# Module Directory

## MA322-7-SP-CO:Bayesian Computational Statistics

The details
2019/20
Mathematical Sciences
Colchester Campus
Spring
Current
Monday 13 January 2020
Friday 20 March 2020
15
01 October 2019

Requisites for this module
(none)
(none)
(none)
(none)

(none)

## Key module for

DIP G10109 Mathematics,
MSC G10112 Mathematics,
MSC G10124 Mathematics,
DIP GN1309 Mathematics and Finance,
MSC GN1312 Mathematics and Finance,
MSC GN1324 Mathematics and Finance,
DIP G20109 Statistics and Operational Research,
MSC G20312 Statistics and Operational Research,
DIP G30009 Statistics,
MSC G30012 Statistics

## Module description

This module focuses principally on Bayesian computational statistics. The module introduces basic Bayesian statistical modelling and methods, such as Bayes' Theorem, posterior and prior distributions and Markov chain Monte Carlo methods. Other Monte Carlo simulation methods, such as rejection sampling, importance sampling, coupling from the past will also be covered in the module.

## Module aims

Syllabus

1. Bayesian statistical methods:
likelihood function, prior distribution, posterior distribution, predictive distribution, exchangeability, de Finetti theorem
2. Random variable generation and Monte Carlo integration,
Clasical Monte Carlo Integration
transformation methods,
importance sampling
3. Other methods for random variable generation:
rejection sampling,
ratio of uniform methods
envelope function,
log-concave densities.
5. Simulation from posterior distribution via Markov chain Monte Carlo:
Markov chains, stationary distribution,
transition probability,
general balance, detail balance.
the MCMC principle
6. Metropolis-Hastings algorithm,
Convergence of Metropolis-Hastings algorithm
Independent Metropolis-Hastings algorithm,
Random walks
7. Gibbs sampler
Hammersley-Clifford Theorem
Mixture of distributions
8. Slice sampler
9. Diagnostic of MCMC convergence
10. Recent development in exact Monte Carlo simulation,
coupling from the past,
perfect slice sampler

## Module learning outcomes

On completion of the course students should be able to (learning outcomes):
Understand Bayes' theorem and Bayesian statistical modelling
Understand the difference between certain Bayesian inferences and corresponding frequentist ones.
Understand Markov chain Monte Carlo simulation
Understand rejection sampling, importance sampling and the slice sampler
Understand the convergence diagnostic for MCMC.
Develop a Monte Carlo simulation algorithm for simple probability distributions

## Learning and teaching methods

The module has 28 lectures and 5 lab sessions. In the summer term 3 revision lectures are given.

## Bibliography

This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

## Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   Homework 1
Coursework   Homework 2
Exam  1440 minutes during Summer (Main Period) (Main)

Coursework Exam
20% 80%

### Reassessment

Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Hongsheng Dai, email: hdaia@essex.ac.uk.
Dr Hongsheng Dai, email hdaia@essex.ac.uk
Dr Hongsheng Dai (hdaia@essex.ac.uk)

Availability
Yes
No
No

## External examiner

Prof Fionn Murtagh
University of Huddersfield
Professor of Data Science
Resources
Available via Moodle
Of 177 hours, 24 (13.6%) hours available to students:
153 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information
Mathematical Sciences

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