MA318-7-AU-CO:
Statistical Methods
2016/17
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Postgraduate: Level 7
Current
15
05 March 2014
Requisites for this module
(none)
(none)
(none)
(none)
MA322
DIP G30009 Statistics,
MSC G30012 Statistics
The module introduces decision theory, hypothesis testing, "Monte Carlo" simulation, Bayesian inference, comparative inference and the generalised linear model.
On completion of the course students should be able to (learning outcomes):
- Understand concepts of decision theory;
- Understand hypothesis testing, exact and asymptotic tests, properties of tests;
- Understand basic principles of Bayesian inference;
- Understand principles and methods to choose good estimators
- Understand basic concepts of a generalised linear model.
Syllabus:
Decision theory
Loss, risk, admissible and inadmissible decisions, randomised decisions. Minimax decisions and Bayes' solutions, including simple results.
Hypothesis testing
Simple and composite hypotheses, types of error, power, operating characteristic curves, p-value. Neyman-Pearson method. Generalised likelihood ratio test.
Use of asymptotic results to construct tests. Central limit theorem, asymptotic distributions of maximum likelihood estimator and generalised likelihood ratio test statistic.
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.
No information available.
No information available.
No additional information available.
The module consist of 25 lectures, 5 classes. In the summer term 3 revision lectures are given.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test |
|
|
| Exam |
Main exam: 180 minutes during Summer (Main Period)
|
Additional coursework information
Information about coursework deadlines can be found in the "Coursework and Exams" section of the Current Students, Information for Students Maths web pages: Coursework and Test Information
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 Hongsheng Dai, email hdaia@essex.ac.uk, tel 01206 873304
Mrs Shauna Meyers - Graduate Administrator. email: smcnally (Non essex users should add @essex.ac.uk to create the full email address), Tel 01206 872704
Yes
No
No
Prof John Nigel Scott Matthews
The University of Newcastle-upon-Tyne
Professor of Medical Statistics
Available via Moodle
Of 35 hours, 33 (94.3%) hours available to students:
2 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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