Uncertainty Assessment and Bayesian Computation (ODL) STATS5084

  • 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: No
  • Available to Erasmus Students: No
  • Taught Wholly by Distance Learning: Yes

Short Description

This course introduces students to the Bayesian paradigm and different approaches to posterior inference.

Timetable

The course mostly consists of asynchronous content.

Requirements of Entry

The course is only available to students on the online MSc in Data Analytics.

Excluded Courses

Bayesian Statistics

Bayesian Statistics (Level M)

Advanced Bayesian Methods

Advanced Bayesian Methods (Level M)

Co-requisites

-/-

Assessment

100% Continuous Assessment

Project work is assessed by a report as well as an oral assessment and/or video presentation.

Course Aims

The aims of this course are:

■ to develop the foundations of modern Bayesian statistics;

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

■ to introduce students to advanced stochastic simulation methods such as Markov-Chain Monte Carlo;

■ to illustrate how to fit Bayesian models using high-level software for Bayesian hierarchical modelling such as BUGS or STAN as well as implementing stochastic simulation methods such as Markov Chain Monte Carlo (MCMC).

■ to set out how different models can be compared in a Bayesian setting.

Intended Learning Outcomes of Course

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

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

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

■ 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;

■ Perform inference in Bayesian models using high-level software such BUGS or STAN as well as implementing Gibbs sampling and the Metropolis-Hastings algorithm in R;

■ Apply diagnostic procedures to check convergence and mixing of MCMC methods

■ Implement Bayesian approaches to model selection.

■ Describe alternative approaches to Bayesian computation such as variational inference and explain their use in simple examples.

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.