# Data Analytics for Government MSc/PgDip/PgCert: Online distance learning

## Uncertainty Assessment and Bayesian Computation (ODL) STATS5084

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 5 (SCQF level 11)
• Typically Offered: Semester 1
• Available to Visiting 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.

### Excluded Courses

Bayesian Statistics

Bayesian Statistics (Level M)

-/-

### Assessment

100% Continuous Assessment

This will typically be made up of a project, assessed in terms of code and a report (40%) and three homework exercises, including online quizzes  (60%). Full details are provided in the programme handbook.

### 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.