Postgraduate Course: Bayesian Theory (MATH11177)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Not available to visiting students
|Summary||This course will provide the underlying theory for Bayesian statistics. Students will understand the role of the prior distribution and be able to formulate a posterior distribution (up to proportionality). They will also be exposed to the ideas of summarising posterior distributions and associated statistics. The underlying theory of Markov chain Monte Carlo will be introduced (Metropolis-Hastings and Gibbs sampler) with associated issues of implementation.
1. Bayes theorem (discrete and continuous)
2. Prior specification
3. Posterior distribution and associated summary statistics (point and interval)
4. Predictive distributions
5. Hypothesis testing (simple and composite hypotheses)
6. Monte Carlo integration
7. Markov chain Monte Carlo (MCMC): Metropolis-Hastings (MH) and Gibbs sampler
Course Delivery Information
|Academic year 2023/24, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Seminar/Tutorial Hours 5,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 15%, Examination 85%
The final examination, which will be comprehensive, counts for 85% of the course mark. The coursework assessment will be largely based on a few timed exercises focussed on a few specific topics.
||Auto marked quizzes and peer feedback during workshops.
||Hours & Minutes
|Main Exam Diet S1 (December)||Bayesian Theory (MATH11177)||2:00|
On completion of this course, the student will be able to:
- Demonstrate an understanding of the Bayesian philosophy.
- Specify a prior distribution and derive a posterior distribution (up to proportionality).
- Derive additional related posterior distributions and quantities algebraically.
- Demonstrate an understanding of the theory of Markov Chain Monte Carlo (MCMC) and associated implementation issues.
- Use R to perform operations for assessing prior influence and computing posterior distributions for relatively elementary settings.
|Bayesian Statistical Methods, Reich and Ghosh. (2019) CRC Press. |
Applied Bayesian Statistics, With R and OpenBUGS Examples, M. Cowles. (2013) Springer.
Bayesian Methods for Data Analysis, 3rd Ed. Carlin and Louis. (2009) CRC Press.
Bayesian Data Analysis, 3rd Ed. Gelman, Carlin, Stern, Dunson, Vehtari, and Rubin. (2013) CRC Press.
Markov chain Monte Carlo: Stochastic simulation for Bayesian Inference, 2nd Ed. Gamerman and Lopes. (2006) CRC Press.
|Graduate Attributes and Skills
|Keywords||BTh,statistics,Bayesian,Markov chain Monte Carlo
|Course organiser||Prof Finn Lindgren
Tel: (0131 6)50 5769
|Course secretary||Miss Gemma Aitchison
Tel: (0131 6)50 9268