As analytical techniques and instrumentation have advanced, more observations are being produced at higher resolution and incorporating more variables, leading to much larger and more complex datasets. However, statistical methods in the analytical sciences have not always kept pace with the advances in capabilities. In this project you will develop the statistical methods required to extract scientific information from large datasets. Important applications include Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), via which Warwick scientists (including a MAS-CDT student) have recently produced a world record in the number of assigned molecular compositions from a complex petroleum sample. A key aspect of this success was close collaboration between experimentalists and statisticians.
Within the field of NMR crystallography, density-functional theory (DFT) is used to calculate NMR parameters, e.g., chemical shift, so that experimental solid-state NMR results can be compared to predicted values for putative crystal structures. However DFT frequently show a discrepancy of 1% of the chemical shift range when compared with experimental data. This can add considerable uncertainty when trying to identify the correct predicted crystal structure. In this project we will use Bayesian techniques to account for this additional uncertainty in resolving the correct structures.
Technological advances in recent years have resulted in the ample availability of data that can be thought of as realisations of functions defined on some continuous domain. Such data is called "functional data". Examples include hourly temperature measurements in specific locations on the map, speed or heart rate profiles in athletic activity, concentrations of pollutants over space and in time, speech recordings, etc.
One particular type of functional data is obtained by dynamic Optoacoustic Tomography (OT), which is an emerging imaging modality that is currently in clinical trials. OT reveals the distribution of tissue optical absorption in real time, is non-invasive, and allows both high temporal resolution and high spatial resolution imaging. One applications of OT is to quantify how much blood flow there is (also known as 'vascular maturity') in a tumor, and how oxygenated the tumor tissue is, as these are important in cancer staging and therapy monitoring.
While dynamic OT data consists of a high-dimensional temporal profile (curve) per pixel of the imaged tissue, existing methods for dynamic OT analysis are based on univariate user-selected features of the temporal profiles. However much more information is contained in the full temporal profiles obtained by dynamic OT. The goal of this project will be to study such temporal profiles using tools from functional data analysis. In particular, it will be interesting to study the relation between tumor perfusion (as measured by DCE-OT, as particular version of OT) and tumor oxygenation (as measured by OE-OT, another version of OT) using tools from functional regression (the equivalent of regression for functional data), as this could be very useful to better understand tumor function.
There will be expert input from Sarah Bohndiek (Cancer Research UK, Cambridge) and Michal Tomaszewski (Moffitt).