Advanced Bayesian Methods (Level M) STATS5013

  • Academic Session: 2018-19
  • 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.

Timetable

20 lectures (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 (65%)

Project (15%)

Coursework tasks (20%)

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;

■ Read further into one topic related to the course and write an essay to summarise what they have learnt.

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.