## Applied Multivariate Statistics

 Professor: Dr. Markus Kalisch Lectures: Mo 13-15, HG G 3with Suppl: Mo, 15-17, HG E 19 in addition to lecture Tutor: Daniel Stekhoven

Start of lectures: Monday, February 20, 2012.

Exercises: Details for the exercises can be found  here.

### Overview

Multivariate Statistics studies the joint distribution of two or more random variables.

Many procedures rely on the multivariate normal distribution. As in univariate statistics, differences between two or more groups of observations are examined (discriminant analysis), and effects of explanatory variables on several target variables are modeled (regression). In addition, there are methods for reducing dimension (principal component analysis, ordination) and formation of groups (cluster analysis).

The course gives an overview of problems and methods. A selection will be treated more in depth.

### Content and time schedule

 Date Subject (1st hour) Subject (2nd hour) Reading 20.02.12 Introduction Visualization 1 AMR Ch 1 & 2 27.02.12 Visualisation & Outlier Detection Exercise 1 Shading; Outlier Detection 05.03.12 Imputation & Multiple Imputation Imputation & Multiple Imputation Overview, missForest, MICE 12.03.12 MDS Exercise 2 AMR Ch 4, readingV2 19.03.12 PCA PCA AMR Ch 3 26.03.12 Supervised Learning 1: LDA & Logistic Regression Exercise 3 ESL Ch 4 (contains more than we need) 02.04.12 Exploratory Factor Analysis (EFA) Revision AMR Ch 5 23.04.12 Extending univariate methods Exercise 4(Multiple Testing) MSA Ch 5 & 8 (contains much more than we need); Paper on FDR (available from within ETH network) 30.04.12 Cluster Analysis Cluster Analysis AMR Ch 6; Notes on mclust (contains much more than we need) 07.05.12 Supervised Learning 2: Trees Supervised Learning 2: Random Forest ESL Ch 9.2, 15 14.05.12 Repeated Measures Repeated Measures AMR Ch 8 21.05.12 Exercise 5 Exercise 6/7 Paper 9 on the list (Nature Methods)

### Exercises

Details for the exercises can be found here.

### Lecture notes

There will be no script to this lecture, but slides for the lecture presentations can be downloaded each Monday noon (12:00) from here.

Slides:

### Video Tutorials

We offer short video tutorials on how to use R to apply the methods mentioned in the lecture. Note, that this is still at an experimental stage - feedback is welcome!

Datasets are either in the above folder or in the folder for data sets.

### Literature

• (AMR) B. Everitt et.al., "An Introduction to Applied Multivariate Analysis with R", Springer, 2011.
• (ESL) Hastie et.al., "The Elements of Statistical Learning", Springer, 2009.
• (MSA) More mathematical treatment of fundamental methods: Anderson, "An Introduction to Multivariate Statistical Analysis", Wiley, 2nd Edition (not available online, but ETH library has hardcopies)

The whole two books are available online via nebis.

### Exam

It will be an oral exam (30min). You have to be abel to solve case studies in R on a computer and explain different concepts of multivariate statistics seen in the lecture. You may bring a one page summary (DIN A4, text on both sides).

### Misc

• Nice GapMinder Videos
• Background on bias in admission of UC Berkeley (Simpson's Paradox) (this is a paper in Science, one of the most prestigous journals in the world; by this, you can get an impression, how delicate the matter was...)
• More details on Wilks test and Multivariate Regression can be found in W.J. Krzanowski, "Principles of Multivariate Analysis", Oxford Science Publications, 1.Edition, Ch 15.2

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