Overview

Preface

These lecture notes are produced for the University of Leeds module MATH3701 - Statistical Modelling for the academic year 2026-27. They draw on material from several sources, and I am grateful to previous contributors whose work has informed these notes.

This is the first year this module will run. There are likely to be some mistakes in the materials, and I appreciate corrections. Please email me or let me know in lectures if you believe you have spotted an error.

RP Mann, Leeds, 2026


Generative AI usage within this module

For the module exam you will not be able to use Generative AI. It is therefore important that you understand the module material thoroughly and are able to complete the exercises in the notes without the assistance of AI. You may use AI to assist in your learning, but the only way to be sure you are prepared for the exam is to complete exercises under exam conditions: no AI and no internet access.

For the coursework component of the assessment you may use AI to check the spelling and grammar of your report. AI should not be the author of your report. That means you should not use AI to directly create the report text. You should not use AI to perform mathematical or computational analyses. It is essential that you understand everything you have written that is submitted.

If you have used Gen AI to prepare or produce part or all of your submitted work, you must acknowledge your use of AI. As an example: in creating the materials for this module Gen AI (Claude Sonnet/Opus) has been used to (i) check written notes and exercises for consistency and correctness; (ii) draft lecture slides based on the written notes; and (iii) generate proofs for non-examinable supplementary material.


Warning

Statistical ethics and sensitive data
Please note that from time to time we will be using data sets from situations which some might perceive as sensitive. All such data sets will, however, be derived from real-world studies which appear in textbooks or in scientific journals. The daily work of many statisticians involves applying their professional skills in a wide variety of situations and as such it is important to include a range of commonly encountered examples in this module. Whenever possible, sensitive topics will be signposted in advance. If you feel that any examples may be personally upsetting then, if possible, please contact the module lecturer in advance. If you are significantly affected by any of these situations, then you can seek support from the Student Counselling and Wellbeing service.


Official Module Description

Module summary

Statistical models allow us to understand complex data and make principled predictions. This module develops three powerful and widely-used classes of model. Generalised linear models extend ordinary linear regression to handle non-normal responses such as counts and proportions. Generalised additive models relax the linearity assumption, allowing flexible non-parametric smoothing whilst retaining interpretability. Survival analysis addresses data where the response is a time-to-event, subject to censoring, and develops both parametric and semi-parametric approaches including the Cox proportional hazards model.

Learning outcomes

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. understand the use of 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. interpret a fitted generalised additive model;
  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 explanatory variables 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.

Syllabus

Part I (Generalised Linear Models): Normal linear models (revision); exponential family distributions; GLM structure and link functions; maximum likelihood estimation and IRLS; model deviance and residuals; logistic regression; log-linear models.

Part II (Generalised Additive Models): Limitations of parametric models; splines; interpolating and smoothing splines; cross-validation and effective degrees of freedom; generalised additive models.

Part III (Survival Analysis): Survival and hazard functions; censoring; Kaplan-Meier estimation; parametric survival distributions; maximum likelihood with censored data; proportional hazards models; the Cox model; model diagnostics and selection.