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Mathematical statistics

This module provides the mathematical underpinning for statistical methods in general and further statistics modules. You’ll study distribution theory, leading to statistical inference theory developed under classical and Bayesian approaches. In the classical case, you’ll focus on maximum likelihood estimation. You’ll also explore the development of these ideas in the context of linear modelling (regression and extensions).

Modules count towards OU qualifications

OU qualifications are modular in structure; the credits from this undergraduate 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

Credits

  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
30

Study level

Across the UK, there are two parallel frameworks for higher education qualifications, the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ) and the Scottish Credit and Qualifications Framework (SCQF). These define a hierarchy of levels and describe the achievement expected at each level. The information provided shows how OU module levels correspond to these frameworks.
Level of Study
OU SCQF FHEQ
3 10 6

Study method

Module cost

Entry requirements

Student Reviews

I embarked on this module as one of my last two for my degree. Having completed it, there is some...
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I found M347 absolutely fascinating and highly enjoyable. Some of the insights I gained, not just into statistics but into...
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Although students can decide when to start studying M347, we advise that students should have the required statistical and mathematical...
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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 online, with integrated use of exercises, animations, audio and video segments. You will also be provided with printed versions of the main units, extra exercises and a handbook.

The module is divided into four blocks of study.

Block 1: Review and distribution theory
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 requirements 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.

Block 2: Classical inference
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.

Block 3: Bayesian statistics
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.

Block 4: Linear modelling
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 can find the full content list on the Open mathematics and statistics website.

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.

Vocational relevance

This module will provide you with the theoretical underpinning of some important statistical methods, giving you an enhanced understanding of, and the ability to modify and develop, the statistical toolbox used by professional statisticians in practice.

Professional recognition

This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.

This module may also help you to apply for the professional award of Graduate Statistician conferred by The Royal Statistical Society (RSS).

Teaching and assessment

Support from your tutor

Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:

  • Marking your assignments (TMAs) and providing detailed feedback for you to improve.
  • Guiding you to additional learning resources.
  • Providing individual guidance, whether that’s for general study skills or specific module content.
  • Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part.

Assessment

The assessment details for this module can be found in the facts box.

Although your scores on the TMAs will not contribute directly to your final grade, you will need to complete at least four TMAs and score at least 30% on each of them.

Future availability

Mathematical statistics (M347) starts once a year – in October.

This page describes the module that will start in October 2024.

We expect it to start for the last time in October 2026.

Regulations

As a student of The Open University, you should be aware of the content of the academic regulations which are available on our Student Policies and Regulations website.

Course work includes:

6 Tutor-marked assignments (TMAs)
Examination


Entry requirements

There is no formal pre-requisite study, but you must have the required mathematical and statistical skills.

You can check you’re ready for M347 and see the topics it covers here.

Talk to an advisor if you’re not sure if you’re ready.

Preparatory work

You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.

The key topics to revise include:

  • matrices
  • basic differentiation and integration.

You’ll also find it useful to be familiar with the following topics:

  • normal, Poisson and binomial distributions
  • the central limit theorem
  • point estimation
  • maximum likelihood estimation
  • confidence intervals
  • hypothesis testing
  • simple linear regression
  • correlation.

An OU level 2 module in mathematics is ideal preparation, and Analysing data (M248) is also useful.

Register

Start End England fee Register
05 Oct 2024 Jun 2025 £1818.00

Registration opens on 20/03/24

This module is expected to start for the last time in October 2026.

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In the meantime, explore our overview of Fees and funding.

Can you study an Access module for free?

In order to qualify, you must:

  1. be resident in England
  2. have a personal income of less than £25,000 (or receive qualifying benefits)
  3. have not completed one year or more on any full-time undergraduate programme at FHEQ level 4 or above, or completed 30 credits or more of OU study

How to apply to study an Access module for free

Once you've started the registration process, either online or over the phone, we'll contact you about your payment options. This will include instructions on how you can apply to study for free if you are eligible.

If you're unsure if you meet the criteria to study for free, you can check with one of our friendly advisers on +44 (0)300 303 0069 or you can request a call back.

Not eligible to study for free?

Don't worry! We offer a choice of flexible ways to help spread the cost of your Access module. The most popular options include:

  • monthly payments through OUSBA
  • part-time tuition fee loan (you'll need to be registered on a qualification for this option)

To explore all the options available to you, visit Fees and Funding.

What's included

You’ll have access to a module website, which includes:

  • a week-by-week study planner
  • course-specific module materials
  • audio and video content
  • assessment details, instructions and guidance
  • online tutorial access
  • access to student and tutor group forums.

You’ll be provided with printed books covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. You’ll also receive a printed module handbook.

Computing requirements

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Ventura or higher.

Any additional software will be provided or is generally freely available.

To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards, and any modern browser is suitable for most activities.

Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.

If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying M347 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

To find out more about what kind of support and adjustments might be available, contact us or visit our disability support pages.