51福利

Modern data collection is almost always on a large scale, which allows us to study complex dependencies and interactions. Nonparametric statistical methods can be helpful in modelling and understanding such data as they allow for models that adapt more flexibly to the data. For example, rather than assuming a parametric (e.g. Gaussian) distribution to model a population, we can utilise kernel-based methods to approximate the density function based on the observed data, allowing for the use of weaker assumptions.

This module will introduce you to nonparametric methods used in both density estimation and regression settings, the former via kernel methods, and the latter by extending the generalised linear modelling paradigm through the usage of spline functions, thus enabling us to investigate non-linear relationships between variables. Overall, this module equips you with a range of powerful models that can be used (and are demonstrated) in a variety of real-world applications.

Contemporary statisticians work with large and complex datasets, which call for large and complex models. Effective implementation of such models is only possible with modern computing hardware, good programming skills and computational algorithms.

Learn a range of techniques and associated algorithms relevant to statistics and AI and enhance your R and Python programming abilities through the implementation of these algorithms. Develop your competence in constructing computer programs by combining classical statistical programming with appropriate use of large language AI models. You will implement numerical optimisation techniques, such as gradient descent, and learn to select the most appropriate for a given statistical inference problem. You’ll also delve into the toolkit of algorithms used for advanced statistical inference, such as the bootstrap and Markov chain Monte Carlo, while gaining proficiency in your implementation and use.

Statistical models, based on probability distributions or stochastic processes, represent a simplified version of the real-world. By using suitable data to train a statistical model, it can be used to identify patterns or make predictions.

From the fundamentals of statistical inference, such as estimates, estimators and uncertainty, you will explore frequentist and Bayesian estimation. You will construct likelihood functions and learn how to use these to find parameter estimators. Using the asymptotic properties of these estimators, you will quantify the uncertainty in their estimates and conduct principled model selection to obtain a deeper insight into their data. Bayesian estimation starts from the fundamentals of prior and posterior distributions, before tackling more complex concepts such as Bayesian point estimates and predictive distributions. You will conclude the module with an introduction to Monte Carlo estimation.

A highlight of your Master’s degree will be a significant individual project that you will complete under the guidance of a supervisor after finishing your taught modules. You will be allocated a project according to the current research interests of our academic staff along with a dissertation supervisor. You will have the opportunity to find relevant resources and steer the direction of the project supported by regular meetings with your supervisor. At the end, you will be able to showcase your findings, both in written and oral form.

Your dissertation represents a capstone for your degree and will provide you with concrete evidence of your achievements that you will be able to share with others and a strong dissertation may become an entrance point to a PhD if you are interested in further study.

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 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.

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 how to implement 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.

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.

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.

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.

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.