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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

## Related modules

• None

### Prohibited combinations

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

## Module will run

Occurrence Teaching cycle
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
Online Exam
Bayesian Statistics
N/A 100

None

### Reassessment

Task Length % of module mark
Online Exam
Bayesian Statistics
N/A 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.