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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Bayesian Theory (MATH11177)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits10 ECTS Credits5
SummaryThis 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.
Course description 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
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) AND Statistical Methodology (MATH10095)
Prohibited Combinations Other requirements Note that PGT students on School of Mathematics MSc programmes are not required to have taken pre-requisite courses, but they are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.
Course Delivery Information
Academic year 2024/25, Not available to visiting students (SS1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 20, Seminar/Tutorial Hours 5, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 73 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20%, Examination 80%

The final examination, which will be comprehensive, counts for 80% of the course mark. The coursework assessment will be largely based on a few timed exercises focussed on a few specific topics.
Feedback Auto marked quizzes and peer feedback during workshops.
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)Bayesian Theory (MATH11177)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate an understanding of the Bayesian philosophy.
  2. Specify a prior distribution and derive a posterior distribution (up to proportionality).
  3. Derive additional related posterior distributions and quantities algebraically.
  4. Demonstrate an understanding of the theory of Markov Chain Monte Carlo (MCMC) and associated implementation issues.
  5. Use R to perform operations for assessing prior influence and computing posterior distributions for relatively elementary settings.
Reading List
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.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsBTh,statistics,Bayesian,Markov chain Monte Carlo
Course organiserProf Finn Lindgren
Tel: (0131 6)50 5769
Course secretaryMiss Kirstie Paterson
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