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Mathematical statistics

This 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 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.
OU SCQF FHEQ
3 10 6
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
See Entry requirements

Student Reviews

By far the hardest of the modules in my BSc maths/stats. The material is very intensive and whilst well written...
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This was the final course I took, and as I had done mostly stats and probability courses I thought this...
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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 and extra exercises. 

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 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.

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 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

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 us 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

Mathematical statistics starts once a year – in October. This page describes the module that will start in October 2018. We expect it to start for the last time in October 2022.

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:

    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 requirements

    You need no pre-requisites to study Mathematical statistics. However, we recommend that you’re familiar with the following mathematical topics:

    • calculus
    • algebra
    • matrices
    • basic differentiation and integration

    We recommend you also have previous basic knowledge of statistical science; we’ll include some revision of 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

    Check you’re ready to study Mathematical statistics with our self-assessed quiz.

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

    Preparatory work

    Essential mathematics 1 (MST124) and Essential mathematics 2 (MST125) are ideal preparation to reach the mathematical competence level we recommend for studying Mathematical statistics. However, we recommend also completing Mathematical methods, models and modelling (MST210) or Pure mathematics (M208).

    Register

    Start End Fee
    - - -

    No current presentation - see Future availability

    This module is expected to start for the last time in October 2022.

    Additional Costs

    Study costs

    There may be extra costs on top of the tuition fee, such as a laptop, travel to tutorials, set books and internet access.

    If you're on a low income you might be eligible for help with some of these costs after your module has started.

    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 monthly fee and number of instalments based on the cost of the module you are studying. APR 5.1% representative.

    Joint loan applications

    If you feel you would be unable to obtain an OUSBA loan on your own due to credit history or affordability issues, OUSBA offers the option to apply for a joint loan application with a third party. For example, your husband, wife, partner, parent, sibling or friend. In such cases, OUSBA will be required to carry out additional affordability checks separately and/or collectively for both joint applicants who will be jointly and severally liable for loan repayments.

    As additional affordability checks are required when processing joint loan applications, unfortunately, an instant decision cannot be given. On average the processing time for a joint loan application is five working days from receipt of the required documentation.

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

    Employer sponsorship

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

    More than one in ten OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the module 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 module.  

    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. 

    Mixed payments

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


    For more information about combining payment options, speak to an adviser or book a call back at a time convenient to you.


    Please 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 valid for modules starting before 31 July 2019. Fees normally increase annually in line with inflation and the University's strategic approach to fees. 

    This information was provided on 19/12/2018.

    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 also be provided with printed versions of the main units and extra exercises.

    You will need

    Calculator with basic mathematical functions (exp, log, etc.), but not necessarily with statistical functions.

    Computing requirements

    A computing device with a browser and broadband internet access is required for this module.  Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

    Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

    A desktop or laptop computer with either:

    • Windows 7 or higher
    • macOS 10.7 or higher

    The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

    To participate in our online-discussion area you will need both a microphone and speakers/headphones. 

    Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students. 

    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 website.