BAYESIAN STATISTICS
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours and Master programmes in Mathematical Statistics.
Prerequisite: Mathematical Statistics 318, 344, 354.
Objectives of the module:
The aim of the module is to introduce the students to the basic principals 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.
BIOSTATISTICS
Duration: One semester
Credits: 12
Who may take the module: Optional module for Honours in Statistics and Mathematical Statistics; Master’s in Statistics
and Mathematical Statistics
Prerequisite: Degree majoring in Statistics or Mathematical Statistics or Biometry
Objectives:
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 several study designs that are used (almost) exclusively in medical research.
It is not a mathematically strenuous course. It deals primarily with the philosophy and terminology of epidemiology, as
well as the statistical techniques and statistical problems encountered in the medical field in particular. Topics wthat will
be covered are: Basic epidemiology , Clinical trials, Power and sample size analysis, Longitudinal data analysis,
Handling missing data and Statistical genetics.
DATA MINING
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours and Master programmes in Statistics, Mathematical
Statistics or Financial Risk Management
Prerequisite: Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module:
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.
EXPERIMENTAL DESIGN
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours and Master programmes in Statistics or Mathematical
Statistics
Prerequisite: Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module:
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.
FINANCIAL RISK MANAGEMENT A and B
Duration: Two semesters
Credits: 24 (or 2 X 12)
Who may take the module: Compulsory for the Honours programme in Financial Risk Management
Prerequisite: Financial Risk Management 314 & 344, Mathematical Statistics as third year subjects and Financial
Mathematics 378.
Objectives of the module:
To train students in the theoretical and practical aspects of Financial Risk Management in such a way that they are able
to apply it in the financial world
FINANCIAL MATHEMATICAL STATISTICS A and B
Duration: Two semesters
Credits: 24 (or 2 X 12)
Who may take the module: Compulsory module for the Honours programme in Financial Risk Management
Prerequisite: Financial Risk Management 314 & 344, Mathematical Statistics as third year subjects and Financial
Mathematics 378.
Objectives of the module:
The purpose of this module is to give students the basic mathematical tools needed for pricing modern financial
instruments. The module consists of two parts, a first, short part at a relatively low mathematical level with the aim of
quickly getting to the Arbitrage Theorem and the Black-Scholes Theorem. In the second part a mathematically more
advanced approach is followed in which the following are covered: Relevant probability theory, Martingales and
martingale representations, Relevant stochastic processes, Stochastic calculus, including Ito’s Lemma, Pricing of
derivatives using the above covered tools.
ADVANCED FINANCIAL MATHEMATICAL STATISTICS A and B
Duration: Two semesters
Credits: 30 (or 2 X 15)
Who may take the module: Compulsory module for the Master programme in Financial Risk Management.
Prerequisite: Financial Mathematical Statistics A en B.
Objectives of the module:
The purpose of this course is to build on the topics covered in Financial Mathematical Statistics I and to cover more
advanced topics. This will give students the mathematical tools to determine the prices of the more exotic instruments
as well as to enable them to read the latest literature in this field. Furthermore, the students will be exposed to Extreme
Value Theory and its application in risk management.
ADVANCED INFERENCE A and B
Duration: Two semesters
Credits: 12
Who may take the module: Optional module for the Honours and Master programmes in Mathematical Statistics.
Prerequisite: Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module: To learn the principles and different directions in modern statistical inference. Statistical
models, Bayes, fiducial and likelihood approaches to inference, frequentist approach to inference, large sample theory
and robust inference
INTRODUCTION TO S-PLUS / R
Duration: Block module in the beginning of the first semester
Credits: 6
Who may take the module: Optional module for the Honours programme in Statistics or Mathematical Statistics and
the Master programme in Statistics or Mathematical Statistics.
Prerequisite: Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module:
This module is an introduction to programming and data analysis within the S-PLUS 2000 / R 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 S-PLUS/R plays a role is in agreement with the aim of the
S computer language: “S has a simple goal: To turn ideas into software, quickly and faithfully”.
CONSULTATION PRACTICE
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours programme in Statistics or Mathematical Statistics, as
well as the Master programme in Statistics.
Prerequisite: Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module: General consultation skills and practical experience in Statistical Consultation. Work in the
Centre for Statistical Consultation under supervision.
MULTIVARIATE CATEGORICAL DATA ANALYSIS A and B
Duration: Two semesters
Credits: 24 (or 2 X 12)
Who may take the module: Optional module for the Honours and Master programmes in Statistics or Mathematical
Statistics.
Prerequisite: Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module:
To educate students in the basic and advanced theories as well as the practical procedures according to which
multivariate discrete data sets compounded in two- or multi-dimensional contingency tables are analysed and modelled.
MULTIVARIATE METHODS IN STATISTICS A and B
Duration: Two semesters
Credits: 24 (2 X 12)
Who may take the module: Optional module for the Honours programme in Statistics.
Prerequisite: Statistics 314 and 348; Introduction to S-PLUS/R
Objectives of the module:
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.
MULTIVARIATE STATISTICAL ANALYSIS A and B
Duration: Two semesters
Credits: 24 (Module A: 12 credits; Module B: 12 credits)
Who may take the module: Optional module for the Honours programme in Mathematical Statistics or Financial Risk
Management and the Master programme in Mathematical Statistics or Financial Risk Management.
Prerequisite: Mathematical Statistics 318, 344, 354 or 364, Introduction to S-PLUS/R
Objectives of the module:
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.
ADVANCED MULTIVARIATE STATISTICAL ANALYSIS A and B
Duration: Two semesters
Credits: 30 (or 2 X 15)
Who may take the module: Optional module for the Master programme in Mathematical Statistics or Financial Risk
Management.
Prerequisite: Multivariate Statistical Analysis A and B.
Objectives of the module:
The aim of this module is a study of graphical displays of multidimensional data. The book: Gower, JC & Hand, DJ.
1996. Biplots. Chapman & Hall: London, is studied in detail and forms the background for an in-depth study of the
following topics:
Self-consistency and linear principal components; finite mixture distributions, the EM-algorithm and model-based cluster
analysis; cluster analysis techniques of Kaufman and Rousseeuw; multidimensional scaling; correspondence analysis.
Graphical displays of multidimensional data.
LARGE SAMPLE THEORY A and B
Duration: Two semesters
Credits: 30 (or 2 X 15)
Who may take the module: Optional module for the Master programme in Mathematical Statistics.
Prerequisite: Honours in Mathematical Statistics.
Objective of the module:
NONPARAMETRIC STATISTICS
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours and Master programmes in Statistics or Mathematical
Statistics
Prerequisite: Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module:
Teach students techniques for exact statistical inference under minimal distributional assumptions. The main theme of
this course is exact statistical inference under minimal distributional assumptions. Issues of relative efficiency have to
addressed so as to be assured that the methods do not compare too unfavourably with their optimal parametric
counterparts. The course covers three broad areas: one-sample problems, two-sample problems, linear models.
PORTFOLIO MANAGEMENT THEORY A and B
Duration: Two semesters
Credits: 24 (or 2 X 12)
Who may take the module:
Compulsory module for the Honours programme in Financial Risk Management
Prerequisite:
Financial Risk Management and Mathematical Statistics in the third year, as well as Financial
Mathematics 378
Objectives of the module:
STATISTICAL QUALITY CONTROL AND -IMPROVEMENT
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours and Master programmes in Statistics or Mathematical
Statistics.
Prerequisite: Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module:
Statistical process control and the uses thereof must be observed in context to the whole setup of a company. The aim
is to make people in the company aware of quality in the wide sense of the word. Quality control and improvement
includes the management of the company and therefore each facet of the company:
SURVIVAL ANALYSIS
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours and Master programmes in Statistics or Mathematical
Statistics.
Prerequisite: Introduction to S-Plus/R as well as Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or
364.
Objectives of the module:
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 and parametric techniques are introduced
in this course. The emphasis of this course is on the practical analysis of survival data, with the necessary underlying
theoretical background. SAS and S-Plus/R are used extensively to analyse the data.
BOOTSTRAP AND OTHER RESAMPLING TECHNIQUES A and B
Duration: Two semesters
Credits: 30 (or 2 X 15)
Who may take the module: Optional module for the Master programme in Statistics or Mathematical Statistics or
Financial Risk Management.
Prerequisite: Honours in Mathematical Statistics or Statistics; Multivariate Statistical Analysis A and B or Multivariate
Methods A and B; S-Plus/R programming skills.
Objectives of the module:
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.
TIME SERIES ANALYSIS A and B
Duration: Two semesters
Who may take the modules: Optional module for Honours and Master’s in Mathematical Statistics and Financial Risk
Management
Credits: 24 (or 2 X 12)
Prerequisite: Mathematical Statistics 318, 344, 354 or 364, Knowledge of Excel and Word in the Windows environment.
Module A for module B
Objectives of the module:
Time Series Analysis – Module A
Introductory concepts
1. Fundamental concepts in Time Series Analysis: Filters (moving averages, convolutions such as double
moving averages, polynomial curve fitting, differences).
2. Transformations (variance stabilization, Taylor series approximations).
3. Stationarity and time series.
4. Sample autocorrelation function (SACF) of observed time series; use of the correlogram.
5. Introduction to Fourier Analysis, spectrum of a periodic time series, estimation of the spectrum, periodogram
analysis, smoothing of the spectrum.
6. Classical decomposition of a time series into seasonal-, trend-, cyclical- and random components.
7. Modeling of seasonality using dummy variable regression and trigonometric functions.
Probabilistic models
1.
2.
Stochastic processes (white noise, “random walk”-processes).
ARMA(p,q)-processes. Theoretical autocovariance-, autocorrelation- and partial autocorrelation
functions.
ARIMA(p,d,q)-processes. Theoretical autocovariance-, autocorrelation- and partial autocorrelation
3.
functions.
4.
SARIMA(p,d,q) × (P,D,Q)-processes. Theoretical autocovariance-, autocorrelation- and partial
autocorrelation functions.
The Box & Jenkins methodology of tentative model identification, parameter estimation and diagnostic
5.
methods.
Case studies using STATISTICA and SAS.
6.
Time Series Analysis – Module B
This module concentrates on short-term forecasting techniques. Techniques are theoretically derived. Lectures are
practical by nature. Use of software packages such as EXCEL, STATISTICA and SAS are illustrated.
Topics that are covered include,
1. Measures of forecasting accuracy (ME, MAD, MSE, MAPE).
2. Model selection (forward validation).
3. Forecasting using the naïve-method, moving averages, exponential smoothing (methods of Brown, Holt,
Holt-Winters), ARIMA(p,d,q)-models.
4. Confidence intervals for forecasts.
5. Transfer function models and intervention analysis.
6. Multiple regression with ARMA errors.
PROBABILITY THEORY A and B
Duration: Two semesters
Credits: 30 (or 2 X 15)
Who may take the module: Optional module for the Master programme in Mathematical Statistics.
Prerequisite: Honours in Mathematical Statistics.
Objectives of the module:
To teach students advanced probability theory based on measure theory and the properties of different stochastic
quantities that are useful in advanced mathematical statistics.
STOCHASTIC SIMULATION
Duration: One semester
Credits: 12
Who may do this module: Optional module for students doing Honours and Masters in Mathematical Statistics,
Honours in Actuarial Science; Honours or Masters in Financial Risk Management, and possibly Honours in Mathematics
and Computer Science.
Requirements for admission: Knowledge of probability theory and distribution theory, as well as stochastic processes
as covered in Mathematical Statistics 344. Students who did not follow Mathematical Statistics 344 may be admitted to
the module if they have the necessary prior knowledge obtained from other modules.
Objectives of the module:
The aim of the module is to make the students aware of the following important concepts:
a. the important role played by assumptions in identification of an appropriate probability model for a given practical
situation.
b. the wide applicability of stochastic simulation in the analysis of probability models.
c. the standard techniques of mathematical statistics that can be used in the analysis of probability models.
The specific outcomes of the module are related to the specific topics that receive attention. These topics include the
following:
• using conditioning to calculate expected values and probabilities
• the principles of stochastic simulation
• general and specific methods to generate observations from the standard probability distributions
• the use of simulation in solving probability problems
• variance reduction techniques in stochastic simulation
• Gibbs sampling
APPLIED STOCHASTIC SIMULATION
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours programme in Statistics
Prerequisite: Statistics 318, 348.
Objectives of the module: On completion of this module the student should:
• Understand the underlying mathematical principles behind stochastic simulation.
• Be able to use and apply such theory in practical simulation problems.
•
Be able to write computer programs to solve simulation problems.
STOCHASTIC MODELS
Duration: One semester
Credits: 12
Who may take the module: Optional module for the Honours programme in Statistics
Prerequisite: Statistics 318, 348.
Objectives of the module:
STATISTICAL LEARNING THEORY A and B
Duration: Two semesters
Credits: 30 (or 2 X 15)
Who may take the module: Compulsory module for the Master programme in Mathematical Statistics or Financial Risk
Management.
Prerequisite: Honours in Mathematical Statistics.
Objectives of the module: Statistical learning theory entails the study of various techniques that can be used to identify
and describe important patterns and trends in (large) datasets. Some of the techniques that are studied in this field are
well established in traditional statistics, for example regression analysis and discriminant analysis. However, statistical
learning theory also includes several new techniques – techniques that owe their existence to the huge computing power
that is nowadays available to analyse large data sets. Examples of such techniques are regression and classification
trees, and support vector machines. These techniques, and many others, are studied in this module.
EXTREME VALUE THEORY A and B
Duration: Two semesters
Credits: 30 (or 2 X 15)
Who may take the module: Compulsory module for the Master programme in Mathematical Statistics or Financial Risk
Management.
Prerequisite: Honours in Mathematical Statistics.
Objectives of the module:
ADVANCED REGRESSION TECHNIQUES A and B
Duration: Two semesters
Credits: 30
Who may take the module: Optional module for the Masters programme in Statistics
Prerequisite: Honours in Statistics
Objectives of the module: On completion of this module the student should:
• be familiar with alternative regression fits, analyses and modelling techniques.
• get an understanding of the underlying theory.
• be able to read papers in journals and to summarise them.
• be able to apply techniques on data sets.
Concepts that are covered:
• Sensitivity Analysis
• Nonlinear Regression
• Nonparametric Regression
• Poisson Regression
• Elemental Regression
• Quantile Regression
• Robust Regression
• Use SAS® and R language for analysis
APPLIED EXTREME VALUE THEORY
Duration: One semester
Credits: 15
Who may take the module: Optional module for the Master programme in Statistics
Prerequisite: Honours in Statistics
Objectives of the module: Student should be able to:
Understand the underlying theory of extreme values as well as to apply the theory of inference within extreme value
contexts.
Understand the primary parameters of interest in extremes and to conduct inference related to these parameters.
Be able to apply inference results on data sets.
Specific subjects:
Underlying principles of extreme value theory.
Statistical aspects to do inference with in the extreme value theory context.
Apply results when analysing data sets.
Use R as computer language to analyse.
SAMPLING TECHNIQUES
Duration: One semester
Credits: 12
Who may take the module: Optional module for Honours and Master’s in Mathematical Statistics and Statistics
Prerequisite: Statistics 318 and 348 or Mathematical Statistics 318 and 344, 354 or 364.
Objectives of the module: 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 nonrespons.
APPLIED TIME SERIES ANALYSIS A and B
Duration: Two semesters
Who may take the modules: Optional module for Honours in Statistics
Credits: 24 (or 2 X 12)
Prerequisite: Statistics 318, 348, Knowledge of Excel and Word in the Windows environment. First semester for second
semester.
Objectives of the module: The purpose of the course is to provide students in applied disciplines the necessary “tools”
to analyze univariate time series data and to a lesser extent multivariate time series data in the time domain. The
emphasis will be on fitting suitable models to data, evaluating the models using numerical and graphical techniques,
and interpreting the results in the context of the original problem, as opposed to derivation of mathematical properties
of the models. However an appreciation of these mathematical properties is required. At the end of this course students
will be able to analyze many kinds of univariate time series data as well simple multivariate time series (involving one
input series and one output series), where causal relationship is assumed, using Splus and SAS.
PRACTICAL FINANCIAL MODELING
Duration: Block module
Who may take the modules: Compulsory block module for Honours in Financial Risk Management
Credits: 12
Prerequisite:
Objectives of the module:
INTRODUCTION TO COMMUNICATION AND CONFLICT MANAGEMENT
Duration: Block module
Who may take the modules: Compulsory module for Honours in Financial Risk Management
Credits: 2
Prerequisite:
Objectives of the module:
ADVANCED SAMPLING TECHNIQUES
Duration: One semester
Who may take the modules: Optional module for Masters in Statistics or Mathematical Statistics
Credits: 15
Prerequisite: Sampling theory
Objectives of the module: 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 and B
Duration: Two semesters
Who may take the modules: Optional module for Masters in Statistics or Mathematical Statistics
Credits: 15 or 30
Prerequisite: Multivariate statistical analysis A and B or Multivariate methods in statistics A and B, programming skills
in S-Plus / R
Objectives of the module: 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.
ADVANCED PORTFOLIO MANAGEMENT THEORY A and B
Duration: Two semesters
Who may take the modules: Optional module for Masters in Financial Risk Management
Credits: 30 (or 2 X 15)
Prerequisite: Portfolio Management theory A and B plus Honours degree.
Objectives of the module:
CREDIT DERIVATIVE INSTRUMENTS A and B
Duration: Two semesters
Who may take the modules: Optional module for Masters in Financial Risk Management
Credits: 30 (or 2 X 15)
Prerequisite:
Objectives of the module:
ADVANCED FINANCIAL RISK MANAGEMENT PROGRAMMING
Duration: One semester
Who may take the modules: Optional module for Masters in Financial Risk Management
Credits: 15
Prerequisite:
Objectives of the module:
FINANCIAL RISK MANAGEMENT PRACTICE
Duration: One semester
Who may take the modules: Optional module for Masters in Financial Risk Management
Credits: 15
Prerequisite:
Objectives of the module: