STAT 2221: Advanced Applied Multivariate Analysis

Spring 2015, Tuesday - Thursday 2:30-3:45 at 218 Cathedral of Learning

Instructor: Sungkyu Jung

e-mail address: sungkyu (at) pitt.edu
Office: CL 2734
Phone: 412-624-9033
Office Hours: Tuesday and Thursday 4 – 4:30 or by appointments

Grader: Ms. Qiyao Wang

email: QIW31 (at) pitt.edu

News:

Homework 1, data file, due Thursday January 22, 2015. solution
Homework 2, due Thursday Feb. 5, 2015. (Problem 2 revised on 2/3/2015, Problem 5 revised on 2/5/2015.) solution
Homework 3, data files: homeless_smalldata.csv pendigit3.txt pendigit8.txt, due Feb 24, 2015. solution
Practice Midterm (Revised on 2/24), PCA_Olympic.R
Homework 4, data files pendigit3.txt pendigit8.txt due Mar 24, 2015. solution
Homework 5, data files 24psychtests.csv due Apr 9, 2015. solution
Final Project guidelines

Proposal due: Thursday, March 26
Paper due: Thursday, April 16

Class canceled on Thursday, April 2.

Description:

Important statistical methods and relevant theory for analyzing continuous multivariate data are introduced. The first half of the course examines traditional and fundamental topics in some depth, and the second half of the course surveys modern topics. There is no prerequisite for this course. However, I assume students have working knowledge of probability, statistics and matrix algebra.

Lecture notes / Class Materials

Multivariate Data Exploration, Slides, Reading: HS Ch. 1, Izenman Ch. 4

Matrix algebra review, notes, Reading: HS Ch. 2, Izenman Sec. 3.2

matrix_manipulation.R

Multivariate normal distribution, notes, Reading: HS Ch. 4-5, Izenman Sec. 3.3

MVN.R
Bivariate_Normal.txt (lines of Matlab codes, used to generate Figure 1)

The Wishart distribution, notes, Reading: HS Ch. 4-5, Izenman Sec. 3.4
Inference for MVN, notes, Reading: HS Ch. 6-7, Izenman Sec. 3.5

InferenceExamples.R

Linear Dimension Reduction: PCA and CCA, slides, Reading: HS Ch. 9-10, 15, Izenman Ch 7

Classification, slides, Reading: HS Ch. 13, Izenman 8

LDAexamples.R

Latent Variable Models - Factor Analysis, slides, Reading: HS Ch. 11, Izenman 15.4

Factor_24psych.R with 24psychtests.csv

Clustering, slides, Reading: HS Ch. 12, Izenman 12

clustering.R

Multidimensional Scaling, slides, Reading: HS 16, Izenman 13

mds.R

Classification and Regression Trees, slides, Reading: HS 19.5, Izenman 9

rpart.R

Computing

There is no designated software for this course. You may use the software that makes the most sense for you. Many pharmaceutical companies use SAS for compliance with FDA regulations. Academic intuitions as well as labs often use R and python. Corporations often use MATLAB, Stata, Minitab, S, etc. because of the relatively high reliability despite the cost. However, it is expected that the student immerse herself with use of at least one software.

SAS is available on the PCs at all campus computing labs, such as Cathedral, Posvar, Forbes Quad and Benedum. If in addition you would like to have SAS on your PC, Pitt's Software Download Service offers SAS for free. SAS can only be installed on Windows or Unix environments (No Mac OS).
R is a free, open-source software package/programming language for statistical computing, and is available on the PCs at all campus computing labs, such as Cathedral, Posvar, Forbes Quad and Benedum. If in addition you would like to have R on your PC/Mac/Unix, it can be downloaded for free at http://www.r-project.org/
Matlab is available on the PCs at all campus computing labs, such as Cathedral, Posvar, Forbes Quad and Benedum. If in addition you would like to have Matlab on your PC, Pitt's Software Download Service offers it for free.

Johnson, Richard Arnold, and Dean W. Wichern. 2007. Applied multivariate statistical analysis. Upper Saddle River, N.J: Pearson Prentice Hall.
Hardle, Wolfgan g, and Leopold Simar. 2012. Applied multivariate statistical analysis. Heidelberg: Springer Berlin Heidelberg (Also visit here for sample codes)

Advanced and applied

Izenman, Alan Julian. 2008. Modern multivariate statistical techniques: Regression, classification, and manifold learning. New York: Springer New York.
Hastie, Trevor, Robert Tibshirani, and J. H. Friedman. 2009.The elements of statistical learning: Data mining, inference, and prediction. New York, NY: Springer New York.

Theoretical

Anderson, T. W. 2003. An introduction to multivariate statistical analysis. Hoboken, N.J: Wiley-Interscience.
Muirhead, Robb J. 1982. Aspects of multivariate statistical theory. New York: Wiley.

Working with R or SAS

Everitt, Brian, and Torsten Hothorn. 2011. An introduction to applied multivariate analysis with R. New York: Springer.
Khattree, Ravindra, and Dayanand N. Naik. 1999. Applied multivariate statistics with SAS software. Cary, NC: SAS Institute.
Khattree, Ravindra, and Dayanand N. Naik. 2000. Multivariate Data Reduction and Discrimination with SAS Software. Cary, NC: SAS Institute.
Check out the course webpage for Statistical Packages for an extensive list of resources on R and SAS.

Course Requirements and Grading:

Homework 55%
Midterm exam 25% - Thursday, February 26
Final project 20%
Lecture attendance and participation 5%

University Policies:

Academic Integrity

Students in this course will be expected to comply with the University of Pittsburgh's Policy on Academic Integrity. Any student suspected of violating this obligation for any reason during the semester will be required to participate in the procedural process, initiated at the instructor level, as outlined in the University Guidelines on Academic Integrity. This may include, but is not limited to, the confiscation of the examination of any individual suspected of violating University Policy. Furthermore, no student may bring any unauthorized materials to an exam, including dictionaries and programmable calculators.

Disability Services

If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services (DRS), 140 William Pitt Union, (412) 648-7890, drsrecep@pitt.edu, (412) 228-5347 for P3 ASL users, as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

Copyright Notice

Course materials may be protected by copyright. United States copyright law, 17 USC section 101, et seq., in addition to University policy and procedures, prohibit unauthorized duplication or retransmission of course materials. See Library of Congress Copyright Office and the University Copyright Policy.