This is an extension of the Fellowship 'New challenges in high-dimensional statistical inference' (EP/J017213/1). The project will involve developing methodology and theory for a range of modern statistical problems from high-dimensional and nonparametric statistical inference. Such problems lie at the heart of modern data science, an area where the UK urgently needs to grow its capacity. Specific challenges to be addressed include the development of methods for dimension reduction, variable selection and uncertainty quantification, among several others. These are some of the fundamental problems faced by practitioners in the Big Data era, and demand highly innovative solutions. Our proposed techniques will be proven to be robust via appropriate theoretical justification, and will be implemented in free, open source software so as to maximise the impact of the research.

Brain infections, such as bacterial meningitis, still cause death and disability in the UK and worldwide. The key decision for a doctor is to decide whether a patient has bacterial meningitis, or whether they have a similar condition (a clinical mimic), such as viral meningitis. In both cases the patient often looks the same. However, bacterial infection needs immediate treatment with antibiotics whereas a mimic does not. The essential test for distinguishing between the two is the lumbar puncture (a needle passing between the bones in the spine). The lumbar puncture is often delayed, or not performed at all. This can result in delayed antibiotic treatment for those who need it, or unnecessary antibiotics in those who do not, as well as a patient not receiving a diagnosis. We offer a novel test measuring the body's response to bacterial infection in the blood. This means patients can be tested without having to wait for the lumbar puncture. We believe this test will help doctors to more accurately decide which patients do or do not need antibiotics. This will promote appropriate treatment, reduce unnecessary antibiotics, reduce in-patient stay, improve patient care and reduce the burden on health staff and hospitals. We are working with an industrial company who are experts in developing diagnostic tests, to develop our test for clinical use. We are also linking with many expert clinical teams in the UK, Europe, Brazil and Africa to assess our test on a large number of patients to ensure it is accurate. Through this project we will confirm the test is accurate and refine the test so that it can be used in hospitals in under the next 5 years.