We are interested in applications of pure mathematics and mathematical statistics to causal questions in population biomedicine and public health policy. We take a cross-disciplinary approach, collaborating closely with experts from diverse backgrounds. Where possible, we develop and take advantage of model-independent methods in mathematical statistics and machine learning, such as Targeted Learning.

Targeted Learning allows for the construction of estimators of biological quantities that can be mathematically proven to have an optimal bias-variance trade-off. This is essential in light of the arrival of truly large-scale databases, such as the UK Biobank, as size presents novel challenges to current statistical techniques: ever more precise measurements (smaller variance) expose untrue biological or modelling assumptions (bias). Since it is rarely possible to quantify bias a posteriori, we employ deep mathematical theory to obtain a priori control over bias.

Currently, our research is focussed on two contexts:

1. Pure mathematics: We are interested in repurposing and extending existing parts of pure mathematics for applications to biomedicine, such as topological data analysis, algebraic statistics, and model-independent statistics, applied to, e.g., single-cell sequencing data.
2. Population biomedicine: We develop and apply mathematical and statistical techniques in the framework of Targeted Learning to extract precise answers to causal biological questions from large population-scale databases, such as the UK Biobank and Generation Scotland. The aim is to identify variants in the genome that are causal of complex trait or disease, as well as designing public health policy more generally.