This module runs in Term 1 and will provide students with the tools for advanced statistical modelling and associated estimation procedures based on computer-intensive methods known as Monte Carlo techniques.
Pre-requisites:
Statistics Students: ST218 Mathematical Statistics A AND ST219 Mathematical Statistics B
Non-Statistics Students: ST220 Introduction to Mathematical Statistics
When modelling real world phenomena statisticians are often confronted with the following dilemma: should we choose a standard model that is easy to compute with or use a more realistic model that is not amenable to analytic computations such as determining means and p-values. We are faced with such choice in a vast variety of application areas, some of which we will encounter in this module. These include financial models, genetics, polymer simulation, target tracking, statistical image analysis and missing data problems. With the advent of modern computer technology we are no longer restricted to standard models as we can use simulation-based inference. Essentially we replace analytic computation with sampling of probability models and statistical estimation. In this module we discuss a variety of such methods, their advantages, disadvantages, strengths and pitfalls.
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Introduction and Examples: The need for Monte Carlo Techniques; history; example applications.
Basic Simulation Principles: Rejection method; variance reduction; importance sampling.
Markov chain theory: convergence of Markov chains; detailed balance; limit theorems.
Basic MCMC algorithms: Metropolis-Hastings algorithm; Gibbs sampling.
Implementational issues: Burn In; Convergence diagnostics, Monte Carlo error.
More advanced algorithms: Auxiliary variable methods; simulated and parallel tempering; simulated annealing; reversible jump MCMC; Metropolis-adjusted Langevin algorithms.
By the end of the module, students should be able to:
View reading list on Talis Aspire
TBC
TBC
| Type | Required | Optional |
|---|---|---|
| Lectures | 30 sessions of 1 hour (20%) | 2 sessions of 1 hour |
| Practical classes | 10 sessions of 1 hour (7%) | |
| Private study | 110 hours (73%) | |
| Total | 150 hours |
Weekly revision of lecture notes and materials, wider reading, practice exercises and preparing for the examination.
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Assignment 2 | 10% | Yes (extension) | |
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The assignment will contain a number of questions for which solutions and / or written responses will be required. |
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| Assignment 1 | 10% | Yes (extension) | |
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The assignment will contain a number of questions for which solutions and / or written responses will be required. |
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| In-person Examination | 80% | No | |
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The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.
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| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination - Resit | 100% | No | |
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The examination paper will contain four questions, of which the best marks of THREE questions will be used to calculate your grade.
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Marked assignments will be available for viewing at the support office within 20 working days of the submission deadline. Cohort level feedback and solutions will be provided.
Solutions and cohort level feedback will be provided for the examination.
This module is Optional for:
This module is Option list A for:
This module is Option list B for:
This module is Option list D for:
This module is Option list E for: