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# Bayesian Statistics - MAT00003H

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• Department: Mathematics
• Module co-ordinator: Dr. Agostino Nobile
• Credit value: 10 credits
• Credit level: H
• Academic year of delivery: 2022-23
• See module specification for other years: 2021-22

## Related modules

• None

### Additional information

Pre-requisites for Natural Sciences students: must have taken Statistics Option MAT00033I.

## Module will run

Occurrence Teaching period
A Autumn Term 2022-23

## Module aims

• To introduce the basic notions of Bayesian statistics, showing how Bayes Theorem provides a natural way of combining prior information with experimental data to arrive at a posterior probability distribution over parameters.

• To illustrate the differences between classical (sampling theory) statistics and Bayesian statistics.

## Module learning outcomes

At the end of the module you should be able to:

• Understand the basic notions of Bayesian statistics;

• Prove and use Bayes Theorem in its various forms;

• Carry out an analysis of normally distributed data with a normal prior distribution;

• Carry out analyses of data from Binomial, Poisson and Exponential distributions using conjugate priors;

• Perform a Bayesian analysis of data following simple hierarchical models.

## Module content

Syllabus

• Introduction, review of Probability Theory, Bayes Theorem, Exchangeability

• Binomial model: prior, likelihood and posterior; predictive distributions

• Point estimation, Credibility regions

• Poisson model, Poisson model with exposure, Exponential model

• Normal model: unknown mean, unknown variance, both mean and variance unknown

• Monte Carlo approximation, full conditional distributions, Gibbs sampling

• Exponential families and conjugate priors, weakly informative priors, Jeffreys' principle

• Hierarchical Models

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Bayesian Statistics
2 hours 100

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Bayesian Statistics
2 hours 100

## Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

## Indicative reading

Hoff, P.D. (2009). A First Couse in Bayesian Statistical Methods, Springer

Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. (2004). Bayesian Data Analysis, Second Edition, Chapman & Hall/CRC

Lee, P.M. (2012). Bayesian Statistics: An Introduction, Fourth Edition, Wiley

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.