MSc Statistics

MTH3028: Statistical Inference

Statistical inference concerns how we use data to describe and predict the world. It is important in a wide range of sectors, including finance, insurance, economics, medicine, retail, industry, sport, environment and government, to name only a few. This module provides a foundation in modern statistical inference from a frequentist perspective and will benefit anyone considering a career in the data sciences. We introduce key inferential concepts and procedures, study their theoretical properties, and apply them to a range of statistical models using the statistical programming environment 'R'.

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MTH3045: Statistical Computing

When we want to fit a statistical model to some data it is almost inevitable that a computer will make this process much easier. Computers can speed up calculations, avoid the tedium or potential for error of doing calculations by hand, and have allowed us to analyse amounts of data and fit new models that were simply impractical without them. Data Science is built on the fitting of statistical models to data. While such models continue to evolve, we must balance what's theoretically and practically possible; otherwise we have data that we can't analyse and models that we can't estimate. We can achieve more by fitting statistical models efficiently.

To efficiently fit statistical models, we often use fundamental mathematical concepts, including some that you will have previously seen, such as matrix decompositions. You will learn a variety of these concepts from the theory behind them to their role in analysing real-life data. You will see some important statistical models that rely on these concepts and how the R programming language can be used for computation, in particular some of its more advanced features for calculations and analysing data. You will gain experience in programming while learning new statistical methods and models, through interesting examples and exercises. After this module you will be able to analyse more complex data with more advanced statistical techniques.

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MTHM033: Statistical Modelling in Space and Time

In this course, we explore Gaussian processes (GPs), a powerful class of non-linear regression models widely used in Artificial Intelligence (AI), Machine Learning (ML), and modern statistics. We will look at the theoretical basis for the GPs and show how they can be used in statistics to model spatially correlated data (for example temperature across a domain such as the North Atlantic). In AI/ML, GPs serve as an alternative to Neural Networks for modelling complex patterns in data (a setting often referred to as GP regression). Finally, the course highlights the use of GPs for functional approximation and Uncertainty Quantification (UQ). Examples include approximating solutions to Partial Differential Equations or emulating the behaviour of computationally expensive numerical simulators. An important advantage of GPs is that they naturally produce estimates of uncertainty, which can be used as a measure of prediction reliability. This year, time series will not be covered.

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MTHM047: Bayesian Statistics, Philosophy and Practice

Since the 1980s, computational advances and novel algorithms have seen Bayesian methods explode in popularity, today underpinning modern techniques in data science and machine learning with applications across science, social science, the humanities and finance.

This module will cover the Bayesian approach to modelling, data analysis and statistical inference. The module describes the underpinning philosophies behind the Bayesian approach, looking at subjective probability theory, the notion and handling of prior knowledge, posterior inference, and how this approach differs to classical approaches to statistics. It will explore simulation-based inference in Bayesian analyses and develop important algorithms for Bayesian simulation by Markov Chain Monte Carlo (MCMC) such as the Gibbs sampler and the Metropolis-Hastings algorithm. Finally, we’ll apply the techniques and tools developed through the module to fit a wide range of models using modern Bayesian inference software, enabling you to apply techniques discussed in the course to a variety of real datasets.

At M-level, in addition to the above, students are introduced to topics in Bayesian approximation such as Laplace approximation and variational inference via material for self-study.

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MTHM050: Research Project in Statistics

In this module, you will gain experience of independent work by conducting in-depth research into a statistical problem agreed with your Project Supervisor. A Good Research Practice portfolio (20%) recognises your professionalism and research performance, and your participation in the wider research, academic, or professional environment associated with your project. Partway through the project, you will present your work to date to a group of academics and fellow students in order to obtain feedback on your progress and to help guide the remainder of your study. This forms 10% of the assessment. At the end of the project, you will write a coherent and comprehensible account of your work in the form of a dissertation that forms 70% of the assessment. Computational work using appropriate software may form part of the Research Project in Statistics.

This module provides the opportunity for you to produce a well-researched project in statistics, either complementing or extending material in the taught part of the programme. By taking this module, you will develop research skills, including literature review, methodological selection, data analysis, and communication of statistical results.

You will receive guidance on the responsible use of AI-assisted tools to support aspects of your research, report writing and presentation preparation, in line with University policy.

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MTHM503: Applications of Data Science and Statistics

This module will enable you to learn new Data Science and Statistical methods, and to use the techniques learnt in other modules, by working on analyses of real data examples. There will be a strong emphasis throughout on understanding the practical application of statistical and machine learning methods including clustering, data reduction, methods for handling missing data, study design and introductory methods for time series data. Theory and ideas will be developed to allow the implementation of methods in examples drawn from industry, medicine, finance, public health and environmental challenges, including climate change and air pollution.

Pre-requisites: None

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MTHM506: Statistical Data Modelling

Statistical modelling lies at the heart of modern data analysis and is a vital part of the wider landscape of data science/machine learning/AI. There is currently an increasing pressure to regulate AI (used as a general umbrella term), so the future lies in interpretable and explainable AI approaches. As it happens, statistical modelling is both interpretable and explainable and has been used for the last 50 years or so. The point of this module is to introduce statistical modelling as such an approach and illustrate how it can be used to conduct both advanced and flexible data analyses with outputs that can be directly used for decision making. The module starts from simple linear regression familiar from most foundation courses in statistics and places this is the very broad framework of statistical data modelling. Generalized Additive Models (non-linear, hierarchical regression) will be introduced as a unifying modelling framework, that includes estimation, validation, selection and uncertainty quantification as part of the framework. The module will provide you with a toolbox and the ability to analyse any real world data set, including binary data, count data, contingency tables, data with temporal and spatial structure as well as data that are missing or partially missing. We will use the statistical software R (Rstudio) as the main platform to fit this wide range of models, and will use it in practical sessions so that, as well as a sound theoretical basis, you will develop an understanding of how to apply techniques discussed in the module in practical data analysis. The module will introduce a plethora of real data sets spanning a wide range of applications such as public health, weather, climate, ecology, biology, epidemiology, natural hazards and many others.

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MTHM507: Communicating Data Science

Critical to every successful academic and industrial career is the ability to  communicate data analysis in your area of expertise. Through engaging with and discussing  papers and data in this data science specialism we will explore the techniques of reading research/policy papers and presenting on new data analysis developments. You will develop the skills that are essential in a fast-paced and constantly developing environment.

This module aims to introduce you to the important aspects of how to develop your own original consulting/research analyses and how to communicate them effectively.  To develop in you the key skills required to stay up-to-date with and communicate your subject knowledge and succeed in the professional and academic environment.

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ECMM422: Machine Learning

Machine learning has emerged mainly from computer science and artificial intelligence, and draws on methods from a variety of related subjects including statistics, applied mathematics and more specialized fields, such as pattern recognition and neural computation. Applications are, for example, image and speech analysis, medical imaging, bioinformatics and exploratory data analysis in natural science and engineering. This module will provide you with a thorough grounding in the theory and application of machine learning, pattern recognition, classification, categorisation, and concept acquisition. Hence, it is particularly suitable for Computer Science, Mathematics and Engineering students and any students with some experience in probability and programming.

In this data-driven era, modern technologies are generating massive and high-dimensional datasets. This module aims to give you an understanding of computational methods used in modern data analysis.

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ECMM450: Stochastic Processes

A stochastic process is one that involves random variables. A large number of practical systems within industry, commerce, finance, biology, nuclear physics and epidemiology can be described as stochastic and analysed using the techniques developed in this module. The systems considered may exist in any one of a finite, or possibly countably infinite, number of states. The state of a system may be examined continuously through time or at fixed and regular intervals of time.

You will study processes whose changes of state through time are governed by probabilistic laws, and you will learn how models of such processes can be applied in practice.

Pre-Requisite Modules:

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MTHM002: Methods for Stochastics and Finance

The module explores a diverse range of mathematical topics, emphasising their applications to financial modelling. The topics covered will range from matrix algebra to differential systems and stochastic calculus. This module will play an important role in underpinning the mathematical and computational methods needed for the subsequent modules in the financial mathematics MSc programme.

The module aims to engender an understanding of mathematics useful for the theory of financial modelling and financial derivatives. It will also develop your mathematical ability and reasoning skills.

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MTHM006: Mathematical Theory of Option Pricing

On this module you will study the mathematical basis, including Ito Calculus, for a range of methods used to price financial options. The methods include the binomial method, the Monte Carlo method, and the Black-Scholes equation. The common principles that underpin these approaches will be emphasised. You will see how to apply the methods both analytically and in computer implementations. The strengths and limitations of each of the approaches will be discussed.

Pre-requisite modules: MTH3024 Stochastic Processes, or MTHM002 Methods for Stochastics and Finance.

By taking this module, you will gain an understanding of the theoretical assumptions on which the mathematical models underlying option pricing depend, and of the methods used to obtain analytic or numerical solutions to a variety of option pricing problems.

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SOCM033: Data Governance and Ethics

Data science, machine learning, artificial intelligence and 'big data' have become central to every aspect of social life. How can these complex and powerful technologies best be managed and governed for the benefit of society now and in the future? In this module you will: (1) identify some of the main risks and ethical/legal challenges involved in the widespread automation and digitalisation of services characterising 21st century life (for example, the clash between individual desire for privacy, frameworks for data ownership and the institutional commodification of personal data); (2) examine whether and how such concerns can be handled; and (3) discuss the responsibilities of data scientists and other producers of technologies for data analysis towards their proper use.

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