Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2025/26
| MATH1000 | Core Mathematics |
| MATH1700 | Probability and Statistics |
Current MATH2715, partly MATH2735, MATH3714
This module is not approved as a discovery module
Statistical models are important in many applications. They contain two main elements: a set of parameters with information of scientific interest and an "error distribution" representing random variation. This module lays the foundations for the analysis of such models. We shall use practical examples from a variety of statistical applications to illustrate the ideas.
This module will introduce students to mathematical techniques for analysing probability distributions and the tools for statistical model building. Students will begin to develop the ability to assess appropriateness of methods and to appreciate different statistical viewpoints.
On successful completion of the module students will have demonstrated the following learning outcomes:
1. Use univariate and bivariate transformations of probability distributions to construct alternative distributions, with particular reference to the normal distribution;
2. Use moment generating functions to derive the classic limit theorems of probability;
3. Understand the principles of statistical modelling, from data collection to model assessment and refinement;
4. Use alternative methods to estimate parameters in a statistical model and derive distributions of the estimators in simple cases;
5. Construct a variety of linear models and select the appropriate model to analyse given data sets;
6. Analyse real data using linear models and interpret the results;
7. Assess whether linear modelling assumptions are met;
8. Describe and apply methods to deal with robustness problems in statistical estimation;
9. Carry out closed-form Bayesian statistical modelling;
10. Use a statistical package to carry out data analysis.
Skills Learning Outcomes
On successful completion of the module, students will have demonstrated the following skills learning outcomes:
a. Understand and communicate efficiently key principles of statistical modelling
b. Use IT skills and appropriate digital technology in work and studies
c. Take a logical and self-reflective approach to problem-solving tasks
d. Use a critical approach in accessing the problems: identify the appropriate method, apply and interpret the results
1. Moments and transformations for univariate probability densities.
2. The normal distribution and its relation to chi-squared, and F distributions.
3. Conditional and marginal distributions for bivariate distributions; bivariate normal distribution.
4. Moment generating functions; law of large numbers; central limit theorem.
5. Estimation; method of moments; least squares; maximum likelihood.
6. Hypothesis testing. Type 1 and Type 2 errors; power; likelihood ratio test.
7. Robustness; median and trimmed mean; transformations to normality.
8. Issues in statistical modelling: data collection; model formulation; model assessment; model diagnostics; model refinement.
9. Simple linear regression - matrix formulation; parameter estimation; confidence and prediction intervals.
10. Fixed effects ANOVA; parameter estimation; use of residuals in diagnostic plots.
11. Multiple linear regression model. Parameter and residual estimation, selection of variables, multicollinearity.
12. Bayesian modelling; interpretation; comparison with frequentist approach.
Additional topics that build on these may be covered as time allows. Further details of possible topics will be delivered closer to the time that the module runs.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Seminar | 5 | 2 | 10 |
| Private study hours | 157 | ||
| Total Contact hours | 43 | ||
| Total hours (100hr per 10 credits) | 200 | ||
Online quizzes (with automated feedback) will be given throughout the course; students will have the opportunity to get additional feedback during the workshops on request.
The reading list is available from the Library website
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team