Statistics and Actuarial Science
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Nagraadse Statistiek

Aansoeke vir 2021 nagraadse studies is nou gesluit. Sluitingsdatum vir nagraadse studies in 2021 was 31 Oktober 2020. Besoek vir verdere besonderhede omtrent die aansoek-prosedures.

Neem kennis dat al die nagraadse programme is keuringsprogramme. Afgesien van die minimum akademiese vereistes wat bestaan vir elk van die programme (Honneurs en/of Magister), word keuring gedoen op voortreflike akademiese meriete en slegs 'n beperkte aantal studente sal jaarliks toegelaat word om vir hierdie programme te kan registreer. Om slegs aan die minimum vereistes van die progranm te voldoen, waarborg geensins outomatiese toelating tot die program nie.

Hier vind u meer inligting oor die volgende nagraadse programme in Statistiek:

'n Kort omskrywing en opsomming van die verskillende nagraadse modules word gevind deur op die module te klik of om te gaan na onder op hierdie bladsy. Vir verdere inligting omtrent hierdie programme, kontak Prof Lubbe by .

Die R module begin reeds 3 Februarie 2021. Verpligtende module vir all honneurs studente in die Departement.

Spesiale registrasie vir Honneurs en Magister modules

Studente wat vir enige van hierdie nagraadse modules wil registreer as deel van 'n graadprogram en wat aangebied word buite die Departement Statistiek en Aktuariele Wetenskap, moet formeel aansoek doen by die departement vir die betrokke module(s) deur:

·        Stuur persoonlike / kontak details;

·        die module(s) waarvoor jy aansoek doen, asook die huidige graadprogram waarvoor jy registreer het, aan​;

·        verskaf volledige studierekord in die epos;

·        Maak seker van die voor- en newevereistes van die modules wat jy wil neem by of, spesifiek wat betref die R blok module wat reeds aangebied word ongeveer twee voordat amptelike lesings begin.

·        Sluitingsdatum vir hierdie aansoeke is 31 Januarie elke jaar (en 20 Januarie vir 13074-723 Inleiding tot R).

Honneursprogram in Statistiek

19658 – 778 (120) HonsBCom in Statistiek  

Sien die Jaarboek hier vir 'n volledige omskrywing van die program. Modules wat aangebied word in hierdie program:

ModuleKode Semester (2021) Krediete Verpligte Modules
Capita Selecta in Statistiek A​11920-725​1*​12
​Capita Selecta in Statistiek B​11921-755​NVT​12
Eksperimentele ontwerp ​10440-713NVT​12
Meerveranderlike Metodes in Statistiek A​10600-721​1​12​****
Meerveranderlike Metodes in Statistiek B *
Toegepaste Tydreeksanalise​10748-722​1​12​****
Toegepaste Stogastiewe Simulasie​65269-746​2​12
​Inleiding tot R Programmeting​10547-723​1​6​****
​Navorsingswerkstuk: Statistiek​11226-792​1 & 2​30​****

NVT - Hierdie modile word nie aangebied in 2021 nie.

1* - Stogastiese modelle - aangebied onder Capita Selecta (Statistiese modelle en inferensie)

* Die MMS A module is 'n voorvereiste vir die MMS B module.

Magisterprogramme in Statistiek

19658 – 879 (180) MCom (Statistiek) – tesis opsie  

19658 – 889 (180) MCom (Statistiek) – werkstuk opsie

Sien die Jaarboek hier vir 'n volledige omskrywing van die programme. Modules wat aangebied word in hierdie programme:

ModuleKode Semester (2021) Krediete Verpligte Modules
​Gevorderde Statistiek A​10521-8211*
​Gevorderde Statistiek B​10522-8512​**​15
Gevorderde Steekproefnemingstegnieke​10523-818​NVT​15
Meerdimensionele Skalering A​10597-822​1​15
Meerdimensionele Skalering B​11910-852​2​15
Skoenlus en ander Steekproefhergebruitegnieke A​10694-811​1​15
​Skoenlus en ander Steekproefhergebruitegnieke B​10695-841​2​15
​Tesis: Statistiek​11244-891 ​1 & 2​90 saam met 879
​Navorsingswerkstuk: Statistiek​11226-893​1 & 2​60saam met 889​

NVT - Hierdie modile word nie aangebied in 2021 nie.
* -   Module in Toegepaste Leerteorie.

2** - Survival Analysis (Hons).   

Doktoraleprogram in Statistiek

19658 – 978 (240) PhD (Statistiek)

Sien die Jaarboek hier vir 'n volledige omskrywing van die programme.


Module Inhoud - Honneurs

Introduction to R (13074-723)

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".

Biostatistics (10408-712)

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.

Multivariate Methods in Statistics A & B (10600-721 & 10601-751)

Objectives and content: The objective of the course is to teach students the practical application of multivariate analysis. Various multivariate methods are dealt with. Students learn when and where to apply these techniques.  The consequences of the assumptions made on some of these techniques are also studied. The following topics are studied: Matrix algebra, Characterising and displaying multivariate data, The multivariate normal distribution, Inferences on one or two mean vectors, Multivariate analysis of variance, Inferences on the covariance matrix, Discriminant analysis,  Classification analysis, Multivariate regression, Canonical correlation, Principal component analysis, Factor analysis and Cluster analysis. The R and SAS software are used in all the applications to datasets. The A module is a prerequisite for the B module.

Financial Mathematical Statistics (11164-732)

Objectives and Content: In this module an introduction is given to Extreme Value Theory (EVT) and its role in Financial Risk Management. EVT entails the study of extreme events and for this theory has been developed to describe the behaviour in the tails of distributions. The module will disduss the theory in a conceptual fashion without proving the results. It will be shown how this theory can be used to carry out inferences on the relevant parameters of the underlying distribution. Both the classical approach of block maxima based on the Fisher-Tippett Theorem and the more modern threshold approach based on the Pickands-Balkema-de Haan Theorem will be discussed and applied. Results for both independent and dependent data will be covered.

Experimental Design (10440-713)

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.

Data mining (58777-741)

Objectives and content: Data mining is a relatively new discipline using techniques developed in statistics, data base technology, pattern recognition, machine learning and other related areas.  It is concerned with the analysis of large data bases in order to identify trends and patterns in the data, which can be of value to the data base owners. Examples of applications of data mining in practice are: credit assessment, fraud detection, prediction of stock prices and marketing and sales forecasting. The purpose of this module is to introduce students to the philosophy and methodology of data mining, to study statistical and other techniques that are applied in data mining, and to learn to apply data mining software to practical problems.

Sampling Techniques (10705-742)

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.

Applied Time series Analysis (10748-722)

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.
  • ARIMA and Seasonal ARIMA-processes.
  • Introduction to Fourier Analysis, spectrum of a periodic time series, estimation of the spectrum, periodogram analysis, smoothing of the spectrum.
  • Case studies using STATISTICA, R and SAS.
  • Forecasting with ARMA models and prediction intervals for forecasts.
  • Transfer function models and intervention analysis.
  • Multiple regression with ARMA errors, cointegration of non-stationary time series.
  • Conditional heteroscedastic time series models, ARCH and GARCH.

Applied Stochastic simulation (65269-746)

Objectives and content: In this module the student learns to understand and apply the underlying mathematical principles behind stochastic simulation. Statistical theory is applied to practical problems which are modelled on computer. To achieve this, the student revises probability theory, including conditional probability and independence, discrete and continuous distributions, probability integral transformation, and Bayes' theorem. Pseudorandom number generation is studied to simulate stochastic problems. These pseudorandom numbers are used to evaluate integrals, and to generate discrete and continuous random variables. It is also important to do a statistical analysis of simulated data using point and interval estimates of the mean and variance, as well as bootstrap techniques. Input data for simulation models are analysed with the chi-squared and Kolmogorov-Smirnoff goodness-of-fit tests. The student finally develops practical simulation models of discrete-event, dynamic stochastic processes using a dedicated simulation software package.

Capita Selecta in Statistics A & B (11920-725 & 11921-755)

Objectives and content: Selected and specialised topics to be followed in Applied Statistics. Content varies from year to year when offered.


Module Inhoud - Magister

Bootstrap and other Resampling techniques A & B (10694-811 & 10695-841)

Objectives and content: Traditional procedures of statistical inference in many cases are true only asymptotically or under strict assumptions for small samples.  For many problems it is impossible to find solutions analytically.  Re-sampling techniques are computer intensive methods using repeated re-sampling from the original sample in order to obtain solutions for inferential statistical problems.  The aim of this module is to introduce the student to the bootstrap and related computer intensive methods enabling him/her to use correctly these methods with confidence in practice. The A module is a prerequisite for the A module.

Applied Statistical Learning Theory

Objectives and content: The outcomes of these modules can be summarised as follows:

  • The students should develop a holistic view of the subject of statistics, gaining an appreciation of the general principles underlying many (seemingly unrelated) statistical methods.
  • The students should develop an awareness of the size, complexity and diversity of data sets which one encounters in practice.
  • The students should develop an appreciation of the challenges and problems posed to a statistician wishing to analyse a data set, especially the problem referred to as the "curse of dimensionality" in high-dimensional problems.
  • The students must gain knowledge of the various approaches to the "curse of dimensionality" problem and the manner in which these approaches compromise between underlying assumptions and sample size requirements.
  • The students must understand the important role played by more traditional, established statistical procedures such as multiple regression analysis, logistic regression analysis and linear discriminant analysis in modern data mining.
  • The students should become sensitive to and appreciative of the valuable contributions made to the development of data mining procedures in areas such as computer science and machine learning.
  • The students should be granted the opportunity to enhance their programming skills through writing appropriate programs to solve various data analysis problems.

Regarding the content of the modules, statistical learning theory is a collective noun for a variety of techniques that can be used to identify, describe and model important patterns and trends in data sets.  The topics which are studied in these modules include techniques that are well established in traditional statistics, namely regression analysis, discriminant analysis, spline models and smoothing splines, as well as more recently developed approaches such as regression and classification trees, additive models, bagging, boosting (also from a functional gradient descent point of view), neural networks, random forests and support vector machines.

Advanced Sampling Techniques (10523-818)

Objectives and content: In practice, complex sampling techniques are usually applied to design sample surveys.  Furthermore, nonresponse and skewness generally manifest in sampling surveys that need to be addressed scientifically.  This course covers both theoretical and practical aspects regarding sampling and include the following: two-stage cluster sampling; design and estimation of complex sample surveys; design effects; dealing with nonresponse and missing data; weighting of surveys; inferential statistics for complex survey data.

Multi-dimensional Scaling A & B (10597-822 & 11910-852)

Objectives and content: Multi-dimensional scaling (MDS) consists of various techniques from the field of multivariate statistical analysis. MDS focuses on dimension reduction and graphical displays of multi-dimensional data. This module introduces the theory and practical implementation of classical metrical scaling, non-metrical scaling, various forms of Procrustes analysis, unfolding techniques, individual differences models, as well as m-mode n-way models. Biplot methodology is emphasised. MDS techniques for both quantitative and qualitative data are considered. Correspondence analysis, multiple correspondence analysis, homogeneity analysis, analysis of distance as well as non-linear principal component analysis and canonical variate analysis are also discussed. The A module is a prerequisite for the B module.

Advanced Statistics A & B (10521-821 & 10522-851)

Objectives and content: Selected and specialised topics to be followed in Applied Statistics. Content varies from year to year when offered.