Advanced Bayesian Methods (Level M) STATS5013
- Academic Session: 2022-23
- School: School of Mathematics and Statistics
- Credits: 10
- Level: Level 5 (SCQF level 11)
- Typically Offered: Semester 1
- Available to Visiting Students: Yes
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
STATS4038 Advanced Bayesian Methods
90 - minute, end of course examination (85%)
Main Assessment In: April/May
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.