- An undergraduate course
in
Mathematics and Statistics.
Mathematical statistics
- On this page
| Course facts | |
|---|---|
| About this course: | |
| Course code | M347 |
| Credits | 30 |
| OU Level | 3 |
| SCQF level | 10 |
| FHEQ level | 6 |
| Course work includes: | |
| 4 Tutor-marked assignments (TMAs) | |
| 14 Interactive computer-marked assignments (iCMAs) | |
| Examination | |
| No residential school | |
This online course provides you with the mathematical underpinning for statistical methods in general and – in particular – for other OU statistics courses. You will gain a thorough grounding in mathematical statistics, together with generic skills. You will study distribution theory, leading on to the theory of statistical inference developed under both classical and Bayesian approaches. In the classical case, you will focus on maximum likelihood estimation. You’ll also explore the development of these ideas in the context of linear modelling (regression and extensions). To study this course, you should have a sound knowledge of basic statistical ideas and competence in calculus, algebra and matrices, as provided by the appropriate Level 1 and 2 study.
Modules at Level 3 assume that you are suitably prepared for study at this level. If you want to take a single module to satisfy your career development needs or pursue particular interests, you don’t need to start at Level 1 but you do need to have adequately prepared yourself for OU study in some other way. Check with our Student Registration & Enquiry Service to make sure that you are sufficiently prepared.
Register for the course
What you will study
Other OU statistics courses focus on hands-on practical applications of statistical techniques and interpretation of data and statistical analyses. This course complements these courses by providing the mathematical theory underlying the methods and concepts, including a treatment of both classical and Bayesian statistics. A considerable amount of mathematics is sometimes required for this development.
This course is delivered entirely online, with integrated use of exercises, animations, audio and video segments. The course is divided into four blocks.
The first block comprises a review unit and units introducing distribution theory. The review is mostly of fundamental statistical ideas of the type taught in Analysing data (M248), (see Entry section below for details); there is also a speedy reminder of basic topics in mathematics, including calculus and matrices. Two units in this block introduce the theory of continuous distributions. You will learn, for example, how to evaluate moments of distributions and about other properties of some important univariate distributions. The mathematical structure of multivariate distributions will be explored, with some emphasis on the multivariate normal distribution.
The second block is about the classical approach to statistical inference. You will learn how to use calculus to obtain maximum likelihood estimators of parameters. You will also learn about the properties of maximum likelihood estimation and of point estimation more generally. The mathematics underlying hypothesis tests and confidence intervals will be explored. There is also a unit on asymptotic (large sample) analysis, giving an insight into how statisticians study properties of statistical procedures by approximate methods.
In the third block you’ll consider the Bayesian approach to statistical inference. The emphasis is first on so-called conjugate analysis which constitutes the type of Bayesian analysis most amenable to straightforward mathematical development. You’ll consider prior to posterior analysis first, followed by Bayesian estimation based on decision theory. Markov chain Monte Carlo (MCMC) is a technique often used for tackling Bayesian problems which are not conjugate; you’ll investigate the mathematical ideas leading to the basic methods of MCMC.
The fourth and final block gives some of the mathematical development underlying linear modelling. The material covers linear regression on a single explanatory variable; multiple linear regression where there is more than one explanatory variable; and generalised linear modelling for regression situations where the normal distribution is not a suitable model for variation in the response. Both classical and Bayesian approaches to the analysis of these models are considered.
You will learn
Successful study of this course should enhance your skills in understanding some useful mathematical theory, interpreting mathematical results in a statistical context, constructing logical arguments, and finding solutions to problems.
Entry
This is a Level 3 course. Level 3 courses build on study skills and subject knowledge acquired from studies at Levels 1 and 2. They are intended only for students who have recent experience of higher education in a related subject, preferably with the OU.
You should have a basic knowledge of the ideas and concepts of statistical science at the level of Analysing data (M248). Relevant topics include: normal, Poisson and binomial distributions; the central limit theorem; point estimation; maximum likelihood estimation; confidence intervals; hypothesis testing; simple linear regression; correlation. All these are reviewed in the course.
It would be an advantage if you have also studied Practical modern statistics (M249), especially Book 4 on Bayesian statistics. However, such knowledge is not assumed but re-developed from scratch.
Block 4 of M347 covers some of the same topics as Linear statistical modelling (M346), but from a quite different viewpoint (theoretical rather than practical). It is not expected that you will have studied M346 before you study M347 (or vice versa); if you are taking both courses they can be studied in either order.
You are also expected to have a reasonable degree of mathematical competence. This could be acquired from studying Using mathematics (MST121) and Exploring mathematics (MS221) or, from February 2014, Essential mathematics 1 (MST124) and Essential mathematics 2 (MST125). The most relevant mathematical techniques are calculus, algebra and matrices. The more at ease you are with basic differentiation and integration the better; there will be quite a lot of algebraic manipulation; matrix properties and manipulations will be kept simple. Supporting mathematical material will be provided as part of the course.
You are more likely to successfully complete this Level 3 course if you have acquired your prerequisite knowledge through passing one or more of the Level 1 and 2 courses listed above.
If you are planning to study Mathematical methods and models (MST209), Pure mathematics (M208) or, from October 2014, Mathematical methods, models and modelling (MST210), we recommend that you study at least one of them before this course.
If you have any doubt about the suitability of the course, please contact our Student Registration & Enquiry Service.
Regulations
As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are available on our Essential documents website.
If you have a disability
At present the mathematical equations in the course text are not accessible to a screen reader. We hope that soon they will be. Mathematics read in this way may, however, be difficult to understand. Descriptions of core figures and animations will be available, as will written transcripts of any audio component. Other alternative formats of the study materials may be available in the future. Our Services for disabled students website has the latest information about availability.
If you have particular study requirements please tell us as soon as possible, as some of our support services may take several weeks to arrange. Visit our Services for disabled students website for more information, including:
- help to determine your study requirements and how to request the support that you need
- Disabled Students' Allowances (DSAs)
- using a computer for OU study
- equipment and other support services that we offer
- examination arrangements
- how to contact us for advice and support both before you register and while you are studying.
Study materials
What's included
Website.
You will need
Calculator with basic mathematical functions (exp, log, etc), but not necessarily with statistical functions.
Computing requirements
You will need a computer with internet access to study this course as it includes online activities, which you can access using a web browser.
- If you have purchased a new desktop or laptop computer since 2007 you should have no problems completing the online activities.
- If you’ve got a netbook, tablet or other mobile computing device check our Technical requirements section.
- If you use an Apple Mac you will need OS X 10.6 or later.
You can also visit the Technical requirements section for further computing information including the details of the support we provide.
Teaching and assessment
Support from your tutor
You will have a tutor who will help you with the course material and mark and comment on your written work, and who you can ask for advice and guidance. Tutorials will mainly be held online.
Contact our Student Registration & Enquiry Service if you want to know more about study with The Open University before you register.
Assessment
The assessment details for this course can be found in the facts box above.
Please note that although your scores on the TMAs and iCMAs will not contribute directly to your final grade, and not all the TMAs and iCMAs are compulsory, you will need to complete about three-quarters of them (the total workload for all TMAs and iCMAs will be less than 4 standard TMAs). You will be given more information when you begin the course.
Please note that tutor-marked assignments (TMAs) for all undergraduate mathematics and statistics courses must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.
Future availability
The details given here are for the course that starts in October 2013. We expect it to be available once a year.
Students also studied
Students who studied this course also studied at some time:
How to register
To register a place on this course return to the top of the page and use the Click to register button.
Distance learning
The Open University is the world’s leading provider of flexible, high quality distance learning. Unlike other universities we are not campus based. You will study in a flexible way that works for you whether you’re at home, at work or on the move. As an OU student you’ll be supported throughout your studies – your tutor or study adviser will guide and advise you, offer detailed feedback on your assignments, and help with any study issues. Tuition might be in face-to-face groups, via online tutorials, or by phone.
For more information read Distance learning explained.
Undergraduate
| Course facts | |
|---|---|
| About this course: | |
| Course code | M347 |
| Credits | 30 |
| OU Level | 3 |
| SCQF level | 10 |
| FHEQ level | 6 |
| Course work includes: | |
| 4 Tutor-marked assignments (TMAs) | |
| 14 Interactive computer-marked assignments (iCMAs) | |
| Examination | |
| No residential school | |
Your questions
Try our frequently asked questions.
Come and meet us at an event near you.
Or contact an adviser by Email or call +44(0) 845 300 60 90 +44(0) 845 366 60 35
Get a prospectus
Download ororder
Share
This PageThe University wishes to emphasise that, while every effort is made to regularly update this site, the material on it is subject to alteration or amendment in the light of changes in regulations or in policy or of financial or other necessity.