MA322-6-SP-CO:
Bayesian Computational Statistics
2021/22
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Undergraduate: Level 6
Current
Monday 17 January 2022
Friday 25 March 2022
15
28 October 2021
Requisites for this module
MA200
MA318
(none)
(none)
(none)
This module focuses principally on Bayesian and 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.
No information available.
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,
Clasical 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
This module has 24 lectures and 5 lab sessions. In the summer term 3 revision lectures are given.
In the summer term 3 revision lectures are given.
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 |
|
|
| Coursework |
Assignment 2 |
|
|
| Exam |
Main exam: 240 minutes during Summer (Main Period)
|
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
Yes
No
Dr Yinghui Wei
University of Plymouth
Available via Moodle
Of 1232 hours, 24 (1.9%) hours available to students:
1208 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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