# Modules

### MAS8384 : Bayesian Methodology

• Offered for Year: 2019/20
• Module Leader(s): Dr Sarah Heaps
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 2 Credit Value: 10 ECTS Credits: 5.0

#### Aims

Bayesian inference provides an ideal approach for synthesizing information from different sources in a coherent way. In recent years great advances have been made in the application of Bayesian statistical inference to problems across a wide variety of areas within industry, such as drug development, voice recognition and credit card fraud detection. This has been made possible by the development of computational algorithms which allow posterior distributions to be found in complicated models. This module starts with an introduction to the principles of Bayesian inference before moving on to address the fundamental practical problem of calculating the posterior distribution for complex models. The theory behind some modern Bayesian computational methods, which provide a simulation-based solution, is developed and put into practice using R.

Specifically, the module aims to equip students with the following knowledge and skills:
- To gain an understanding of the principles of the Bayesian approach to inference and experience in the application of Bayes rule to update a prior distribution to a posterior distribution using a likelihood function.
- To gain an understanding of the theory behind some modern Bayesian computational methods for approximating a posterior distribution and practical experience of their application in R to solve a variety of applied problems.

#### Outline Of Syllabus

- Conjugate Bayesian inference
- Non-conjugate models
- Markov chain Monte Carlo (MCMC): methods such as Gibbs sampling, Metropolis-Hastings sampling, slice sampling; assessment of mixing and convergence
- Posterior summaries
- Applications, such as linear models, generalized linear models, mixture models, hidden Markov models, dynamic linear models, Gaussian process regression
- Computation using R and R packages such as rjags

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion10:300:30Oral Examination
Guided Independent StudyAssessment preparation and completion50:302:30Preparation for oral examination
Guided Independent StudyAssessment preparation and completion151:0015:00Completing Practical Reports
Scheduled Learning And Teaching ActivitiesLecture122:0024:00Lectures
Scheduled Learning And Teaching ActivitiesPractical62:0012:00Practical Sessions
Guided Independent StudyProject work211:0021:00Completing Project
Guided Independent StudyIndependent study91:009:00Lecture follow-up (working through lecture notes)
Total100:00
##### Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Practicals are used both for solution of problems and work requiring extensive computation and to give insight into the ideas/methods studied; they are also used to discuss the course material, identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. The project allows the students to develop their problem solving techniques and practise the methods learnt in the module.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Other Assessment
Description Semester When Set Percentage Comment
Practical/lab report2M45Up to 3, equally weighted, practical reports (15% each) 1000 words per report
Report2M55Project report (up to 1500 words)
##### Zero Weighted Pass/Fail Assessments
Description When Set Comment
Oral PresentationMA structured discussion including a software demonstration and reflection on the key learning objectives of the coursework project
##### Assessment Rationale And Relationship

Written assignments (3 pieces of work of equal weight) followed by a larger piece of project work allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback.

The semi-structured oral examination facilitates a reflective discussion about how individual students have met the learning objectives of the module and how the principles of fundamental statistics are embedded in the functionality of their project work.