MA318-6-AU-CO:
Statistical Methods
2020/21
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 6
Current
Thursday 08 October 2020
Friday 18 December 2020
15
16 July 2020
Requisites for this module
MA108 and MA200
(none)
(none)
(none)
MA322
BSC N233 Actuarial Science (Including Placement Year),
BSC N323 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
The module introduces decision theory, loss distributions, risk modelling, "Monte Carlo" simulation, Bayesian inference, comparative inference and the generalised linear model.
This module covers part of the required material for the Institute and Faculty of Actuaries CS2 and CM2 syllabus.
The aims of this module are:
1. to learn the concept and basic principle of Bayesian inference.
2. to learn the concept of decision theory.
3. to learn the principles and methods of choosing good estimators.
4. to learn the basic concept of ruin theory.
5. to learn concepts and how to implement “Monte-Carlo” simulation with R.
6. to learn concepts and how to implement generalised linear model with R.
On completion of the module students should be able to:
- Understand concepts of decision theory;
- Apply concepts of decision theory (risk models);
- Understand techniques for analysing a delay (or run-off) triangle and projecting the ultimate position;
- Understand "Monte-Carlo" simulation;
- Understand basic principles of Bayesian inference;
- Understand principles and methods to choose good estimators;
- Understand basic concepts of a generalised linear model;
- Apply R to do GLM and Monte-Carlo Simulation.
Syllabus:
Decision theory
Loss, risk, admissible and inadmissible decisions, randomised decisions. Minimax decisions and Bayes' solutions, including simple results.
Explain the concepts of decision theory and apply them. Calculate probabilities and moments of loss distributions both with and without limits and risk-sharing arrangements. Construct risk models involving frequency and severity distributions and calculate the moment generating function and the moments for the risk models both with and without simple reinsurance arrangements. Explain the concept of ruin for a risk model. Calculate the adjustment coefficient and state Lundberg's inequality. Describe the effect on the probability of ruin of changing parameter values and of simple reinsurance arrangements. Describe and apply techniques for analysing a delay (or run-off) triangle and projecting the ultimate position.
"Monte-Carlo" simulation.
Bayesian inference
Prior and posterior distributions. Choice of prior: bets, conjugate families of distributions, vague and improper priors. Predictive distributions. Bayesian estimates and intervals for parameters and predictions. Bayes factors and implications for hypothesis tests. Use of Monte Carlo simulation of the posterior distribution to draw inferences. Bayesian and Empirical Bayes approach to credibility theory and use it to derive credibility premiums in simple cases.
Comparative inference
Different criteria for choosing good estimators, tests and confidence intervals. Different approaches to inference, including classical, Bayesian and non-parametric.
Generalised linear model
Explain the fundamental concepts of a generalised linear model (GLM), and describe how a GLM may apply.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
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 |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test |
|
|
| 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 & Dr Peng Liu
Dr Yanchun Bao (ybaoa@essex.ac.uk), Dr Peng Liu (peng.liu@essex.ac.uk)
Yes
Yes
No
Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 1797 hours, 2 (0.1%) hours available to students:
1795 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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