Bayesian Computational Statistics
Postgraduate: Level 7
Monday 13 January 2020
Friday 20 March 2020
01 October 2019
Requisites for this module
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
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.
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
3. Other methods for random variable generation:
ratio of uniform methods
4. Adaptive rejection sampling
5. Simulation from posterior distribution via Markov chain Monte Carlo:
Markov chains, stationary distribution,
general balance, detail balance.
the MCMC principle
6. Metropolis-Hastings algorithm,
Convergence of Metropolis-Hastings algorithm
Independent Metropolis-Hastings algorithm,
7. Gibbs sampler
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
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
No additional information available.
The module has 28 lectures and 5 lab sessions. In the summer term 3 revision lectures are given.
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
||180 minutes during Summer (Main Period) (Main)
Module supervisor and teaching staff
Dr Hongsheng Dai, email email@example.com
Dr Hongsheng Dai (firstname.lastname@example.org)
Prof Fionn Murtagh
Professor of Data Science
Available via Moodle
Of 36 hours, 28 (77.8%) hours available to students:
8 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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