ST412 Multivariate Statistics with Advanced Topics
Please note that all lectures for Statistics modules taught in the 202223 academic year will be delivered on campus, and that the information below relates only to the hybrid teaching methods utilised in 202122 as a response to Coronavirus. We will update the Additional Information (linked on the right side of this page) prior to the start of the 2022/23 academic year.
Throughout the 202122 academic year, we will be adapting the way we teach and assess your modules in line with government guidance on social distancing and other protective measures in response to Coronavirus. Teaching will vary between online and oncampus delivery through the year, and you should read the additional information linked on the right hand side of this page for details of how this will work for this module. The contact hours shown in the module information below are superseded by the additional information.You can find out more about the University’s overall response to Coronavirus at: https://warwick.ac.uk/coronavirus.
All dates for assessments for Statistics modules, including coursework and examinations, can be found in the Statistics Assessment Handbook at http://go.warwick.ac.uk/STassessmenthandbook
ST41215 Multivariate Statistics with Advanced Topics
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 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. 

Assignment 2  10%  15 hours 
Due in Term 2 Week 4. 

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

Assessment group R1
Weighting  Study time  

Inperson 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

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.
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