Bayesian Computational Statistics

The details
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Postgraduate: Level 7
Monday 13 January 2025
Friday 21 March 2025
08 January 2024


Requisites for this module
MA318 and MA319



Key module for

DIP G30009 Statistics,
MSC G30012 Statistics,
DIP N32309 Actuarial Science,
MSC N32312 Actuarial Science,
MSC N32324 Actuarial Science,
MPHDG30048 Statistics,
PHD G30048 Statistics,
MPHDN32348 Actuarial Science,
PHD N32348 Actuarial Science

Module description

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 and importance sampling will also be covered in the module.

Module aims

The aims of this module are:

  • To introduce the philosophy of Bayesian statistics.

  • To familiarize students with a Monte Carlo approach to Bayesian statistical analysis.

  • To develop students’ R programming skills.

  • To extend understanding of statistical inference, statistical modelling and statistical application.

Module learning outcomes

By the end of this module, students will be expected to be able to understand:

  1. Bayes' theorem and Bayesian statistical modelling.

  2. The difference between certain Bayesian inferences and corresponding frequentist ones.

  3. Markov chain Monte Carlo simulation.

  4. Rejection sampling, importance sampling and the slice sampler.

  5. The convergence diagnostic for MCMC.

  6. Developing a Monte Carlo simulation algorithm for simple probability distributions.

  7. Coupling from the Past based on recent research development in this area.

Module information


  • Bayesian statistical methods:likelihood function, prior distribution, posterior distribution, predictive distribution, exchangeability, de Finetti theorem.

  • Random variable generation and Monte Carlo integration, Clasical Monte Carlo Integration transformation methods, importance sampling.

  • Other methods for random variable generation:;rejection sampling,;ratio of uniform methods.

  • Adaptive rejection sampling, envelope function, log-concave densities.

  • Simulation from posterior distribution via Markov chain Monte Carlo:Markov chains, stationary distribution, transition probability, general balance, detail balance, the MCMC principle.

  • Metropolis-Hastings algorithm, Convergence of Metropolis-Hastings algorithm, Independent Metropolis-Hastings algorithm, Random walks.

  • Gibbs sampler, Hammersley-Clifford Theorem, Mixture of distributions.

  • Slice sampler.

  • Diagnostic of MCMC convergence.

Learning and teaching methods

Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.


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   Lab test     
Exam  Main exam: In-Person, Open Book (Restricted), 180 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 180 minutes during September (Reassessment 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

Coursework Exam
20% 80%


Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Yanchun Bao, email:
Dr Yanchun Bao; Alex Diana



External examiner

Dr Yinghui Wei
University of Plymouth
Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Available via Moodle
Of 1289 hours, 36 (2.8%) hours available to students:
1253 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information

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