Please note: there may be some adjustments to the teaching arrangements published in the course catalogue for 2020-21. Given current circumstances related to the Covid-19 pandemic it is anticipated that some usual arrangements for teaching on campus will be modified to ensure the safety and wellbeing of students and staff on campus; further adjustments may also be necessary, or beneficial, during the course of the academic year as national requirements relating to management of the pandemic are revised.

Bayesian Statistics (Level M) STATS5014

  • Academic Session: 2021-22
  • School: School of Mathematics and Statistics
  • Credits: 10
  • Level: Level 5 (SCQF level 11)
  • Typically Offered: Semester 2
  • Available to Visiting Students: Yes
  • Available to Erasmus Students: Yes

Short Description

This course introduces methods of modern Bayesian inference, with an emphasis on practical issues and applications.

Timetable

16 lectures (1 or 2 each week)

4 1-hour tutorials

5, 2-hour computer-based practicals

Requirements of Entry

Some optional courses may be constrained by space and entry to these is not guaranteed unless you are in a programme for which this is a compulsory course.

Excluded Courses

STATS4041 Bayesian Statistics

Assessment

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

Main Assessment In: April/May

Course Aims

■ To develop the foundations of modern Bayesian statistics;

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

■ to formulate, analyse and interpret hierarchical models, fitting them using either WinBUGS, Stan, or R;

■ to demonstrate how decision making is performed in Bayesian framework.

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, but not exclusively, 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 different approaches to the choice of prior distribution;

■ Explain the role of hyperparameters in Bayesian inference, introduce them appropriately into statistical models and use the empirical Bayes approach for their determination;

■ Explain the use of independent simulation techniques for posterior sampling and apply them in simple contexts using R;

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

■ Describe and apply simple checks of mixing, and explain when mixing is likely to be poor;

■ Explain the role of decision theory in Bayesian analysis, formulate the decision process mathematically, and prove simple results.

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.