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Zhao Mei Zheng, The University of Sydney

Multivariate Statistical Analysis

Lecturers

Dr Sharon Lee, The University of Adelaide

Synopsis

Multidimensional data arise frequently in many fields of scientific research, from engineering, computer science, finance, medicine, to social sciences. Multivariate statistics provide powerful and flexible tools to extract meaningful information from these data.

This course provides an introduction to various classical statistical methods for analyzing multivariate data, including multivariate extensions of univariate techniques and other tools that are specific for multidimensional data. Students will gain a conceptual understanding and the mathematical underpinnings of the procedures, and be able to applied these to datasets using R.

Course Overview

  • Introduction to multivariate data, distributions, and analysis
  • Inference about multivariate means and regression
    • Inference for a single population
    • Comparison of multiple populations
    • Multivariate regression
  • Analysis of a covariance structure
    • Principal component analysis
    • Factor analysis
    • Canonical correlation analysis
  • Clustering, classification, and grouping
    • Discriminant analysis
    • Hierarchical clustering
    • k-means and mixture models
    • Multidimensional scaling
    • Correspondence analysis

Prerequisites

  • working knowledge of second year probability and statistics (distribution theory, hypothesis testing, ANOVA, linear regression)
  • basic multivariate calculus
  • familiarity with the R software

Assessment

  • 2 assignments: 20% each
  • Final examination: 60%

(Assessment subject to change)

Resources/pre-reading (if available)

Lecture notes will be provided during the course.

  • Hastie, T.R., Tibshirani, R. J., & Friedman, J. H. (2011). The elements of statistical learning: data mining, inference, and prediction, 2nd ed. Springer.
  • Johnson, R.A., and Wichern, D.W. (2008). Applied Multivariate Statistical Analysis, 6th ed. Pearson, New Jersey.

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Dr Sharon Lee
The University of Adelaide

Dr Sharon Lee is a senior lecturer in Statistics at the University of Adelaide. Prior to this, she was with the University of Queensland, where she held an Australian Research Council DECRA fellowship from 2016 to 2018. Her current research focuses on model-based clustering and non-normal statistical models. Her broad areas of interests include mathematical statistics, statistical modelling, computational statistics, machine learning, and artificial intelligence.