Shape the future of AI with advanced statistical and machine learning expertise. The MSc in Statistics and Artificial Intelligence at Lancaster University is your gateway to a future in AI, machine learning, and data science. Mastering the statistical foundations behind AI models is essential to driving innovation. At Lancaster University, our MSc in Statistics and Artificial Intelligence empowers you to go beyond using off-the-shelf AI tools. You’ll gain a deep understanding of the powerful statistical techniques underpinning modern AI, enabling you to apply and modify these models for real-world challenges.
Why Choose Lancaster's MSc in Statistics and AI?
Our programme offers a unique blend of rigorous statistical theory and cutting-edge AI applications. You’ll not only learn how to apply machine learning techniques but also gain insights into the construction of these algorithms. With a strong foundation in statistics, you’ll be equipped to modify and enhance AI models, preparing you for high-demand roles across various industries or further academic study. With a blend of statistical theory and practical AI skills, you’ll be equipped to lead in the development and application of AI technologies across a range of industries. Start your journey with us and shape the future of AI.
Who is This Programme For?
This MSc is ideal for students with a strong background in quantitative disciplines, such as mathematics. Whether you’re looking to enter the AI industry or advance into academic research, this course will provide the tools you need to succeed.
Programme Highlights
Term 1: Build Your Foundation in Statistical Inference and Algorithms
Start by developing core skills in statistical theory, algorithms, and computing. This term provides the essential knowledge you need to understand the mechanics of AI and machine learning models. You'll also learn how to communicate complex data insights effectively, preparing you for a successful career in data science or AI.
Term 2: Advanced Training in Machine Learning
In the second term, you’ll dive deep into machine learning. Go beyond simply applying pre-built models—understand the mathematical and computational ideas behind them. You’ll cover both supervised learning methods for tasks like prediction and classification, and unsupervised learning techniques for clustering and anomaly detection. You’ll also gain hands-on experience with neural networks, deep learning, and state-of-the-art Bayesian inference, ensuring you can tackle complex problems across various domains.
Term 3: Individual Dissertation Project
During the summer, you’ll undertake an independent research project on a topic of your choice, supervised by experts from Lancaster’s School of Mathematical Sciences. These projects may even involve collaboration with industry partners, providing real-world context to your learning. This research will give you the opportunity to apply your newly acquired skills in machine learning and statistics, culminating in a dissertation that showcases your expertise.
2:1 Hons degree (UK or equivalent) in Mathematics or Statistics.
We may also consider non-standard applications where you have studied a degree in other quantitative subjects that include courses in probability, statistics, linear algebra, and calculus, or you have a 2:2 honours degree equivalent result combined with extensive relevant experience.
You should clearly be able to demonstrate how your skills have prepared you for relevant discussions and assessments during postgraduate study.
If you have studied outside of the UK, we would advise you to check our list of international qualifications before submitting your application.
Pre-master’s programmes
Delivered in partnership with INTO Lancaster University, our one-year tailored pre-master’s pathways are designed to improve your subject knowledge and English language skills to the level required by a range of Lancaster University master’s degrees. Visit the INTO Lancaster University website for more details and a list of eligible degrees you can progress onto.
Course structure
You will study a range of modules as part of your course, some examples of which are listed below.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research. Not all optional modules are available every year.
Core
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This module introduces the expectation-maximisation algorithm, an iterative algorithm for obtaining the maximum likelihood estimate of parameters in problems with intractable likelihoods. Students will explore the use of Markov chain Monte Carlo (MCMC) methods, and will discover the features of the Metro-Hastings algorithm, with emphasis on the Gibbs sampler, independence sampler and random walk Metropolis. Whilst relating to this, students will consider how such methods are closely integrated with Bayesian modelling techniques such as hierarchal modelling, random effects and mixture modelling.
Data augmentation will receive recurring coverage over the course of the module. Students will also gain transferrable knowledge of the usefulness of computers in assisting statistical analysis of complex methods, in addition to experience with the computer statistical package R.
This module provides a comprehensive introduction to deep neural networks, covering key mathematical concepts, network architecture, and optimization techniques. You'll gain hands-on experience by building models from scratch and advancing to industry-standard software tools for tasks like image classification and natural language processing.
Through real-world applications, you’ll tackle modern machine learning challenges, develop coding expertise, and enhance your ability to analyse and present data. Coursework will refine your technical communication skills, preparing you to excel in both individual and collaborative settings.
The three month dissertation period (mid-June to mid-September) will involve the application of statistical methodology to a substantive problem. This dissertation is written by the student under the direction of a supervisor. Some projects are collaborative: examples include GlaxoSmithKline; AstraZeneca; Wrightington Hospital; Royal Lancaster Infirmary; Leahurst Veterinary Centre; and the Department of the Environment.
Students will gain a thorough understanding of advanced statistical methods which go beyond the scope of MSc taught components, and will learn about the development of original statistical methodology which will contribute to a fuller understanding of existing methodology. Students are required to make innovative use of the statistical method, leading to substantive findings which would not readily be obtainable by routine application of standard techniques.
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This module is only core for those with the required mathematical background to complete it. Some students may require an introduction to the area, at the graduate level, and they will study the core module titled ‘Statistical Fundamentals I’. If you complete this module, you will not be required to take Statistical Fundamentals I.
The areas that will be covered are statistical inference using maximum likelihood and generalised linear models (GLMs). Building on an undergraduate-level understanding of mathematics, statistics (hypothesis testing and linear regression) and probability (univariate discrete and continuous distributions; expectations, variances and covariances; the multivariate normal distribution), this module will motivate the need for a generic method for model fitting and then demonstrate how maximum likelihood provides a solution to this. Following on from this, GLMs, a widely and routinely used family of statistical models, will be introduced as an extension of the linear regression model.
This module will develop the core topic of maximum likelihood inference previously introduced in MATH501 Statistical Fundamentals I by expanding on numerical and theoretical aspects. Numerical aspects will include obtaining the maximum likelihood estimate using numerical optimisation functions in R, and using the profile likelihood function to obtain both the maximum likelihood estimate and confidence intervals. Theoretical elements covered will include derivation of asymptotic distributions for the maximum likelihood estimator, deviance and profile deviance.
The second half of the module will introduce Bayesian inference as an alternative to maximum likelihood inference. Building on existing knowledge of the likelihood function, the prior and posterior distributions will be introduced. For simple models, analytical forms for the posterior distribution will be introduced and point estimates for the parameter obtained. For more complex models, numerical methods of sampling from the posterior distribution will be demonstrated.
This module provides a practical introduction to statistical learning from model training to deployment. The student will learn about optimisation as a means for model training; the statistical principles and methods that underpin model selection, and the application of classification and regression models to real data problems.
A variety of supervised learning models and their estimation will be covered, including linear models and their connection to kernel based methods; feed-forward neural networks; and tree based models. Tree based models will be extended to their use in random forests and gradient boosted models. In addition topics relevant to big-data problems including dimensionality reduction variable selection; and stochastic gradient descent will be covered.
Students will be introduced to the widely-used statistical computing package R, which will be the primary tool for data analysis and modelling in this module. In addition to learning how to use R effectively and efficiently, students will also be encouraged to compare and contrast with their existing or developing knowledge of general-purpose languages such as Python.
The aim of this module is to provide students with a range of skills that are necessary for applied statistical work including team-working, oral presentation, statistical computing, and the preparation of written reports including statistical analyses. All students will obtain a thorough grasp of R (including R objects and functions, graphs, basic simulations and programming) and be given an introduction to a second statistical computing package.
Students will also learn how to utilise LaTex for writing a complex and structured scientific report that may include mathematical formulae, tables and figures, as well as learn the intricacies of effective scientific writing style such as grammar, referencing, and the presentation of results in appropriate tables and graphs. They will enhance their oral presentation technique using LaTex Beamer to create slides that include complex mathematical formulae, as well as embark on an in-depth team project using Git, R Markdown or iPython notebooks.
This module introduces key statistical techniques for analysing high-dimensional data, starting with the multivariate normal distribution and its properties. You'll explore matrix decompositions, low-rank approximations, and their roles in dimension reduction and matrix completion. Unsupervised learning methods such as Principal Component Analysis (PCA), Factor Analysis (FA), and clustering algorithms like K-means and Gaussian Mixture Models will be covered. The module also introduces graphical models to represent conditional dependencies in data and methods like the graphical Lasso for graph selection.
Throughout the course, both theoretical concepts and practical applications will be emphasized. You’ll use R to implement these methods, giving you hands-on experience analysing real-world data.
Optional
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This module aims to equip students with a deep understanding of the rapidly evolving field of Artificial Intelligence (AI), focusing on both cutting-edge methods and applications. You'll explore AI's role in areas like cybersecurity, ethical considerations, human-AI interaction, and emerging technologies like Quantum AI. The module prepares you to apply AI to real-world challenges or pursue research in innovative AI techniques, ensuring alignment with current industry and academic trends. Additionally, you'll develop skills in implementing AI solutions, making ethical decisions, and effectively communicating your findings in professional settings.
This module offers an in-depth exploration of the mathematical and algorithmic foundations of artificial intelligence, with a specific focus on machine learning. You will learn how to analyse real-world challenges, design appropriate AI models, and apply machine learning algorithms to complex datasets. Key algorithms will be discussed in detail, including their motivation, underlying theory, implementation, and practical applications using programming and statistical software.
By the end of the module, you will have the skills to model real-world phenomena, assess the effectiveness of various machine learning algorithms, and make evidence-based decisions grounded in statistical learning theory.
There may be extra costs related to your course for items such as books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation, you may need to pay a subscription to a professional body for some chosen careers.
Specific additional costs for studying at Lancaster are listed below.
College fees
Lancaster is proud to be one of only a handful of UK universities to have a collegiate system. Every student belongs to a college, and all students pay a small College Membership Fee which supports the running of college events and activities. Students on some distance-learning courses are not liable to pay a college fee.
For students starting in 2025, the fee is £40 for undergraduates and research students and £15 for students on one-year courses.
Computer equipment and internet access
To support your studies, you will also require access to a computer, along with reliable internet access. You will be able to access a range of software and services from a Windows, Mac, Chromebook or Linux device. For certain degree programmes, you may need a specific device, or we may provide you with a laptop and appropriate software - details of which will be available on relevant programme pages. A dedicated IT support helpdesk is available in the event of any problems.
The University provides limited financial support to assist students who do not have the required IT equipment or broadband support in place.
For most taught postgraduate applications there is a non-refundable application fee of £40. We cannot consider applications until this fee has been paid, as advised on our online secure payment system. There is no application fee for postgraduate research applications.
For some of our courses you will need to pay a deposit to accept your offer and secure your place. We will let you know in your offer letter if a deposit is required and you will be given a deadline date when this is due to be paid.
The fee that you pay will depend on whether you are considered to be a home or international student. Read more about how we assign your fee status.
If you are studying on a programme of more than one year’s duration, tuition fees are reviewed annually and are not fixed for the duration of your studies. Read more about fees in subsequent years.
Scholarships and bursaries
You may be eligible for the following funding opportunities, depending on your fee status and course. You will be automatically considered for our main scholarships and bursaries when you apply, so there's nothing extra that you need to do.
Unfortunately no scholarships and bursaries match your selection, but there are more listed on scholarships and bursaries page.
The information on this site relates primarily to 2025/2026 entry to the University and every effort has been taken to ensure the information is correct at the time of publication.
The University will use all reasonable effort to deliver the courses as described, but the University reserves the right to make changes to advertised courses. In exceptional circumstances that are beyond the University’s reasonable control (Force Majeure Events), we may need to amend the programmes and provision advertised. In this event, the University will take reasonable steps to minimise the disruption to your studies. If a course is withdrawn or if there are any fundamental changes to your course, we will give you reasonable notice and you will be entitled to request that you are considered for an alternative course or withdraw your application. You are advised to revisit our website for up-to-date course information before you submit your application.
More information on limits to the University’s liability can be found in our legal information.
Our Students’ Charter
We believe in the importance of a strong and productive partnership between our students and staff. In order to ensure your time at Lancaster is a positive experience we have worked with the Students’ Union to articulate this relationship and the standards to which the University and its students aspire. View our Charter and other policies.
