MAS465 Multivariate Data Analysis

Semester 1, 2014/15 10 Credits
Lecturer: Dr Frazer Jarvis uses MOLE Reading List
Aims Outcomes Teaching Methods Assessment Full Syllabus

The analysis of multivariate data requires the extension of standard univariate statistical models and methods but also introduces new problems. Initial attention is given to data mining techniques such as summarising and displaying high dimensional data and to ways of reducing multivariate problems to more manageable univariate ones. This is followed by routine generalisations of standard distributions and statistical tests before consideration of new strategies for constructing hypothesis tests. Finally, problems specific to multivariate data such as discrimination and classification (use in medical diagnosis problems for example) are studied. Most of these methods can be implemented in standard computer packages.

Prerequisites: MAS205 (Statistics Core); MAS274 (Statistical Reasoning) recommended
No other modules have this module as a prerequisite.


Outline syllabus

  • Multivariate data summary: sample estimates of mean, covariance and variance
  • Graphical displays: scatterplots, augmented plots, Andrews' plots, special techniques.
  • Exploratory analysis and dimensionality reduction: principal component analysis, principal component and crimcoord displays, implementation in R.
  • Construction of statistical hypothesis tests: the likelihood ratio method and the union-intersection principle.
  • Single and two sample methods: Hotelling's T2 test, practical implementation in R.
  • Multisample methods: multivariate analysis of variance and connection with crimcoords, interpretation of R analyses.
  • Discriminant analysis: probabilities of misclassification, likelihood rules, linear discriminant analysis in R.

Office hours

By appointment only, please email me with a subject line "MAS645" or "Multivariate Data Analysis".



Aims

  • To illustrate extensions of univariate statistical methodology to multivariate data.
  • To introduce students to some of the statistical methodologies which arise only in multivariate data.
  • To introduce students to some of the computational techniques required for multivariate analysis available in standard statistical packages

Learning outcomes

  • have some understanding of techniques of multivariate data summary and graphical display and of the principles of multivariate exploratory data analysis and dimensionality reduction;
  • have some understanding of the construction of multivariate likelihood ratio tests and of the union-intersection principle in multivariate testing;
  • be able to perform and interpret principal component analysis and linear discriminant analysis using a computer package;
  • be able to understand the results of computer based multivariate analyses of one and two sample tests;
  • be familiar with facilities offered by computer packages for multivariate analysis.

Teaching methods

Lectures, problem solving


20 lectures, no tutorials

Assessment

One formal 2 hour written examination. Format: 3 questions from 4 [75%]. Project [25%].

Full syllabus

Multivariate data summary

  • basic notation, sample estimates of mean, covariance and variance (1 session)
Graphical displays
  • scatterplots, augmented plots, Andrews’ plots, special techniques (1 session)
Exploratory analysis and dimensionality reduction
  • principal component analysis (2 sessions),
  • principal component and crimcoord displays (2 sessions),
  • implementation in R (1 session).
Construction of statistical hypothesis tests
  • revision of univariate likelihood ratio tests (1 session)
  • the likelihood ratio method in multivariate data (2 sessions)
  • the union-intersection principle (2 sessions).
Single and two sample methods
  • Hotelling’s T2 test (1 session)
  • practical implementation in R (1 session).
Multisample methods
  • multivariate analysis of variance and connection with crimcoords (1 session)
  • interpretation of R analyses (1 session).
Discriminant analysis
  • probabilities of misclassification (2 sessions)
  • likelihood rules (1 session)
  • linear discriminant analysis in R. (1 session)

Reading list

Type Author(s) Title Library Blackwells Amazon
B Cox, T. An introduction to multivariate data analysis 519.535 Blackwells Amazon
B Everitt An R and S-PLUS companion to multivariate analysis 519.535 Blackwells Amazon
B Gnanadesikan Methods for statistical data analysis of multivariate observations 519.53 Blackwells Amazon
B Mardia, Kent and Bibby Multivariate analysis 519.53 Blackwells Amazon
C Everitt Applied multivariate data analysis 519.53 Blackwells Amazon
C Manly Multivariate statistical methods : a primer 519.535 Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop on Mappin Street.