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Mathematical statistics

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 OU level 1 and 2 study.

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OU qualifications are modular in structure; the credits from this undergraduate-level module could count towards a certificate of higher education, diploma of higher education, foundation degree or honours degree.

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Module

Module code
M347
Credits
30
Study level
OU SCQF FHEQ
3 10 6
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
See Am I ready?

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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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.

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.

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.

Course work includes:

4 Tutor-marked assignments (TMAs)
14 Interactive computer-marked assignments (iCMAs)
Examination
No residential school

Course satisfaction survey

See the satisfaction survey results for this course.


Entry

This is an OU level 3 module. OU 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 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) 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.

Register

Start End England fee Register
04 Oct 2014 Jun 2015 -

Registration now closed

The deadline for financial support applications has now passed

03 Oct 2015 Jun 2016 Not yet available

Registration opens on 12/03/15

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

Ways to pay for this module

Open University Student Budget Account

The Open University Student Budget Accounts Ltd (OUSBA) offers a convenient 'pay as you go' option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that The Open University works exclusively with OUSBA and is not able to offer you credit facilities from any other provider. All credit is subject to status and proof that you can afford the repayments.

You pay the OU through OUSBA in one of the following ways:

  • Register now, pay later – OUSBA pays your module fee direct to the OU. You then repay OUSBA interest-free and in full just before your module starts. 0% APR representative. This option could give you the extra time you may need to secure the funding to repay OUSBA.
  • Pay by instalments – OUSBA calculates your annual fees and spreads them out over up to a year, enabling you to pay your fees monthly and walk away with a qualification without any further debt. APR 5.1% representative.

Read more about Open University Student Budget Accounts (OUSBA).  

Employer sponsorship

Studying with The Open University can boost your employability. OU qualifications are recognised and respected by employers for their excellence and the commitment they take to achieve one. They also value the skills that students learn and can apply in the workplace.

More than one in 10 OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the qualification you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees. 

  • Your employer just needs to complete a simple form to confirm how much they will be paying and we will invoice them.
  • You won’t need to get your employer to complete the form until after you’ve chosen your modules.  

Credit/debit card

You can pay part or all of your tuition fees upfront with a debit or credit card when you register for each module. 

We accept American Express, Maestro (UK only), Mastercard, Visa/Delta and Visa Electron. 

Gift vouchers

You can pay for part or all of your tuition fees with OU gift vouchers. Vouchers are currently available in the following denominations, £10, £20, £50 and £100. 

Mixed payments

We know that sometimes you may want to combine payment options. You may, for example wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Accounts (OUSBA).

For more information about combining payment options, speak to an adviser.


Note: Your permanent address/domicile will affect your fee status and therefore the fees you are charged and any financial support available to you. The fees and funding information provided here is based upon current details for  year 1 August 2014 to 31 July 2015.
This information was provided on 02/10/2014.

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 module as it includes online activities, which you can access using a web browser.

  • If you have purchased a new desktop or laptop computer since 2008 you should have no problems completing the online activities.
  • If you’ve got a netbook, tablet or other mobile device check our Technical requirements section.
  • If you use an Apple Mac you will need OS X 10.7 or later.

You can also visit the Technical requirements section for further computing information (including details of the support we provide).

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.

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. Find out more about our services for disabled students.