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 This website is no longer maintained but is available for reference purposes.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: NeymanPearson Lemma, pvalues
 Suggested Reading: Examples 6.1 and 6.2, Definition of pvalues in Section 2.4.2
 January 21: Monotone Likelihood Ratios, 1sided 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: Chisquared Tests and Multinomial Data
 Suggested Reading: Section 6.4.3
 February 4: Goodnessoffit and Bayesian Testing
 Suggested Reading: Section 6.4.4
 February 6: Bayes Factors and pvalues
 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 5.15.3
 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 7.17.3
 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