Mathematical Statistics module (MA52007)

Mathematical Statistics is the application of probability theory to statistics. This is an important area, providing useful connections to other areas of Mathematics. Mathematical Statistics has applications across the sciences, business, government, and more. It is a core topic in the growing area of Data Science.

Build on your previous knowledge of probability and statistics. You will go beyond the fundamentals of Probability and Distribution Theory. You will learn about Statistical Estimation and Models. You will also meet Bayesian methods. Within each area you will work with applications in the computer system R.

What you will learn

In this module, you will:

• learn probability, combinatorics, and discrete and continuous random variables
• gain knowledge about the theory of discrete and continuous distributions
• understand transforming random variables
• gain experience in sampling distributions, random sampling, and the central limit theorem
• be taught the method of moments and the method of maximum likelihood
• learn confidence intervals and hypothesis testing
• understand simple linear regression and forms of correlation
• learn multiple regression and linear models
• learn the Bayesian approaches

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

• understand the theoretical underpinnings of statistics
• rely on a broad knowledge of probability distributions
• understand important concepts in statistical estimation
• apply analysis to methods such as confidence intervals and hypothesis testing
• analyse relationships between quantities in real-world examples
• investigate problems and theory using the system R

Assignments/assessment

• Coursework (40%)
• Final exam (60%)

Coursework may include homework assignments, including those produced in the R system and class tests.

Teaching methods

You should expect a combination of lectures and workshops each week. You will be given material to study in advance of classes to allow you to take part and contribute to make the most of in-person time.