Bayesian Data Analysis: Theory, Applications and Computational Methods (Distance Learning)
| Code | School | Level | Credits | Semesters |
| MATH4076 | Mathematical Sciences | 4 | 20 | Spring UK |
- Code
- MATH4076
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Spring UK
Summary
This course is concerned with the second main theory of statistical inference, Bayesian inference. This module complements the frequentist statistical approach introduced in Statistical Inference. The three basic ingredients of Bayesian inference are a prior distribution, a likelihood and a posterior distribution, which are linked by Bayes' theorem. Statistical inference is determined solely by the posterior distribution. This module will provide a full description of Bayesian analysis and cover popular models, such as the normal distribution and inference for categorical data. Topics include prior elicitation, conjugate models, marginal and predictive inference, hierarchical models and model choice. Well known classical procedures, such as point estimation and confidence intervals, will be compared with their Bayesian counterparts.
The increase in speed and memory capacity of modern computers has dramatically changed their use and applicability for complex statistical analysis, especially for Bayesian inference. This course will explore how computers allow the easy implementation of standard, but computationally intensive, statistical methods such as Markov chain Monte Carlo methods to obtain samples from a posterior distribution. Students will gain experience of linking the underlying statistical concepts to practical applications of the methodology. Students will gain experience of using statistical software and interpreting its output.
Target Students
Available to MSc Statistics Science (Distance Learning) students.
Classes
- One 1-hour tutorial each week for 10 weeks
- One 1-hour computing each week for 10 weeks
This module is designed for distance learning programmes where delivery of material will largely be asynchronous through course notes support by lecture videos, Moodle quizzes and exercises. The tutorial will be used to support and reinforce the asynchronous learning. The computer software learning will be through specially designed workbooks with support sessions through online computer labs.
Assessment
- 20% Project: Project to assess implementation of MCMC to a real-life application and the ability to interpret the output. (12 pages)
- 80% Exam 1 (3-hour): Written exam to assess statistical knowledge and understanding including aspects of computational methods.
Assessed by end of spring semester
Educational Aims
The purpose of this course is to introduce students to Bayesian inference to complement the frequentist inference presented in Statistical Inference. The course will develop students understanding of the key concepts of Bayesian inference, the likelihood and the prior, and an appreciation of computational methods, such as Markov chain Monte Carlo (MCMC), in implementing Bayesian methods to all but the simplest of models. The course will highlight the importance of full integration of statistical theory and computational methods.Learning Outcomes
A student who completes this course successfully will be able to:
- L1 - state, derive and apply results underlying Bayesian inference.
- L2 - perform standard Bayesian calculations in various single-parameter and simple multi-parameter problems.
- L3 - compare and contrast the frequentist and Bayesian approaches to inference.
- L4 - compare competing models in a Bayesian setting.
- L5 - derive, calculate and explain properties of Markov chain Monte Carlo (MCMC).
- L6 - apply computational methods, such as MCMC, to a range of appropriate examples.
- L7 - use of statistical software to perform analyses concerned with statistical inference.
- L8 - explain and interpret statistical results in the context of computational statistics.