## Advanced Bayesian Methods (Level M) STATS5013

• Academic Session: 2023-24
• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 5 (SCQF level 11)
• Typically Offered: Semester 1
• Available to Visiting Students: Yes

### Short Description

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

### Timetable

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

### Assessment

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.