Mathematical Statistics module (MA42008)

Mathematical Statistics takes you from using statistical methods to understanding why they work. Building on MA22004 Statistics and Data Analysis, this module takes you deeper into the theory used to model uncertainty, analyse data, and make reliable decisions from evidence.

You will study probability distributions in greater depth, including important discrete and continuous models. These distributions help describe random behaviour and provide the mathematical foundation for statistical inference.

A central part of the module is learning how sample data can be used to estimate unknown quantities, test hypotheses, and draw conclusions about wider populations. You will explore ideas such as the Central Limit Theorem, point estimation, maximum likelihood, confidence intervals, and hypothesis testing.

Alongside the theory, you will use R to put mathematical statistics into practice. Through regression, correlation, and generalised linear models, you will learn how models describe relationships in data, how assumptions shape conclusions, and how statistical methods can be applied to real examples.

By bringing together theory, modelling, and computation, this module prepares you for advanced work in statistics, postgraduate study, and data-focused roles. You will develop rigorous analytical skills used in data science, finance, policy, industry, research, and evidence-based decision-making.

What you will learn

In this module, you will:

• develop a deeper understanding of discrete and continuous probability distributions
• work with random variables, transformations, and statistical models
• explore how sampling and the Central Limit Theorem underpin statistical inference
• use estimation methods, including maximum likelihood, to learn from data
• construct confidence intervals and test hypotheses using mathematical reasoning
• study regression, correlation, and generalised linear models used in advanced data analysis
• use R to apply mathematical statistics to real data examples.

By the end of this module, you will be able to:

• explain the theory behind advanced statistical methods
• work confidently with probability distributions, random variables, and statistical models
• estimate unknown quantities and assess uncertainty in your results
• apply confidence intervals and hypothesis tests to support evidence-based decisions
• analyse relationships in data using regression and related models
• use R to connect statistical theory with practical data analysis
• communicate statistical conclusions clearly for technical and non-technical audiences

Assignments / assessments

• Coursework (20%)
  
  • Class tests
  • Computer lab reports
• Exam (80%)

Teaching methods / timetable

• lectures, introducing the main ideas in mathematical statistics, statistical inference, modelling, and R
• tutorials, where you will practise solving statistical problems and receive feedback on your understanding
• computer lab work using RStudio, helping you apply statistical methods to data and computational examples
• weekly problem sheets, giving you regular practice with theory, calculations, and interpretation
• online resources, supporting independent study and coursework preparation