MA322-7-SP-CO:
Bayesian Computational Statistics
2016/17
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
15
05 March 2014
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.
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.
- Understand coupling from the past.
- Develop Bayesian models and implement a Monte Carlo simulation algorithm for a given statistical problem
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
No information available.
No information available.
No additional information available.
The module has 28 lectures and 5 lab sessions. In the summer term 3 revision lectures are given.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
R Project |
|
|
| Exam |
Main exam: 180 minutes during Summer (Main Period)
|
Additional coursework information
Information about coursework deadlines can be found in the "Coursework and Exams" section of the Current Students, Information for Students Maths web pages: Coursework and Test Information
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 Hongsheng Dai, email hdaia@essex.ac.uk, tel 01206 873304
Mrs Shauna Meyers - Graduate Administrator. email: smcnally (Non essex users should add @essex.ac.uk to create the full email address), Tel 01206 872704
Yes
No
No
Prof John Nigel Scott Matthews
The University of Newcastle-upon-Tyne
Professor of Medical Statistics
Available via Moodle
Of 40 hours, 31 (77.5%) hours available to students:
9 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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