The number of students selected can be influenced by, for example, staff capacity and the availability of resources within the Department, as well as academic merit and University transformation objectives. As
staff capacity and resources can fluctuate from year to year, the number of students selected can also differ from year to year.
If the Mathematical Statistics background of the applicant is deemed insufficient after a case-by-case determination by the Department of Statistics and Actuarial Science, the Department may require an additional departmental assessment on third-year level Mathematical Statistics topics. Students may also be required to complete additional undergraduate Stellenbosch University Mathematical Statistics modules along with their honours studies.
Students will be required to pass modules totalling at least 120 credits made up as follows:
| Compulsory Modules | Code | Semester | Credits |
|---|---|---|---|
| Introduction to R Programming | 13074-723 | 1 | 6 |
| Multivariate Statistical Analysis A | 10602-715 | 1 | 12 |
| Multivariate Statistical Analysis B* | 10603-745 | 2 | 12 |
| Research Assignment: Mathematical Statistics | 11228-791 | 1 & 2 | 30 |
| Stochastic Simulation | 65250-718 | 2 | 12 |
| Time Series Analysis | 10751-747 | 1 | 12 |
| Modules | Code | Semester | Credits |
|---|---|---|---|
| Bayesian Statistics | 10394-711 | 1 | 12 |
| Biostatistics | 10408-712 | 1 | 12 |
| Capita Selecta in Mathematical Statistics A | 11922-724 | 1 | 12 |
| Capita Selecta in Mathematical Statistics B | 11923-754 | 2 | 12 |
| Experimental Design | 10440-713 | NA | 12 |
| Sampling Techniques | 10705-742 | NA | 12 |
| Statistical Learning Theory | 13360-771 | 2 | 12 |
| Survival Analysis | 10636-746 | 1 | 12 |
NA – This module is not presented in 2024.
This program is presented jointly by the Department of Statistics and Actuarial Science and the Department of Computer Science. Consequently students have to be admitted to postgraduate study by both these departments. A bachelor’s degree with an average mark of at least 65% in Mathematical Statistics 3 is required, together with a satisfactory mark of at least 65% in Computer Science up to at least second year level.
The number of students selected will be influenced by, among other things, staff capacity and the availability of resources within the Department, as well as academic merit and University transformation objectives. As staff capacity and resources may fluctuate from year to year, the number of students selected can also differ from year to year.
If the Financial Risk Management or Mathematical Statistics background of the applicant is deemed insufficient after a case-by-case determination by the Department of Statistics and Actuarial Science, the Department may require an additional departmental assessment on third year level Financial Risk Management and Mathematical Statistics topics. Students may also be required to complete additional undergraduate Stellenbosch University Financial Risk Management and Mathematical Statistics modules along with their honours studies.
Students will be required to pass modules totalling at least 120 credits made up as follows:
| Compulsory Modules | Code | Semester | Credits |
|---|---|---|---|
| Introduction to R Programming | 13074-723 | 1 | 6 |
| Introduction to Statistical Learning Theory | 13360-771 | 2 | 12 |
| Research Assignment: Mathematical Statistics | 58777-741 | 1 & 2 | 30 |
| Elective Modules | Code | Semester | Credits |
|---|---|---|---|
| These have to be selected taking into account the modules from Computer Science | |||
| Bayesian Statistics | 10394-711 | NA | 12 |
| Mathematical Statistics for Data Science | 13361-771 | 1 | 12 |
| Multivariate Statistical Analysis A | 10602-715 | 1 | 12 |
| Multivariate Statistical Analysis B* | 10603-745 | 2 | 12 |
| Stochastic Simulation | 65250-718 | 2 | 12 |
| Time Series Analysis | 10751-747 | 1 | 12 |
NA – This module is not presented in 2024.
* This module follows the A module. MSA A needs to be completed before the MSA B module can be taken.
The detailed description of this programme is availabile in the Faculty Calendar.
Objectives and content
The aim of the module is to introduce the students to the basic principles of Bayesian Statistics and its applications. Students will be able to identify the application areas of Bayesian Statistics. The numerical methods often used in Bayesian Analysis will also be demonstrated. Topics:Decision theory in general; risk and Bayesian risk in Bayesian decisions; use of non-negative loss functions; construction of Bayesian decision function; determining posteriors; sufficient statistics; class of natural conjugate priors; marginal posteriors; class of non-informative priors; estimation under squared and absolute error loss; Bayesian inference of parameters; Bayesian hypothesis testing; various simulation algorithms for posteriors on open source software; numerical techniques like Gibbs sampling and the Metropolis-Hastings algorithm, as well as MCMC methods to simulate posteriors.
Objectives and content
Biostatistics may be regarded as the study of the application of statistics to medicine. It covers medical terminology, the design of clinical trials, the collection and numerical analysis of data, the interpretation of the analyses and the drawing of conclusions. Particular emphasis is given to skills relevant to medical literature (the writing, as well as the understanding of writing by others) and statistical techniques and software that are widely used when doing medical research. It is not a mathematically strenuous course. It deals primarily with the philosophy and terminology of medical research, as well as the statistical techniques problems encountered in the medical field in particular. Topics that will be covered are: SAS,Clinical trials, Power and sample size analysis, Longitudinal data analysis, Handling missing data and Statistical genetics.
Objectives and Content
A problem frequently faced by applied statisticians is the analysis of time-to-event data. Examples of this data arise in diverse fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. Our focus in this course however will be on applications of the techniques in Biology and Medicine. Interest is on analysing data on the time to death from a certain cause, duration of response to treatment, time to recurrence of a disease, time to development of a disease, or simply time to death. Various non-parametric, semi-parametric and parametric techniques are introduced in the course that will also address residual analysis and goodness-of-fit in survival data. The emphasis of this course is on the practical analysis of survival data, with the necessary underlying theoretical background. SAS and R are used extensively to analyse the data.
Objectives and content
This module does not require advanced mathematics and is an option for both statistics and mathematical statistics students. Focus is mainly on the practical implementation of techniques together with computer packages from consultancy perspective. Attention is given to modeling, design matrices, least squares and diagnostics.
Objectives and content
This module is an introduction to programming and data analysis within the R open source environment. It is presented as a block course in the first two weeks of the first semester and commences the week preceding general commencement of classes. The viewpoint of this module as well as of all modules where R plays a role is in agreement with the aim of the R computer language: “R has a simple goal: To turn ideas into software, quickly and faithfully”.
Objectives and content
Data collected in practice rarely consist of one isolated variable. Mostly, data consist of many variables influencing one another. If only one variable upon a time is singled out for analysis, the data analyst is in danger of arriving at completely wrong conclusions. Multivariate statistical analysis entails the study of techniques for analysing data sets consisting of various variables influencing one another. This model aims to provide students with the expertise to confidently come to the right conclusions when analysing multivariate data. Students need to complete the A module before the B module can be taken.
Objectives and content
This module is a continuation of undergraduate time series analyses and concentrates on more advanced forecasting techniques. Topics that are covered include:
The Box & Jenkins methodology of tentative model identification, conditional and unconditional parameter estimation and diagnostic methods for checking the fit of the series.
Objectives and content
The module probability models and stochastic simulation is devoted to a study of the theory and applications of important probability models and stochastic processes. Applications are studied analytically, by means of the techniques of mathematical statistics, and are also illustrated by means of stochastic computer simulation. The broad aim of the module is to make students aware of the following important concepts:
The specific outcomes of the module are related to the specific topics that receive attention. These topics include the following: Methods for generating random variables from distributions; Monte Carlo integration; Markov chains (including applications to Metropolis-Hastings and Gibbs sampler methods); Homogeneous and non-homogeneous Poisson processes; Markov processes; variance reduction techniques in stochastic simulation.
Objectives and content
The design of a sample is one of the most important aspects of any survey: no amount of statistical analysis can compensate for a badly-designed sample. Therefore, the emphasis of this course is the scientific design of samples, determination of sample sizes and is related to methods for analysing the data from a survey. Contents include: Questionnaire design, sampling techniques (simple random, stratified, systematic, cluster, complex), proportional vs disproportional allocation for stratified sampling, ratio and regression estimation, estimation of means, totals proportions and their variances, weighting of survey data, dealing with non-response.
Objectives and content
Statistical Learning Theory is a module presented to honours students in Data Science and in Mathematical Statistics. The module extends over 1 semester and entails 13 contact sessions of approximately 3 hours each.
The following outcomes are envisaged in this module.
Regarding the content of the module, the following topics are discussed: Topics in regression and classification, recommender systems, boosting, probabilistic graphical models, high-dimensional scenarios where p >> N, interpreting black-box models and an introduction to reinforcement learning.
Objectives and content
Selected and specialised topics to be followed in Mathematical Statistics. Content varies from year to year when offered.
Please note: An application has been submitted to externally amend the title of this programme to Master of Commerce in Statistics and Data Science – abbreviation “MCom (Statistics and Data Science)”. This change will be implemented once the amended title has been approved by the Department of Higher Education and Training (DHET) and the Council on Higher Education (CHE), and the change has been registerered by the South African Qualifications Authority (SAQA).
An honours degree in Mathematical Statistics with an average mark of at least 65%.
The number of students selected can be influenced by, for example, staff capacity and the availability of resources within the Department, as well as academic merit and University transformation objectives. As staff capacity and resources can fluctuate from year to year, the number of students selected can also differ from year to year.
If the Mathematical Statistics background of the applicant is deemed insufficient after a case-by-case determination by the Department of Statistics and Actuarial Science, the Department may require an additional departmental assessment on Mathematical Statistics topics. Students may also be required to complete additional Stellenbosch University Mathematical Statistics modules along with their MCom studies.
You can choose between two possible options:
| Module | Code | Semester | Credits |
|---|---|---|---|
| Advanced Sampling Techniques | 10523-818 | NA | 15 |
| Advanced Mathematical Statistics A | 10524-819 | NA | 15 |
| Advanced Mathematical Statistics B | 11173-849 | NA | 15 |
| Advanced Multivariate Statistical Analysis A | 10512-815 | 1 | 15 |
| Advanced Multivariate Statistical Analysis B | 10513-845 | 2 | 15 |
| Bootstrap and other Resampling Techniques A | 10694-811 | 1 | 15 |
| Bootstrap and other Resampling Techniques B | 10695-841 | 2 | 15 |
| Extreme Value Theory A | 10441-813 | 1 & 2 | 15 |
| Extreme Value Theory B | 10442-843 | 1 & 2 | 15 |
| Multi-dimensional Scaling A | 18130-822 | 1 | 15 |
| Multi-dimensional Scaling B | 11910-852 | NA | 15 |
| Statistical Learning Theory A | 10703-812 | 1 & 2 | 15 |
| Statistical Learning Theory B | 10704-842 | NA | 15 |
| Thesis: Mathematical Statistics Compulsory with 879 | 11246-891 | 1 & 2 | 90 |
| Research Assignment: Mathematical Statistics Compulsory with 889 | 11228-895 | 1 & 2 | 60 |
NA – This module is not presented in 2024.
Also take note of the following combinations and prerequisites:
The PhD programme in Mathematical Statistics have a minimum residency of 2 years. Degrees are awarded on the basis of independent research providing an original distinct contribution to the methodological field of Mathematical Statistics. The straightforward statistical analysis of a data set from an applied field might qualify for a PhD in the applied field but does not warrant a PhD in Mathematical Statistics.
Applicants must have completed a Masters degree in Mathematical Statistics with evidence of having passed accredited Masters-level courses in the field where the PhD research will be performed.
If an applicant is interested in pursuing a PhD with potential supervisors who are members of MuViSU the following requirement will apply to applicants who did not complete a Masters degree in Mathematical Statistics at SU: The material of the modules 10597-822 Multi-dimensional Scaling A and 11910-852 Multi-dimensional Scaling B must be self-studied and all assignments must be completed. Only applicants who obtain an average for at least 65% for the assignments will be considered.
Applications are submitted on the SUNstudent application portal.
The following documents are submitted as part of the application:
Applicants are advised to consult the personal research webpages of staff members to establish the possible theoretical research themes in line with the research of potential supervisors.
GEM is managed as a unit in the Dean’s office. It started its operations in 2014 with the purpose of strengthening the Faculty’s doctoral throughput rate by allowing some students to study full-time and enhancing access to doctoral studies in the disciplines that are housed in the Faculty of Economic and Management Sciences. GEM essentially plays a supporting role so that candidates have a better chance of finalising their doctoral studies within the allocated time of three years. Find out more on the GEM website.
The admission requirements for students that are admitted into GEM’s doctoral programme are the same as the requirements stipulated for the PhD degree.
Applications are accepted during the application period that is indicated on the GEM website under Research Themes.
Dr Jaco Franken
Manager: Graduate School of Economic and Management Sciences (GEM)
Room 1017, AI Perold building
Stellenbosch University
Tel: 021 808 9545
E-mail: franken@sun.ac.za
Website: https://www.sun.ac.za/english/faculty/economy/gem