Since the introduction of ChatGPT, large language models are everywhere. Image classification is dominated by artificial intelligence, with widespread applications in medicine and other fields. AI even dominates board games and computer games such as Go, Dota 2 and StarCraft. More impactful applications, such as self-driving cars, are just around the corner.

You will learn how such models are constructed, how they work for both prediction and classification tasks, and how to train these models efficiently from data. You’ll be introduced to the fundamental mathematical concepts for neural network models, including network architectures, activation functions, loss functions, and training approaches such as stochastic gradient descent. You will practice implementing such network models from scratch in simple settings before using powerful packages to train more sophisticated models. Following this experience, you will then investigate modern network architectures and training approaches for tasks such as image classification and natural language processing.

We introduce an array of techniques often referred to as `machine learning’ based methods. You will study these methods in significant detail, learning to apply them in practice, and gaining an understanding of their different motivations, objectives, and implementation (via optimisation).

This module is vital if you are an aspiring data-scientist, as it will give you a variety of baseline methods which you can deploy on a range of supervised (i.e. classification/prediction), or unsupervised (i.e. clustering/exploration) tasks. By studying the mathematical foundations of these techniques alongside their algorithmic implementation, you will be well-placed to generate insights from these methods in practice. Importantly, you will gain an awareness of their limitations, be able to critically reflect on their performance, and suggest appropriate alternatives/extensions for specialist applications.

Many of the more specialist statistical models and procedures are built around a latent, or hidden, stochastic process. This additional layer of structure allows the model to provide a more flexible and realistic representation of the real-world, leading to a more accurate inference. Examples of stochastic mechanisms used include Gaussian processes, which are used in spatial statistics, system emulation and modern experimental design and time-series models, such as the dynamic linear model.

You will gain an understanding of a selection of hidden-process models and the situations in which they are applied, such as in environmental statistics, engineering and health. You will gain an appreciation for why new methods are often required for inference on these models and delve into these new techniques. Models will be developed around example datasets and applications, which you will explore using the new methods.

Clinical trials are planned experiments on human beings designed to assess the relative benefits of one or more forms of treatment. For instance, to study whether aspirin reduces the incidence of pregnancy-induced hypertension or assess whether a new immunosuppressive drug improves the survival rate of transplant recipients. This module combines the study of technical methodology with a discussion of wider research issues.

You will learn about the definition and estimation of treatment effects before progressing to cross-over trials, sample size determination, and equivalence trials. You will explore flexible trial designs that allow modifications to key aspects of the study based on interim data during an ongoing trial. You will also touch on topics such as meta-analysis and accommodating confounding in the design stage.

Throughout, you will develop the ability to recognise and use principles of good study design and improve your skills in the analysis and interpretation of study results.

This module will introduce both non-communicable disease epidemiology and infectious disease epidemiology, starting with the fundamental concepts of measures of disease occurrence and risk and likelihood inference for epidemiological parameters, extending to mathematical modelling of infectious diseases. Along the way, you will cover epidemiological study design and analysis, causal inference, disease screening, and infectious disease models and how they can be fitted to data, including estimation of reproduction numbers of infectious diseases.

Survival analysis involves time to event data, for example the time to recovery when given a new treatment. Such data is often accompanied by censoring, a form of missing data that occurs when the study ends before all subjects experience the event. Longitudinal analysis involves repeated measurements of a response variable made on the same set of individuals across multiple measurement times. These studies are used in public health to identify risk factors for common health conditions.

In this module, you will learn about risk and failure time models for survival data. You will also gain an understanding of generalised linear mixed-effects models (GLMMs) and be able to apply these for all common types of longitudinal or hierarchical data. All analyses will be performed using the software R.