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Mathematical statistics

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This entirely online module provides you with the mathematical underpinning for statistical methods in general and – in particular – for other OU statistics modules. 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 module, 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


Start End Fee Register
04 Oct 2014 Jun 2015
£440.00
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Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£985.00
Choose country above

Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£440.00
Choose country above

Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£440.00
Choose country above

Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£440.00
Choose country above

Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£865.00
Choose country above

Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£1316.00
Choose country above

Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£1316.00
Choose country above

Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£440.00
Choose country above

Registration opens on 30/04/14

This course is expected to start for the last time in October 2018.
Start End Fee Register
04 Oct 2014 Jun 2015
£1316.00
Choose country above

Registration opens on 30/04/14

See below for information about part time tuition fee loans available for study towards a qualification.

This course is expected to start for the last time in October 2018.

*Fees may vary by country.

What you will study

Other OU statistics modules focus on hands-on practical applications of statistical techniques and interpretation of data and statistical analyses. This module complements these modules 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 module is delivered entirely online, with integrated use of exercises, animations, audio and video segments. Although there are no printed study materials, you will be able to print some materials from the module website.

The module is divided into four blocks of study.

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 important relevant methods 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 module 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 module. Level 3 modules 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 are more likely to successfully complete this Level 3 module if you have acquired your prerequisite knowledge through passing one or more of the Level 1 and 2 modules listed below.

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 module.

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.

You are also expected to have good university-level mathematical competence. This could be acquired from studying both Essential mathematics 1 (MST124) and Essential mathematics 2 (MST125) (planned for October 2014) or their predecessors MST121 and MS221. 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 module.

Block 4 of this module 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 modules they can be studied in either order.

If you are planning to study Mathematical methods, models and modelling (MST210) or Pure mathematics (M208), we recommend that you study at least one of them before this module.

To determine whether you are adequately prepared for this module try our diagnostic quiz.

If you have any doubt about the suitability of the module, 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 module 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

All the study materials (including the Study Guide), activities, assessment and study support are delivered online via the module 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 study 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 module can be found in the facts box above.

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

Although your scores on the TMAs and interactive computer-marked assignments (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 four standard TMAs). You will be given more information when you begin the module.

Future availability

The details given here are for the module that starts in October 2014. We expect it to be available once a year.

How to register

To register a place on this course return to the top of the page and use the Click to register button.

Student Reviews

“This was the final course I took, and as I had done mostly stats and probability courses I thought this ...”
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“This is a well-written course that presents the mathematical ideas underpinning statistical theory. Each unit comes with loads of excellent ...”
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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.

Are you already an OU student ? Go to StudentHome for information on choosing your next module.
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

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