Bayesian Statistics, Philosophy and Practice - 2025 entry
MODULE TITLE | Bayesian Statistics, Philosophy and Practice | CREDIT VALUE | 15 |
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MODULE CODE | MTHM047 | MODULE CONVENER | Dr James Salter (Coordinator) |
DURATION: TERM | 1 | 2 | 3 |
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DURATION: WEEKS | 11 |
Number of Students Taking Module (anticipated) | 28 |
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Since the 1980s, computational advances and novel algorithms have seen Bayesian methods explode in popularity, today underpinning modern techniques in data science and machine learning with applications across science, social science, the humanities and finance.
This module will introduce Bayesian statistical inference, describing the differences between it and classical approaches to statistics. It will develop Bayesian methods for data analysis and introduce Bayesian simulation-based techniques for inference. As well as underpinning a philosophical understanding of Bayesian reasoning with theory, we fit a range of models using modern software currently used for Bayesian inference, ensuring the student is equipped to use Bayesian methods in future jobs aligned to data analysis whilst being ready to study Masters and PhD level courses with Bayesian content and to take Bayesian research projects.
Prerequisite modules: MTH1004 and MTH2006 or equivalent mathematics modules covering introduction to probability theory, likelihood inference and regression.
This module will cover the Bayesian approach to modelling, data analysis and statistical inference. The module describes the underpinning philosophies behind the Bayesian approach, looking at subjective probability theory, the notion and handling of prior knowledge, and posterior inference. We then explore simulation-based inference in Bayesian analyses and develop important algorithms for Bayesian simulation by Markov Chain Monte Carlo (MCMC) such as the Gibbs sampler and the Metropolis-Hastings algorithm. Finally, we’ll use the techniques developed through the module to perform parameter estimation and inference for a range of simple and then more complex hierarchical models.
At M-level, in addition to the above, students are introduced to topics in Bayesian approximation such as Laplace approximation and variational inference via material for self-study.
On successful completion of this module you should be able to:
Module Specific Skills and Knowledge
1. Show understanding of the subjective approach to probabilistic reasoning.
2. Demonstrate an awareness of Bayesian approaches to statistical modelling and inference and an ability to apply them in practice.
3. Demonstrate understanding of the value of simulation-based inference and knowledge of techniques such as MCMC and the theories underpinning them
4. Demonstrate the ability to to fit a range of models in a Bayesian framework.
5. Utilise appropriate software and a suitable computer language for Bayesian modelling and inference from data.
Discipline Specific Skills and Knowledge
6. Demonstrate understanding, appreciation of and aptitude in the quantification of uncertainty using advanced mathematical modelling.
Personal and Key Transferable / Employment Skills and Knowledge
7. Show advanced Bayesian data analysis skills and be able to communicate associated reasoning and interpretations effectively in writing;
8. Apply relevant computer software competently;
9. Use learning resources appropriately;
10. Exemplify self-management and time-management skills.
Introduction: Bayesian vs Classical statistics, Nature of probability and uncertainty.
Bayesian inference: Bayes Theorem, Conjugate priors, Objective priors, Subjective priors, Prior and Posterior predictive distributions, Prior elicitation, Posterior summaries and simulation, Normal approximation. .
Bayesian Computation: Monte Carlo, Inverse CDF, Rejection Sampling, Markov Chain Monte Carlo (MCMC), Gibbs sampling, Metropolis Hastings, Hamiltonian Monte Carlo, Diagnostics.
Modelling: Conjugate models, measurement models, Bayesian regression, Bayesian hierarchical models, Generalised Linear Models.
Bayesian Approximation: (Topics from) MAP estimation, Laplace approximation, Mixture approximations, Variational Inference.
Scheduled Learning & Teaching Activities | 33 | Guided Independent Study | 117 | Placement / Study Abroad | 0 |
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Category |
Hours of study time |
Description |
Scheduled learning and teaching activities |
33 |
Lectures/practical classes |
Guided independent study |
33 |
Post lecture study and reading |
Guided independent study |
40 |
Formative and summative coursework preparation and attempting un-assessed problems |
Guided independent study |
44 |
Exam revision/preparation |
Form of Assessment |
Size of Assessment (e.g. duration/length) |
ILOs Assessed |
Feedback Method |
---|---|---|---|
Un-assessed practical and theoretical exercises |
11 hours (1 hour each week) |
All |
Verbal, in class and written on script. |
Coursework | 20 | Written Exams | 80 | Practical Exams | 0 |
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Form of Assessment |
% of Credit |
Size of Assessment (e.g. duration/length) |
ILOs Assessed |
Feedback Method |
---|---|---|---|---|
Written Exam |
80 |
2 Hours |
1-7, 9, 10 |
Verbal on specific request |
Practical and theoretical exercises |
20 |
15 Hours |
All |
Written feedback on script and oral feedback in office hour |
Original Form of Assessment |
Form of Re-assessment |
ILOs Re-assessed |
Time Scale for Re-assessment |
---|---|---|---|
Written Exam |
Written Exam (2 hours, 80%) |
1-7, 9, 10 |
Referral/deferral period |
Practical and theoretical exercises |
Practical and theoretical exercises (15 hours, 20%) |
All |
Referral/deferral period |
Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.
Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 50%.
information that you are expected to consult. Further guidance will be provided by the Module Convener
Other resources:
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Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A. and Rubin, D., Bayesian data analysis, 3rd, CRC, 2008.
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Lindley, Dennis V., Making Decisions, 2nd Edition, John Wiley & Sons, 1991, 9780471908081.
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Sivia, Devinderjit, Data Analysis: A Bayesian Tutorial, 2nd Edition, Oxford University Press, 2006, 9780198568322.
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DeGroot, M.H., Optimal Statistical Decisions, WCL Ed edition, Wiley-Blackwell, 2004, 9780471680291.
Reading list for this module:
Type | Author | Title | Edition | Publisher | Year | ISBN |
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Set | Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A. and Rubin, D. | Bayesian data analysis | 3rd | CRC | 2008 | |
Set | Lindley, Dennis V. | Making Decisions | 2nd Edition | John Wiley & Sons | 1991 | 9780471908081 |
Set | Sivia, Devinderjit | Data Analysis: A Bayesian Tutorial | 2nd Edition | Oxford University Press | 2006 | 9780198568322 |
Set | DeGroot, M.H. | Optimal Statistical Decisions | WCL Ed edition | Wiley-Blackwell | 2004 | 9780471680291 |
CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
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PRE-REQUISITE MODULES | MTH1004, MTH2006 |
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CO-REQUISITE MODULES |
NQF LEVEL (FHEQ) | 7 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Tuesday 12th March 2024 | LAST REVISION DATE | Tuesday 18th March 2025 |
KEY WORDS SEARCH | Bayesian; Bayes; Statistics; Data, Big Data; Analysis; Decision theory; Inference; Mathematics; Probability; Data Science; Artificial Intelligence |
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Please note that all modules are subject to change, please get in touch if you have any questions about this module.