## MA318-6-AU-CO:Statistical Methods

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Current
Thursday 03 October 2024
Friday 13 December 2024
15
16 May 2024

Requisites for this module
MA101 and MA108 and MA200
(none)
(none)
(none)

MA322

## Key module for

BSC N233 Actuarial Science (Including Placement Year),
BSC N233DT Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N323DF Actuarial Science,
BSC N323DT 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 N333DT Actuarial Studies,
BSC N334 Actuarial Studies (Including Placement Year),
BSC N334DT Actuarial Studies (Including Placement Year),
BSC N335 Actuarial Studies (Including Year Abroad)

## Module description

This module introduces decision theory, loss distributions, risk modelling, Bayesian inference, and comparative inference.

## Module aims

The aims of this module are:

• to learn the concept and basic principle of Bayesian inference.

• to learn the concept of decision theory.

• to learn the principles and methods of choosing good estimators.

• to learn the basic concept of ruin theory.

• to learn the basic random variables and distributions for risk modelling.

• to learn how to use R to implement Bayesian analysis.

## Module learning outcomes

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

1. Have a conceptual understanding of basic principles of Bayesian estimation and hypothesis test.

2. Have a conceptual understanding of decision theory.

3. Have a conceptual understanding of principles and methods to choose good estimators.

4. Have a conceptual understanding of ruin theory and distributions for risk models.

5. Have the ability to analyse a delay (or run-off) triangle and project the ultimate position.

6. Have the ability to implement R for Bayesian analysis.

## Module information

Indicative syllabus

Bayesian Statistics (including decision theory) [CS1-5]

1. Use Bayes’ theorem to calculate simple conditional probabilities.

2. Prior, posterior distributions, and conjugate prior distribution.

3. Choice of prior: conjugate families of distributions, vague and improper priors. Predictive distributions.

4. Loss functions and Bayesian estimates, including explain the concepts of decision theory and apply them; loss, risk, admissible and inadmissible decisions, randomised decisions; minimax decisions.

5. Understanding credibility theory using Bayesian framework.

Random variables and distributions for Risk modelling [CS2-1.1,1.2, 1.3]

1. Construct risk models involving frequency and severity distributions

2. Calculate the moment generating function and the moments for the risk models.

3. Describe the operation of simple forms of proportional and excess of loss reinsurance

4. Distributions for modelling aggregated loss

5. Compound distributions and their application in risk modelling; compound Poisson distribution; insurance and reinsurance modelling

6. Introduction to extreme value theory.

Liability valuation [CM2-5]

1. Explain the concept of ruin for a risk model.

2. Explain what is meant by the aggregate claim process and the cash-flow process for a risk.

3. Define a compound Poisson process and define the probability of ruin in infinite/finite and continuous/discrete time and state and explain relationships between the different probabilities of ruin.

4. Describe and apply techniques for analysing a delay (or run-off) triangle and projecting the ultimate position. Describe and apply a basic chain ladder method for completing the delay run-off triangle using development factors, for estimating outstanding claim amounts.

## 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*

The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.

## 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
maths@essex

Availability
Yes
Yes
No

## External examiner

Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Resources
Available via Moodle
Of 34 hours, 32 (94.1%) hours available to students:
0 hours not recorded due to service coverage or fault;
2 hours not recorded due to opt-out by lecturer(s), module, or event type.

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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