STATS426: Introduction to Theoretical Statistics, Fall 2019

STATS426 introduces the principles and mathematical foundations of statistical reasoning. Topics include parameter estimation, hypothesis testing, analysis of variance, regression, nonparametric procedures, Bayesian methods, and the delta method.

  Instructor: Keith Levin, klevin | at | umich | dot | edu
GSI: Rafail Kartsioukas, rkarts | at | umich | dot | edu
Lectures: Tuesdays 5:30pm to 7:00pm in B844 EH and Thursdays 5:30pm to 7:00pm in 2260 USB
Instructor Office Hours: Wednesdays 5:30 to 7:00pm in 438 WH or by appointment
GSI Office Hours: Mondays and Tuesdays, 3:30pm to 5:00pm in 2165 USB
Textbook: Mathematical Statistics and Data Analysis (Third Edition) by John Rice
Syllabus: Available here
Prerequisites: Students are required to have taken STATS425 or equivalent, and to have taken or currently be taking MATH 217, 412 or 451.
Homework submission: Homework is to be handed in before the end of lecture on the due date listed on the assignment.

Course Schedule

Date Topics Readings Notes
Tuesday, Sep 3 Course introduction; Administrivia; Probability Review Rice Chapters 1 through 4 (recommended); Probability review notes from Prof. Moulinath Bannerjee (recommended) HW1 out
Thursday, Sep 5 Probability review (cont'd) Rice Chapters 1 through 4 (recommended)
Tuesday, Sep 10 Probability review (cont'd) Rice Chapters 5 (recommended) and 6 (required) HW2 out
Thursday, Sep 12 Probability review (cont'd) Rice Chapter 5 (recommended) and 6 (required)
Tuesday, Sep 17 Probability review (cont'd) Rice Chapter 5 (recommended) and 6 (required)
Thursday, Sep 19 Distributions derived from the normal Rice Chapter 6 (required) HW3 out
Tuesday, Sep 24 Sampling Rice Chapter 7, sections 7.1 through 7.3 (required) HW4 out
Thursday, Sep 26 Sampling (cont'd) Rice Chapter 7, sections 7.1 through 7.3 (required) No instructor office hours Wednesday due to travel.
Tuesday, Oct 1 Estimation Rice Chapter 8, sections 8.1 through 8.5 (required) HW5 out
Thursday, Oct 3 Estimation (cont'd) Rice Chapter 8, sections 8.1 through 8.5 (required)
Tuesday, Oct 8 Estimation (cont'd) Rice Chapter 8, section 8.1 through 8.5 (required) HW6 out
Thursday, Oct 10 Estimation (cont'd) Rice Chapter 8, section 8.7 and 8.8 (required)
Tuesday, Oct 15 No lecture: fall study break HW7 out; Review session, 5:30pm to 7pm, 411 WH. Instructor office hours as scheduled. No GSI office hours Monday, October 14. Tuesday GSI office hours as scheduled.
Thursday, Oct 17 Exam 1 Review guide
Tuesday, Oct 22 Estimation (cont'd) Rice Chapter 8, sections 8.7 and 8.8 (required)
Thursday, Oct 24 Estimation (cont'd) Rice Chapter 8, section 8.6 (required)
Tuesday, Oct 29 Hypothesis testing Rice Chapter 9, sections 9.1 through 9.4 (required) HW8 out
Thursday, Oct 31 Hypothesis testing (cont'd) Rice Chapter 9, sections 9.1 through 9.4 (required)
Tuesday, Nov 5 Hypothesis testing (cont'd) Rice Chapter 11, sections 11.1 and 11.2 (required) HW9 out
Thursday, Nov 7 Hypothesis testing (cont'd) Rice Chapter 11, sections 11.3 and 11.4 (required)
Tuesday, Nov 12 ANOVA: one-way layout Rice Chapter 12, sections 12.1 and 12.2 (required) HW10 out
Thursday, Nov 14 ANOVA: one-way layout Rice Chapter 12, sections 12.1 and 12.2 (required)
Tuesday, Nov 19 ANOVA: two-way layout Rice Chapter 12, section 12.3 (required)
Thursday, Nov 21 Exam 2 HW11 out; Review guide
Tuesday, Nov 26 p-values and the replication crisis D. Colquhoun. The Problem with p-values Aeon Magazine (recommended); J. P. A. Ionnidis (2005) Why Most Published Research Findings Are False (recommended); R. L. Wasserstein and N. A. Lazar (2016) The ASA Statement on Statistical Significance and p-Values (recommended); J. Bohannon. I Fooled Millions into Thinking Chocolate Helps Weight Loss. Here's How. io9 (recommended) This lecture is intended as an introduction to an important issue in modern statistics. You will not be responsible for material presented in this lecture or its readings.
Thursday, Nov 28 No lecture: Thanksgiving break
Tuesday, Dec 3 Regression Rice Chapter 14, sections 14.1 and 14.2 HW12 out
Thursday, Dec 5 Regression (cont'd) Rice Chapter 14, sections 14.1 and 14.2
Tuesday, Dec 10 Regression (cont'd) Rice Chapter 14, section 14.3