Introductory description
This module runs in Term 1 and is an optional module intended for students in their third or fourth year of study who have previously taken preparatory modules in Statistics.
For Statistics students the prerequisites are ST115 Introduction to Probability, ST218 Mathematical Statistics A, ST219 Mathematical Statistics B.
For NonStatistics students the prerequisites are ST111/112 Probability A&B and ST220 Introduction to Mathematical Statistics.
The coursework uses the statistical software package R, so basic knowledge in R such as covered in ST104 Statistical Laboratory I or ST952 Introduction to Statistical Practice is expected.
Module web page
Module aims
Multivariate data arises whenever several interdependent variables are measured simultaneously. Such highdimensional data is becoming the rule, rather than the exception in many areas: in medicine, in the social and environmental sciences and in economics. The analysis of such multidimensional data often presents an exciting challenge that requires new statistical techniques which are usually implemented using computer packages. This module aims to give you a good and rigorous understanding of the geometric and algebraic ideas that these techniques are based on, before giving you a chance to try them out on some real data sets.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Multivariate data arises whenever several interdependent variables are measured simultaneously. Such highdimensional data is becoming the rule, rather than the exception in many areas: in medicine, in the social and environmental sciences and in economics. The analysis of such multidimensional data often presents an exciting challenge that requires new statistical techniques which are usually implemented using computer packages. This module aims to give you a good understanding of the geometric and algebraic ideas that these techniques are based on, before giving you a chance to try them out on some real data sets.
Students will be given selected advanced research material for independent study and examination.
Learning outcomes
By the end of the module, students should be able to:
 Construct and interpret graphical representations of multivariate data
 Carry out a principal components and canonical correlation analysis to summarise high dimensional data
 Perform clustering analysis to discover and characterize subgroups in the population.
 Use classification and discrimination methods to assign individuals into groups.
 Assess multivariate normality and do multivariate tests for comparing means across groups
 Understand any additional topics covered in the lectures. Time permitting, lectures will cover one or two additional topics such as Factor Analysis, Multidimensional Scaling, random forests, bagging, sparse multivariate methods, Gaussian graphical models, multiple testing, functional data analysis, spatial statistics.
 Understand by independent study an additional advanced topic in multivariate statistics.
Indicative reading list
Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis.: Pearson Prentice Hall. Upper Saddle River, NJ.
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112). New York: Springer.
Friedman, J., Hastie, T., & Tibshirani, R. (2009). The elements of statistical learning (second edition). New York: Springer.
Efron, B., & Hastie, T. (2016). Computer age statistical inference (Vol. 5). Cambridge University Press.
Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical learning with sparsity: the lasso and generalizations. CRC press.
View reading list on Talis Aspire
Subject specific skills
TBC
Transferable skills
TBC
Study time
Type 
Required 
Optional 
Lectures 
30 sessions of 1 hour (20%)

2 sessions of 1 hour

Private study 
90 hours (60%)


Assessment 
30 hours (20%)


Total 
150 hours 

Private study description
Study of advanced topic, weekly revision of lecture notes and materials, wider reading and practice exercises, working on assignments and preparing for examination.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D3

Weighting 
Study time 
Assignment 1

10%

15 hours

Due in Term 1 Week 6. The assignment will contain a number of questions for which solutions and / or written responses will be required. The number of words noted below refers to the amount of time in hours that a wellprepared student who has attended lectures and carried out an appropriate amount of independent study on the material could expect to spend on this assignment. 500 words is equivalent to one page of text, diagrams, formula or equations; your ST412 Assignment 1 should not exceed 15 pages in length.

Assignment 2

10%

15 hours

Due in Term 2 Week 4. The assignment will contain a number of questions for which solutions and / or written responses will be required. The number of words noted below refers to the amount of time in hours that a wellprepared student who has attended lectures and carried out an appropriate amount of independent study on the material could expect to spend on this assignment. 500 words is equivalent to one page of text, diagrams, formula or equations; your ST412 Assignment 2 should not exceed 15 pages in length.

Oncampus Examination

80%


The examination will contain one compulsory question on the advanced topic and four additional questions of which the best marks of TWO questions will be used to calculate your grade.
~Platforms  Moodle
 Answerbook Pink (12 page)
 Students may use a calculator
 Graph paper
 Cambridge Statistical Tables (blue)

Assessment group R1

Weighting 
Study time 
Oncampus Examination  Resit

100%


The examination will contain one compulsory question on the advanced topic and four additional questions of which the best marks of TWO questions will be used to calculate your grade.
~Platforms  Moodle
 Online examination: No Answerbook required
 Students may use a calculator
 Graph paper
 Cambridge Statistical Tables (blue)

Feedback on assessment
Marked assignments will be available for viewing at the support office within 20 working days of the submission deadline. Cohort level feedback and solutions will be provided, and students will be given the opportunity to receive feedback via facetoface meetings.
Solutions and cohort level feedback will be provided for the examination.
Past exam papers for ST412
Antirequisite modules
If you take this module, you cannot also take:

ST32315 Multivariate Statistics
Courses
This module is Core optional for:

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

Year 3 of
G30F Master of Maths, Op.Res, Stats & Economics (Econometrics and Mathematical Economics Stream) Int

Year 4 of
G30F Master of Maths, Op.Res, Stats & Economics (Econometrics and Mathematical Economics Stream) Int
This module is Optional for:

TMAAG1PE Master of Advanced Study in Mathematical Sciences

Year 1 of
G1PE Master of Advanced Study in Mathematical Sciences

Year 1 of
G1PE Master of Advanced Study in Mathematical Sciences

Year 1 of
TMAAG1P9 Postgraduate Taught Interdisciplinary Mathematics

Year 1 of
TMAAG1PD Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc)

Year 1 of
TMAAG1P0 Postgraduate Taught Mathematics

Year 1 of
TMAAG1PC Postgraduate Taught Mathematics (Diploma plus MSc)

Year 1 of
TSTAG4P1 Postgraduate Taught Statistics

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

Year 3 of
G300 Mathematics, Operational Research, Statistics and Economics

Year 4 of
G300 Mathematics, Operational Research, Statistics and Economics
This module is Core option list A for:

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

Year 3 of
G30B Master of Maths, Op.Res, Stats & Economics (Econometrics and Mathematical Economics Stream)

Year 3 of
G30D Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

Year 3 of
G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)

Year 4 of
G30F Master of Maths, Op.Res, Stats & Economics (Econometrics and Mathematical Economics Stream) Int

Year 4 of
G30H Master of Maths, Op.Res, Stats & Economics (Statistics with Mathematics Stream)
This module is Core option list B for:

Year 3 of
USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

Year 3 of
G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int

Year 4 of
G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int
This module is Option list A for:

Year 4 of
USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

Year 5 of
USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)

Year 3 of
G1G3 Mathematics and Statistics (BSc MMathStat)

Year 4 of
G1G3 Mathematics and Statistics (BSc MMathStat)

USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)

Year 4 of
G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)

Year 5 of
G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list B for:

Year 4 of
USTAG304 Undergraduate Data Science (MSci)

Year 4 of
UCSAG4G3 Undergraduate Discrete Mathematics

Year 3 of
USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

Year 3 of
G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int

Year 4 of
G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int
This module is Option list D for:

Year 4 of
USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

Year 5 of
USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated