Module manager: TBC
Email: TBC
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
None
| MATH2701 | Statistical Methods |
| MATH3823 | Generalised Linear Models |
| MATH5824M | Generalised Linear and Additive Models |
MATH2775; MATH3823; MATH5824M
This module is not approved as an Elective
Statistical modelling allows us to infer relationships between predictor variables and responses, for example to understand the factors that are associated with disease. Linear regression models are an enormously useful tool for such modelling but only appropriate for a limited range of data types. Other forms of data require varying approaches. This module covers several models for more complex data. Generalised Linear Models and Generalised Additive Models extend linear regression, allowing us to incorporate categorical and continuous predictors and outcomes from a variety of statistical distributions. Survival analysis models survival times: how long it takes for a certain event to occur, such as the death of a patient after onset of a disease. The appropriate statistical methods to analyse and model survival data are of critical importance in medical studies and actuarial work, as well as in other settings.
This module will teach students mathematical techniques for statistically modelling a variety of different complex data. Students will learn about the limitations of linear regression and the motivation for more general models. They will be introduced to the Exponential Family of distributions and learn how common probability distributions such as the Binomial and Poisson distributions fit into this family. This module will introduce the standard structure and mathematical formalism of Generalised Linear Models. Students will learn about splines and their use in Generalised Additive Models. This module will introduce survival data and appropriate models for its analysis. Students will learn how to select appropriate models for a given data set based on data characteristics and data fit.
On successful completion of the module students will be able to: 1. Carry out regression analysis with generalised linear models including the use of link functions; 2. Use deviance in model selection; 3. Appreciate the problems caused by overdispersion; 4. Fit and interpret the special cases of log linear models and logistic regression; 5. Compare methods for scatterplot smoothing suitable for use in a generalised additive model; 6. Fit and interpret generalised additive models; 7. Describe the characteristic features of survival data including censoring; 8. Use a range of parametric and semi-parametric regression models to assess the effects of covariates on a survival distribution; and 9. Use a statistical package with real data to fit these models to data and to write a report giving and interpreting the results.
1. Exponential family random variables; 2. Matrix formulation for linear models; 3. Generalised linear model, including probit, logistic, and log-linear models; 4. Selection of significant covariates; 5. Scatterplot smoothers; 6. Generalised additive model; 7. The nature of survival data; censoring mechanisms. 8. Functions used to describe survival distributions; 9. The Cox proportional hazards model Additional topics that build on these may be covered as time allows. Such topics may be drawn from the following, or similar: cross-validation; information criteria for model selection; model adequacy and diagnostics; additional models for survival data
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lectures | 44 | 1 | 44 |
| Practicals | 1 | 2 | 2 |
| Private study hours | 154 | ||
| Total Contact hours | 46 | ||
| Total hours (100hr per 10 credits) | 200 | ||
Formative feedback will be provided on regular example sets or other similar learning activity.
Check the module area in Minerva for your reading list
Last updated: 30/04/2026
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