Course: MATH 541B, Graduate Mathematical Statistics II, Fall 2023
Prerequisite: Math 541A
Course Content: Hypotheses testing, Neyman-Pearson lemma, generalized likelihood ratio procedures, confidence intervals, consistency, power, jackknife and bootstrap. Monte Carlo Markov chain methods, hidden Markov models.
Last update: 9 May 2023

Instructor: Steven Heilman, stevenmheilman(@-symbol)
Office Hours: Tuesdays, 9AM-11AM, on zoom [link posted in blackboard]
Lecture Meeting Time/Location: Mondays, Wednesdays and Fridays 11AM-1150AM, KAP 140
TA: Xinze Du, xinzedu(@-symbol)
TA Office Hours: (see the schedule in the Math Center)
Recommended Textbook: Cassella and Berger, Statistical Inference, 2nd Edition. 
Other Textbooks (not required): Lehmann and Romano, Testing Statistical Hypotheses
Ferguson, A Course in Large Sample Theory.
Shao and Tu, The jackknife and bootstrap.
McLachlan and Krishnan, The EM Algorithm and Extensions.
Robert and Casella, Monte Carlo and Statistical Applications.
Haggstrom, Finite Markov Chains and Algorithmic Applications.
Levin and Peres, Markov Chains and Mixing Times.

Midterm 1: Friday, September 29, 11AM-1150AM KAP 140
Midterm 2: Monday, October 30 , 11AM-1150AM KAP 140
Final Exam: Wednesday, December 6, 11AM-1PM, KAP 140
Other Resources: An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

Exam Procedures: Students must bring their USCID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the USC Student Conduct Code. (See also here.)
Accessibility Services: If you are registered with accessibility services, I would be happy to discuss this at the beginning of the course. Any student requesting accommodations based on a disability is required to register with Accessibility Services (OSAS) each semester. A letter of verification for approved accommodations can be obtained from OSAS. Please be sure the letter is delivered to me as early in the semester as possible. OSAS is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.
213-740-0776 (phone)
213-740-6948 (TDD only)
213-740-8216 (fax)

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Exam Resources: Here is a page with some practice exams (at the bottom). Here is a page with some practice exams (see Assignment 3). Here is a page containing USC Stats B Qual Exams with solutions. Here is another page with some related Stats qualifying exams (see e.g. the Theory exams).

Homework Policy:

Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1 Aug 21: 8.1, Hypothesis Testing Aug 22 Aug 23: 8.1, Hypothesis Testing Aug 24 Aug 25: 8.2, Likelihood Ratio Test
2 Aug 28: 8.3.1, Neyman-Pearson Lemma Aug 29 Aug 30: 8.3.2, Karlin-Rubin Theorem Aug 31 Sep 1: Homework 1 due. 8.3, Exponential Families
3 Sep 4: No class Sep 5 Sep 6: 8.3, Unbiasedness Sep 7 Sep 8: 8.3.4, p-values
4 Sep 11: 8.3.5, Loss Function Optimality Sep 12 Sep 13: 9.1, Confidence Intervals Sep 14 Sep 15: Homework 2 due, 9.2, Test Inversion
5 Sep 18: 9.2.2, Pivotal Method Sep 19 Sep 20: 9.2.3, Pivoting CDF Sep 21 Sep 22: 9.2.4, Bayesian Intervals
6 Sep 25: 9.3.4, Loss Function and CI Sep 26 Sep 27: 10.3, Asymptotics of Likelihood Ratio Sep 28 Sep 29: Exam 1
7 Oct 2: 10.3, Asymptotics of GLR Oct 3 Oct 4: 10.3, Asymptotics of GLR Oct 5 Oct 6: Homework 3 due, Jackknife
8 Oct 9: Jackknife Oct 10 Oct 11: Bootstrap Oct 12 Oct 13: No class 
9 Oct 16: Bootstrap Oct 17 Oct 18: Consistency of Jackknife Oct 19 Oct 20: Homework 4 due, Bootstrap/Jackknife Relationship
10 Oct 23: 12.2, Analysis of Variance Oct 24 Oct 25: 12.2, Analysis of Variance Oct 26 Oct 27: 14.2, Linear Regression
11 Oct 30: Exam 2 Oct 31 Nov 1: EM Algorithm Nov 2 Nov 3: Homework 5 due, EM Algorithm
12 Nov 6: Monte Carlo Nov 7 Nov 8: Rejection Sampling Nov 9: Nov 10: No class
13 Nov 13: Importance Sampling Nov 14 Nov 15: Markov Chains Nov 16 Nov 17: Homework 6 due, Markov Chains
14 Nov 20: Metropolis-Hastings Nov 21 Nov 22: No class  Nov 23 Nov 24: No class
15 Nov 27: Markov Chain Monte Carlo Nov 28 Nov 29: Review of course Nov 30 Dec 1: Homework 7 due, Review of course

Advice on succeeding in a math class:


Homework .tex files

Exam Solutions

Supplementary Notes