ST32315 Multivariate Statistics
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 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 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.
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 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.
 Conduct inference for multivariate means, construct confidence regions, and understand their potential uses, such as for group comparisons.
 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, independent component analysis, compositional data analysis, canonical correlation analysis.
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
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 D2
Weighting  Study time  

Assignment 1  10%  15 hours 
Due in Term 1 Week 6. 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 ST323 Assignment 1 should not exceed 15 pages in length. 

Assignment 2  10%  15 hours 
Due in Term 2 Week 4. 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 ST323 Assignment 2 should not exceed 15 pages in length. 

Online Examination  80%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade. ~Platforms  Moodle

Assessment group R
Weighting  Study time  

Online Examination  Resit  100%  
The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade. ~Platforms  Moodle 
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.
Courses
This module is Core optional for:

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)
 Year 3 of G30C Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream)

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 3 of G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int
 Year 4 of G30F Master of Maths, Op.Res, Stats & Economics (Econometrics and Mathematical Economics Stream) Int
 Year 4 of G30G Master of Maths, Op.Res, Stats & Economics (Operational Research and Statistics Stream) Int
This module is Optional for:

UCSAG4G1 Undergraduate Discrete Mathematics
 Year 3 of G4G1 Discrete Mathematics
 Year 3 of G4G1 Discrete Mathematics
 Year 3 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 4 of UCSAG4G2 Undergraduate Discrete Mathematics with Intercalated Year

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 Option list A for:

USTAG302 Undergraduate Data Science
 Year 3 of G302 Data Science
 Year 3 of G302 Data Science
 Year 3 of USTAG304 Undergraduate Data Science (MSci)
 Year 4 of USTAG303 Undergraduate Data Science (with Intercalated Year)
 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)
 Year 4 of USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 3 of GG14 Mathematics and Statistics
 Year 3 of GG14 Mathematics and Statistics
 Year 4 of USTAGG17 Undergraduate Mathematics and Statistics (with Intercalated Year)

USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 3 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 3 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 4 of USTAY603 Undergraduate Mathematics,Operational Research,Statistics,Economics (with Intercalated Year)
This module is Option list B for:

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 3 of G105 Mathematics (MMath) with Intercalated Year
 Year 5 of G105 Mathematics (MMath) with Intercalated Year
 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

UMAAG100 Undergraduate Mathematics (BSc)
 Year 3 of G100 Mathematics
 Year 3 of G100 Mathematics
 Year 3 of G100 Mathematics

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G100 Mathematics
 Year 3 of G103 Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 3 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of UMAAG101 Undergraduate Mathematics with Intercalated Year