Unit information: Multivariate Analysis 34 in 2013/14

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Unit name Multivariate Analysis 34
Unit code MATHM0510
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2C (weeks 13 - 18)
Unit director Dr. Didelez
Open unit status Not open
Pre-requisites

Probability 1 (MATH11300), Statistics 1 (MATH 11400) and Linear Algebra and Geometry (MATH 11005)

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description including 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. A wide range of methods is used for the analysis of multivariate data, both unstructured and structured, and this course will give a view of the variety of methods available, as well as going into some of them in detail. Interpretation of results will be emphasized as well as the underlying theory. Multivariate techniques are used across the whole range of fields of statistical application: in medicine, physical and biological sciences, economics and social science, and of course in many industrial and commercial applications.

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.

Syllabus

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

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).

Intended Learning Outcomes

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.

Transferable Skills:

Self assessment by working examples sheets and using solutions provided.

Teaching Information

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

Assessment Information

The assessment mark for Multivariate Analysis (level M) is calculated as 20% from assessed coursework and 80% from a 1½-hour written examination in May/June.

  • The assessed coursework consist of two take-home assignments where students are asked to apply and compare multivariate methods to realistic data sets.
  • The exam consists of THREE questions; a candidate's TWO best answers will be used for assessment. Calculators of the approved type (non-programmable, no text facility) may be used. Statistical Tables will be provided.

The coursework requires a facility in the statistical computing environment R. Students should not take this Unit unless they are familiar with R, or confident that they can easily acquire the skills. Please consult the Unit Organiser if in doubt.

Reading and References

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.

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