MA322-7-SP-CO:
Bayesian Computational Statistics
2021/22
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
Monday 17 January 2022
Friday 25 March 2022
15
19 August 2021
Requisites for this module
(none)
(none)
(none)
(none)
(none)
DIP G20109 Optimisation and Data Analytics,
MSC G20312 Optimisation and Data Analytics,
DIP G30009 Statistics,
MSC G30012 Statistics
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.
The aims of this module are:
1. To introduce the philosophy of Bayesian statistics;
2. To familiarize students with a Monte Carlo approach to Bayesian statistical analysis;
3. To develop students’ R programming skills;
4. To extend understanding of statistical inference, statistical modelling and statistical application.
On completion of the course students should be able to:
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
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, Classical Monte Carlo Integration, transformation methods, importance sampling
3. Other methods for random variable generation: rejection sampling, ratio of uniform methods
4. Adaptive rejection sampling, 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
This module consists of 24 lectures and eight lab sessions. There are three revision sessions in the summer term.
This module does not appear to have a published bibliography for this year.
Assessment items, weightings and deadlines
Coursework / exam |
Description |
Deadline |
Coursework weighting |
Coursework |
Assignment 1 |
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Coursework |
Assignment 2 |
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Exam |
Main exam: 240 minutes during Summer (Main Period)
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Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Yanchun Bao, email: ybaoa@essex.ac.uk.
Dr Yanchun Bao
ybaoa@essex.ac.uk
Yes
No
Yes
Prof Fionn Murtagh
University of Huddersfield
Professor of Data Science
Dr Yinghui Wei
University of Plymouth
Available via Moodle
Of 1514 hours, 29 (1.9%) hours available to students:
1485 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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