Please note: there may be some adjustments to the teaching arrangements published in the course catalogue for 2020-21. Given current circumstances related to the Covid-19 pandemic it is anticipated that some usual arrangements for teaching on campus will be modified to ensure the safety and wellbeing of students and staff on campus; further adjustments may also be necessary, or beneficial, during the course of the academic year as national requirements relating to management of the pandemic are revised.

Advanced Bayesian Methods (Level M) STATS5013

  • Academic Session: 2021-22
  • School: School of Mathematics and Statistics
  • Credits: 10
  • Level: Level 5 (SCQF level 11)
  • Typically Offered: Semester 1
  • Available to Visiting Students: Yes
  • Available to Erasmus Students: Yes

Short Description

This course develops advanced topics in modern Bayesian statistics, including both the underlying theory and related practical issues.


20 lectures (typically 2 each week for 10 weeks of Semester 1)

4 1-hour tutorials

2 2-hour computer-based practicals

Requirements of Entry

STATS4041/STATS5014 Bayesian Statistics [Level M] or STATS4024/STATS5026 Stochastic Processes [Level M]

Excluded Courses

STATS4038 Advanced Bayesian Methods


90 - minute, end of course examination (85%)

Project (15%)

Main Assessment In: April/May

Course Aims

To introduce students to advanced stochastic simulation methods such as Markov-Chain Monte Carlo in a Bayesian context;

to illustrate the practical issues of application of such methods, with real data examples;

to discuss Bayesian approaches to model selection, model criticism and model mixing;

to give students the opportunity to read further into one topic related to the course.

Intended Learning Outcomes of Course

By the end of this course students will be able to:

■ Illustrate the use of Monte Carlo methods, including importance sampling;

■ Explain the operation and basic theory of the two main Markov-Chain Monte-Carlo methods, Gibbs sampling and the Metropolis-Hastings algorithm;

■ Derive the full conditional distributions for parameters in simple low-dimensional problems;

■ Implement Gibbs sampling and the Metropolis-Hastings algorithm in R;

■ Apply diagnostic procedures to check convergence and mixing of MCMC methods

■ Describe Bayesian approaches to model selection;

■ Calculate Bayes' factors for simple model comparisons;

■ Explain MCMC approaches to model selection and model mixing;

■ Describe posterior predictive checks as a means of model criticism;

■ Carry out a full Bayesian data analysis of a real data set by implementing MCMC methods and write a report to summarise their analysis and conclusions.

Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.