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).
What you will study
Other OU statistics modules focus on hands-on practical applications of statistical techniques, data interpretation, and statistical analyses. This module complements these modules by providing the mathematical theory underlying the methods and concepts, including a treatment of classical and Bayesian statistics. A considerable amount of mathematics is sometimes required for this development.
This module is delivered online, using exercises, animations, audio, and video segments. You will also receive 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 primarily 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 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 provides 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.
The full content list is on the Open mathematics and statistics website.
Entry requirements
There is no formal prerequisite 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.
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.
Teaching and assessment
Support from your tutor
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
marking your assignments and offering detailed feedback to help you improve
providing individual guidance, whether that’s for general study skills or specific module content
guiding you to additional learning resources
facilitating online discussions between your fellow students in the dedicated forums.
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Assessment
Course work includes:
4 Tutor-marked assignments (TMAs)
Examination
Each TMA covers specific module units and includes both graded and developmental questions. Your tutor’s feedback will help you strengthen your understanding of the study material and build essential skills.
For this module, we may use an assessment verification process to meet the requirements of relevant accrediting, professional, statutory or regulatory bodies. As part of this process, you may be asked to attend a short post-assessment video discussion, lasting around 15 minutes. During the discussion, you’ll need to show a photo ID and talk through your answers to a small number of questions with a tutor or a member of the module team. The discussion is not graded and is only used to confirm that you completed the assessment yourself.
We regularly review the assessments in our modules, so we may update the examination method used for this module to an in-person exam or an online invigilated exam. When we are making such a change, we will make it clear on this page. If we need to make a change after you have registered, we will notify you as soon as possible. If you have additional requirements, we will support you to complete your assessments.
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 and submission section
online tutorial access
access to student forums.
We also provide physical:
module books
module handbook.
Computing requirements
Primary device – A desktop or laptop computer with at least 8 GB of RAM and a quad-core processor (2.4 GHz minimum speed). It’s possible to access some materials on a mobile phone, tablet or Chromebook; however, they will not be suitable as your primary device or for taking your online exam.
Peripheral devices – Headphones/earphones with a built-in microphone for online tutorials, plus an external webcam and a microphone.
Operating systems – Windows 11 or the latest supported macOS.
Internet access – A broadband or mobile connection with at least 3 Mbps upload and download speed.
Browser – Google Chrome and Microsoft Edge are recommended. Mozilla Firefox and Safari may be suitable. You may need to use Google Chrome specifically for some activities.
Our OU Study app operates on supported versions of Android and iOS.
Software – Any additional software will be provided or is generally freely available.
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.
Future availability
Mathematical statistics (M347) starts once a year – in October.
It will next start in October 2027.
We expect it to start for the last time in October 2030.