Course Description
The methodology of multivariate statistics and machine learning for students specializing in statistics. Topics include inference on multivariate means, multivariate analysis of variance, principal component analysis, linear discriminant analysis, factor analysis, linear discrimination, classification trees, multi-dimensional scaling, canonical correlation analysis, clustering, support vector machines, and ensemble methods.
Additional Requirements for Graduate Students:
Additional and/or alternative problems of a more challenging
nature will be required for graduate students on homework
assignments and exams. Typically, these problems will be of a
more theoretical nature than those required of undergraduate
students, or will require more self-study of material not
emphasized during lectures, or will require more intricate
and/or time-consuming data analysis tasks.
Athena Title
Applied Multivariate Analysis
Undergraduate Prerequisite
(MATH 3300 or MATH 3300E or MATH 3000) and (MATH 2270 or MATH 2270H or MATH 2500 or MATH 2500E) and STAT 4230/6230 and (STAT 4360/6360 or STAT 4360E/6360E or STAT 4365/6365)
Graduate Prerequisite
STAT 6420 or permission of department
Semester Course Offered
Offered every year.
Grading System
A - F (Traditional)
Course Objectives
Students will learn how to visualize multivariate data. Students will learn some basic matrix algebra for statistical use and be able to use it to understand the methods. Students will learn multivariate analogs of one and two population inference on means, and the multivariate analysis of variance. Students will learn how to determine which multivariate methods are appropriate for a given situation. Students will learn the basic logic behind each method. For each method, students will learn the underlying assumptions and conditions under which the methodology can be expected to perform well, the type of questions it addresses, the results it yields, and the proper interpretation of those results. Students will learn how to implement the methods covered in the course using appropriate statistical software.
Topical Outline
Relevant vector and matrix algebra, basic summary statistics for multivariate data, the multivariate normal distribution, inference for multivariate means, multivariate analysis of variance (MANOVA), principal components, exploratory factor analysis, discriminant analysis, canonical correlation analysis, tree-based methods, support vector machines, and cross-validation.