# Statistics BSc/MSci

## Bayesian Statistics STATS4041

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 4 (SCQF level 10)
• Typically Offered: Semester 2
• Available to Visiting Students: Yes

### Short Description

This is an Honours-level course introducing methods of modern Bayesian inference, with an emphasis on practical issues and applications.

### Timetable

15 lectures (1 or 2 each week)

4 tutorials

5, 2-hour computer-based practical sessions

### Excluded Courses

STATS5014 Bayesian Statistics (Level M)

### Assessment

90-minute, end-of-course examination (100%)

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? Not applicable for Honours courses

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

### Course Aims

■ To introduce students to the main ideas of modern Bayesian statistics;

■ to demonstrate how prior distributions are updated to posterior distributions in simple statistical models;

■ to illustrate the formulation and analysis of hierarchical models in either WinBUGS, Stan, or R.

### Intended Learning Outcomes of Course

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

■ Describe the rules for updating prior distributions in the presence of data, and for calculating posterior predictive distributions;

■ Derive posterior distributions corresponding to simple low-dimensional statistical models, typically with conjugate priors;

■ Describe and compute various summaries of the posterior distribution, including posterior mean, MAP estimate, posterior standard deviation and credible regions (including HPDRs) and the predictive distribution;

■ Explain the choice of prior distribution;

■ Explain the role of hyperparameters in Bayesian inference and introduce them appropriately into statistical models;

■ Use the empirical Bayes approach for the determination of hyperparameters;

■ Explain the use of independent simulation techniques for posterior sampling;

■ Formulate and analyse simple hierarchical models using Gibbs sampling in either WinBUGS, Stan, or R.

### 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.