Module Content - Honours

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 MMS A module is a prerequisite for the MMS B module.

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: Statistical learning is a relatively new area in statistics. It is concerned with modeling and understanding patterns in complex datasets. With to the explosion of "Big Data", there is currently a high demand for individuals with expertise in statistical learning. The methods studied in this module include regularised regression by means of ridge regression and the lasso; classification using linear discriminant analysis, logistic regression, quadratic discriminant analysis and k-nearest neighbors; resampling methods such as k-fold cross-validation, leave-one-out cross-validation and the bootstrap; linear model selection and dimension reduction methods; handling non-linearity via regression splines, smoothing splines, local regression, generalised additive models, bagging, random forests and boosting; and non-linear classification and regression by means of support vector machines. The objectives of the module are to equip students with the following knowledge and skills:

• the theory underlying the above statistical learning techniques;
• application of statistical learning methods in a programming environment;
• assessment and comparison of various models;
• interpretation and effective (written and verbal) communication of results.

We extensively make use of the R programming language, therefore note that the R course is a prerequisite.

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 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 Content - Masters

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 B module.

Statistical Learning Theory A & B (10703-812 & 10704-842)

Objectives and content: The outcomes of these modules can be summarized 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.