## MA322-6-SP-CO:Bayesian and Computational Statistics

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Current
Monday 13 January 2025
Friday 21 March 2025
15
23 May 2024

Requisites for this module
MA200
MA317 and MA318 and MA319
(none)
(none)

(none)

## Key module for

BSC N233 Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N323DF Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
MSCIN399 Actuarial Science and Data Science,
BSC N333 Actuarial Studies,
BSC N334 Actuarial Studies (Including Placement Year),
BSC N335 Actuarial Studies (Including Year Abroad)

## Module description

This module focuses principally on Bayesian computational statistics and covers different types of Monte Carlo methods, including rejection sampling, importance sampling and Markov chain Monte Carlo.

This module will also cover generalised linear models (GLM) and built upon GLM, modern machine learning techniques are also introduced in the end.

## 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;

• To understand the basics of generalised linear regression;

• To understand the basics of machine learning.

## Module learning outcomes

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

1. Have a conceptual understanding of Bayes' theorem and Bayesian statistical modelling.

2. Have a conceptual understanding of Markov chain Monte Carlo simulation and the convergence diagnostic for MCMC.

3. Have a conceptual understanding of rejection sampling and importance sampling.

4. Have ability to develop a Monte Carlo simulation algorithm for simple probability distributions and implement in R.

5. Have a conceptual understanding of a generalised linear model and implement in R.

6. Have a conceptual understanding of elementary principles of Machine Learning and implement in R.

## Module information

Indicative Syllabus

Monte Carlo and Bayesian computational statistical methods [CS1 5, CM2 5.3]

1. Bayesian statistical methods:likelihood function, prior distribution, posterior distribution.

2. Random variable generation and Monte Carlo integration,Classical Monte Carlo Integration, transformation methods, importance sampling, rejection sampling.

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

4. Metropolis-Hastings algorithm,Independent Metropolis-Hastings algorithm, Random walks Metropolis-Hastings algorithm.

5. Gibbs sampler

6. Diagnostic of MCMC convergence

Generalised linear model [CS1-4.2]

1. Understand fundamental concepts of (GLM)

2. Define an exponential family of distributions. Show that the following distributions may be written in this form: binomial, Poisson, exponential, gamma, normal.

3. State the mean and variance for an exponential family and define the variance function and the scale parameter. Explain what is meant by the link function.

4. Explain what is meant by a variable, a factor taking categorical values. Define the linear predictor, illustrating its form for simple models, including polynomial models and models involving factors.

5. Fit a generalised linear model to a data set in R and interpret the output.

Machine learning [CS2-5]

1. Explain the main branches of machine learning and describe examples of the types of problems typically addressed by Machine Learning.

2. Describe and give examples of key supervised and unsupervised Machine Learning techniques, explaining the difference between regression and classification and between generative and discriminative models.

3. Explain in detail and use appropriate package to apply Machine Learning techniques in R to simple problems.

## 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.

## Bibliography*

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   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.

Coursework Exam
30% 70%

### Reassessment

Coursework Exam
30% 70%
Module supervisor and teaching staff
Dr Yanchun Bao, email: ybaoa@essex.ac.uk.
Dr Yanchun Bao; Alex Diana
maths@essex.ac.uk

Availability
Yes
Yes
No

## External examiner

Dr Yinghui Wei
University of Plymouth
Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Resources
Available via Moodle
Of 1034 hours, 31 (3%) hours available to students:
1003 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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