Title: New challenges in high-dimensional statistical inference
Funder: Engineering and Physical Sciences Research Council

Abstract: As a society, more and more of the activities that we take for granted rely on sophisticated technology, and are dependent on the fast and efficient handling of large quantities of data. Obvious examples include the use of internet search engines and mobile telephones. Similarly, recent advances in healthcare are partly due to improved, highly data-intensive scanning equipment in hospitals, and the development of new, effective drug treatments, which have been the result of extensive scientific study with data at its core. Nevertheless, such advances can only be achieved through the development of appropriate statistical models and methods which enable practitioners to extract useful information from these vast quantities of data. In order to capture the complexity of the data generating processes, these models are inevitably high-dimensional, and have been the topic of an enormous amount of research in Statistics over the last 15 years or so. This proposal addresses some of the fundamental and important challenges in handling the huge data sets that routinely arise in the applications above, as well as many others. For instance, in high-dimensional models, sparse estimators are crucial for stability and interpretability. But these give only a point estimate of a parameter, and typically practioners require more sophisticated inferential statements to assess uncertainty. We will show how this by done by proposing easy-to-use and robust p-values based on these sparse estimators. One of the most important applications of sparse estimators is in biotechnology. Indeed, we will apply our methodology described above in a high-dimensional cancer study carried out by Danish biostatisticians that uses microarray techniques. We will select, with an associated quantification of uncertainty, a handful of stable distinguishing genes for diffuse large B-cell lymphomas, thereby enhancing our understanding of these cancers. Another application area facing high-dimensional challenges is neuroscience, and we will work on a study of dyscalculia that uses the brain imaging technique of Electroencephalography (EEG). Dyscalculia is a mathematical disability that prevents normal arithmetic function. Here, existing statistical techniques used by experimental psychologists in this area are inadequate, and modern high-dimensional methods have the potential to improve dramatically our understanding of this disability. In classification problems, the challenge is to assign an observation to one of two or more classes based on its similarity to (labelled) data from each of these classes. They are some of the most frequently encountered high-dimensional statistical problems, particularly in fields such as machine learning and areas of computer science such as computer vision and robotics. We will provide a simple and robust improvement to perhaps the most popular method (the k-nearest neighbour classifier), by weighting the nearest neighbours in an optimal fashion. We will also give a quantification of the improvement. A related problem we will study is to quantify the uncertainty of a classifier constructed from training data. As an example this could be used to give a doctor a measure of uncertainty in a diagnosis. The final main issue we will address concerns model misspecification. This is a particularly important issue in high-dimensional statistical problems, where it is almost inevitable that our model misses some important effects, or does not model them in the correct way. We will provide understanding of how statistical procedures perform in such circumstances and develop new ones that are robust to model misspecification. A particularly important application will be to Independent Component Analysis models that are very popular in statistical signal processing for analysing data arising from multiple sources, including microarray and brain imaging data.


Research activity codes: 2.4 SURVEILLANCE AND DISTRIBUTION;2.1 BIOLOGICAL AND ENDOGENOUS FACTORS
Health categories: NEUROLOGICAL;CANCER AND NEOPLASMS