Statistical Methods

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 6
Thursday 03 October 2019
Saturday 14 December 2019
01 October 2019


Requisites for this module
MA108 and (MA200 or MA207)



Key module for

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)

Module description

The module introduces decision theory, loss distributions, risk modelling, "Monte Carlo" simulation, Bayesian inference, comparative inference and the generalised linear model.

Module aims

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.

Module learning outcomes

On completion of the module students should be able to (learning outcomes):
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.

Module information

No additional information available.

Learning and teaching methods

The module consist of 26 lectures, 4 classes. 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 Description Deadline Weighting
Coursework Homework 1 08/11/2019 50%
Coursework Homework 2 13/12/2019 50%
Exam 180 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Yanchun Bao (
Dr Yanchun Bao (



External examiner

Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 40 hours, 40 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

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