Math 460: Multivariate Statistical Analysis
Spring 2020

Instructor: Todd Kuffner

Lecture: MWF 11:00-11:50am

Course Description: A modern course in multivariate statistics. Elements of classical multivariate analysis as needed, including multivariate normal and Wishart distributions. Clustering; principal component analysis. Model selection and evaluation; prediction error; variable selection; stepwise regression; regularized regression. Cross-validation. Classification; linear discriminant analysis. Tree-based methods. Time permitting, optional topics may include nonparametric density estimation, multivariate regression, support vector machines, and random forests.

Prerequisite: Multivariable calculus (Math 233), linear or matrix algebra (Math 429 or Math 309), multivariable-calculus-based probability and mathematical statistics (Math 493, Math 494) and linear models (Math 439). Prior knowledge of R at the level introduced in Math 439 is assumed.

Textbooks: 

These books are required for many of the topics in the course. For other topics in the course, the lectures are the primary reference, but freely-available references will also be suggested.


Important Dates and Course Schedule:   Details will be posted on Canvas. I will probably update the table below later in the semester to detail what was covered for future reference.

Jan. 13
 First day of classes
Jan. 20
 No class (Martin Luther King Holiday)
Jan. 23
 Last day to drop/add
March 9-13
 No classes (Spring Break)
April 24
 Last day of classes


Course Policies and Grades

Canvas: During the semester, all course-related materials and announcements will be posted to Canvas and/or sent by email to registered students.

Grades: Homework 25%, Midterm 20%, Final Exam 25%, Participation 10%, Group Project & Presentation 20%

Homework: Roughly 1 homework for every 4-5 lectures. You may discuss problems with other students, but the solutions you submit must be entirely your own work. Explanations detailing the steps of proofs or other mathematical arguments are required for full credit. You are encouraged, but not required, to write your solutions in TeX/LaTeX, and submit the printed version. I will drop the lowest homework grade under the condition that you have submitted all homeworks and genuinely attempted all of the problems; I will not drop the lowest homework grade if you did not do this.

Exams: There will be a take-home midterm exam and a take-home final exam.

Participation: Attendance and participation are required for all lectures. Attendance is not enough. Participation includes: (i) answering questions that I ask the class; (ii) providing a summary, definition, or result from the previous lecture when I ask you to.

Group Project & Presentation: Groups will be assigned. Each group will be given a project, which may include reading a paper or studying a topic not covered during lectures, or doing a literature search on an open problem in statistical learning. The group must submit a 5-10 page report, written in LaTeX, and prepare a 25-minute presentation for the rest of the class using slides (made with the Beamer document class in LaTeX). The speaking roles in the presentation must be shared equally with all members of the group. The final report and presentation will be due during the final two weeks of classes.

Final Course Grade: The letter grades for the course will be determined according to the following numerical grades on a 0-100 scale.
A+
 impress me
 B+
 [87, 90)
 C+
 [77, 80)
 D+
 [67, 70)
 F
 [0,60)
A
 93+
 B
 [83, 87)
 C
 [73, 77)
 D
 [63, 67)

A-
 [90, 93)
 B-
 [80, 83)
 C-
 [70, 73)
 D-
 [60, 63)



Other Course Policies: Students are encouraged to look at the Faculty of Arts & Sciences policies.