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Multivariate Analysis (MATH 30510)

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Administrative Information

  1. Unit number and title: MATH 30510 Multivariate Analysis
  2. Level: H/6
  3. Credit point value: 10 credit points
  4. Year: 12/13
  5. First Given in this form: 1990
  6. Unit Organiser: Jonty Rougier
  7. Lecturer: Yiannis Papastathopoulos
  8. Teaching block: 2
  9. Prerequisites: MATH11300 Probability 1, MATH 11400 Statistics 1, and MATH 11005 Linear Algebra & Geometry

Unit aims

Multivariate analysis is a branch of statistics involving the consideration of objects on each of which are observed the values of a number of variables.   Multivariate techniques are used in medicine, physical, environmental, and biological sciences, economics and social science, and of course in many industrial and commercial applications.

A wide range of methods is used for the analysis of multivariate data, both unstructured and structured, and this course will review some of the more common and useful methods, with emphasis on implementation and interpretation.

General Description of the Unit

For more details, see the course webpage at  http://www.maths.bris.ac.uk/~ip12483/multivariate/home.html

Relation to Other Units

As with the units Linear Models, Generalized Linear Models, and Time Series Analysis, this course is concerned with developing statistical methodology for a particular class of problems.

Applications will be implemented and presented using the statistical  computing environment R (used in Probability 1 and Statistics 1).

Teaching Methods

Lectures (including both theory and illustrative applications), exercises to be done by students.

Learning Objectives

To gain an understanding of:

  • Dimensional reduction and visualisation of high-dimensional datasets;
  • Structured and unstructured learning approaches, including classification and clustering;
  • Approaches based on notions of similarity/dissimilarity;
  • Implementation in the statistical computing environment R.

Assessment Methods

The assessment mark for Multivariate Analysis is calculated from a 1½-hour written examination in May/June consisting of THREE questions. A candidate's TWO best answers will be used for assessment.   Calculators of an approved type (non-programmable, no text facility) are allowed. From 2012-13 ONLY calculators carrying a 'Faculty of Science approved' sticker will be allowed in the examination room.  Statistical Tables will be provided.

Award of Credit Points

Credit points are gained by:

  • either an examination score of 40 or more;
  • or getting a mark of 30 or over, and making reasonable attempts at two specified pieces of written work.

Transferable Skills

Self assessment by working examples sheets and using solutions provided.

Texts

There is no one set text. Any one of the following will be useful, particularly the first one (from which the notation for the course is taken):

  1. K V Mardia, J T Kent and J Bibby, Multivariate Analysis, Academic Press, 1979.
  2. W J Krzanowski, Principles of Multivariate Analysis: A User's Perspective. Clarendon Press, 1988.
  3. C Chatfield and A J Collins, Introduction to Multivariate Analysis. Chapman and Hall, 1986.
  4. Krzanowski, W. J. and Marriott, F. H. C. Multivariate Analysis, Parts I and II. Edward Arnold. 1994.

Syllabus

  1. General introduction to multivariate data and revision of relevant matrix algebra.
  2. Principal components analysis for dimensional reduction and data visualisation (biplots).
  3. Discriminant analysis for classification.
  4. Cluster analysis for unsupervised learning.
  5. Multidimensional scaling for visualisation based on similarity/dissimilarity.