecture Notes, R
• April 23: Uncertainty in Local fdr Estimates
  • Suggested Reading: Chapter 7.1-7.3
  • Lecture Notes, R

Homeworks

There will be approximately 9 homeworks over the course of the semester. Unless otherwise noted, problems are from Shao or Efron.

• Homework 1 due January 23 Section 6.6 on page 454. Questions 1, 3, 5a, 6a, 14ab, 15 Solutions
• Homework 2 due January 30 Section 6.6 on page 454. Questions 91, 94a, 97, 100 Solutions
  • HW Option: You may substitute 1 of the exercises in HW2 for completing the exercise proposed between equations 6.60 and 6.61 on p 428 in Shao. This claim is false in older printings of the book (which have c_0 > 0 condition) but true in newer printings of the book (which have the stricter c_0 > 1 condition). So depending on your printing of the book, you can either prove the result claimed in Shao or provide a counterexample.
  • In question 91, the denominator of W should be a product (rather than a sum) and raised to the 1/2 power. You can write down the distribution of W without deriving it and state how you would use this distribution to construct size alpha rejection regions.
• Homework 3 due February 6 Section 6.6 on page 454. Questions 101 and 105. Solutions
• Homework 4 due February 27 Section 7.6 on page 527. Questions 1a,2a,14, and this problem. Solutions to Extra Problem
• Homework 5 due March 5 Section 7.6 on page 527. Questions 11a,28,33,67ab
• Homework 6 due March 31 Section 7.6 on page 527. Questions 67c,70,80,89
• Homework 7 due April 7 Exercises 3.2 and 3.4 in Efron
• Homework 8 due April 16 Exercises 4.5 and 4.6 in Efron
• Homework 9 due April 23 Exercises 4.9, 5.1, and 5.2 in Efron

Exams

• Exam 1 Solutions
• Exam 2 Solutions