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## ST3BDA-Bayesian Data Analysis

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Spring term module
Pre-requisites: MA2PT1 Probability Theory I or ST2PST Probability and Statistical Theory
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Module version for: 2017/8

Module Convenor: Dr Richard Everitt

Summary module description:
Bayesian methods are not new, but it is only relatively recent developments in computational methods such as Markov Chain Monte Carlo (MCMC), that has led to the methods becoming a practical possibility for a wide range of statistical models. This module covers the Bayesian philosophy of combining prior information with current data, Bayesian data analysis for general and generalised linear models as well as simple hierarchical models, and the computational methods that underpin the whole approach.

Aims:
• to introduce students to the Bayesian framework for statistical inference;
• to provide students with an understanding of how computational methods are used to solve problems in Bayesian inference;
• to give students practical skills in carrying out Bayesian inference using the statistical software package WinBUGS;
• to show how models that students have seen in other modules (linear models, generalised linear models and simple hierarchical models) can be fitted within a Bayesian framework, explore reasons for doing this and similarities/differences between the inferences;
• to show the potential of Bayesian methods for solving problems that might be difficult to solve in other frameworks.

Assessable learning outcomes:
On completion of this module students should:
• derive explicit posterior distributions for simple one or two parameter problems: conjugate, non-informative and informative priors;
• understand the principles of modern computational methods for Bayesian inference;
• be able to derive posterior distributions up to a constant of proportionality and use R to simulate from these distributions and summarise results appropriately;
• formulate Bayesian models and use WinBUGs to fit these models and check for convergence, and be able to interpret results;
• describe differences/similarities between classical and Bayesian approaches, how Bayesian methods can be used to solve real-life problems and the issues surrounding the use of Bayesian methods.

Additional outcomes:

Outline content:
Bayesian inference: likelihood, prior and posterior distributions, the use of Bayes’ theorem and posterior summaries, explicit derivations of simple one or two parameter problems with conjugate non-informative and informative priors.
Computational methods for more complex problems or those with non-conjugate priors: Simulation, Gibbs sampling, MCMC, Metropolis Hastings
Introduction to using WinBUGS
Bayesian analysis of linear models and generalised linear models
Hierarchical models

Brief description of teaching and learning methods:
Lectures supported by problem sheets and practicals.

Contact hours:
 Autumn Spring Summer Lectures 15 Practicals classes and workshops 5 Guided independent study 80 Total hours by term 100.00 Total hours for module 100.00

Summative Assessment Methods:
 Method Percentage Written exam 80 Set exercise 20

Other information on summative assessment:
One assignment and one examination.

Formative assessment methods:
Problem sheets and practicals.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Length of examination:
Two hours

Requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:
One examination paper of 2 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (80% exam, 20% coursework).

Additional Costs (specified where applicable):
1) Required text books:
2) Specialist equipment or materials:
3) Specialist clothing, footwear or headgear:
4) Printing and binding:
5) Computers and devices with a particular specification:
6) Travel, accommodation and subsistence:

Last updated: 24 April 2017