Module manager: Matthew Aldridge
Email: m.aldridge@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
None
| MATH2701 | Statistical Methods |
MATH5825M Statistical Computing
This module is not approved as an Elective
Statistical computing is the branch of mathematics that involves solving statistical problems by combining human ingenuity with the immense calculating power of computers to go beyond what would be possible with pencil and paper alone. A key concept is simulation: using randomness to repeatedly run a mathematical model, and to make use of those repeated samples within statistical estimation algorithms.
The module aims to equip students with understanding and skills in pseudo-random number generation methods and tools that depend on being able to generate pseudo-random numbers. Particular emphasis will be placed on Monte Carlo methods for numerical integration; bootstrap methods, and Markov chain Monte Carlo as a tool for sampling from posterior distributions. Methods will be studied both theoretically and through practical application using appropriate programming tools.
Subject specific learning outcomes:
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
Understand the importance of simulation.
Understand and be able to apply Monte Carlo methods to statistical estimation, including importance sampling.
Understand methods for random number generation, and be able to generate random variates using methods including rejection sampling.
Understand and be able to implement Markov chain Monte Carlo (MCMC), and appreciate its use in Bayesian inference.
Understand and be able to apply resampling methods, including the bootstrap, to statistical estimation.
Be able to implement statistical computing algorithms in an appropriate programming language.
Skills learning outcomes:
On successful completion of the module students will have demonstrated the following skills learning outcomes:
Make a critical assessment of varied data sets
Follow a logical approach for selecting and performing an analysis
Use IT skills and appropriate digital technology in work and studies
Reflect on statistical findings and draw relevant conclusions in academic and practical contexts
Communicate statistical processes and findings effectively
Monte Carlo estimation: Definition, examples, and error analysis. Variance reduction methods, including importance sampling.
Random number generation: Methods including the inverse transform method and rejection sampling.
MCMC: Markov chain Monte Carlo using the Metropolis–Hastings algorithm and, in particular, the random walk Metropolis algorithm, in discrete and continuous space. Application to Bayesian statistics.
Resampling methods: Empirical distribution; plug-in estimation. Estimation using the bootstrap.
Implementation of these methods using R.
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.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Practical | 1 | 2 | 2 |
| Private study hours | 115 | ||
| Total Contact hours | 35 | ||
| Total hours (100hr per 10 credits) | 150 | ||
115
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
Errors, omissions, failed links etc should be notified to the Catalogue Team