The current working title of the thesis is "Bayesian Methods and Stochastic Variability Modelling in High-Energy Astrophysics".

The aim of this thesis is to review, apply and extend current methods in Bayesian statistical modelling for astronomical data. In particular, the primary focus of this research is the modelling of the time variability of high-energy astrophysical sources such as quasars or X-ray binaries. Under this theme, the structure of the project will integrate two main research sub-components. The first sub-component will attempt to solve the problem of overlapping astronomical sources, and the method currently under development has potential applications in statistical satellite imagery processing. The astrophysics community is worried that the SpaceX satellite constellation will pollute the imagery produced by the much anticipated Legacy Survey of Space and Time (LSST) of the Vera C. Rubin Observatory. This method could be used to pre-process satellite trails off the LSST imagery and provide clean images for follow-up analysis. In addition to improving and extending the models currently used to solve this problem, the project also focuses on designing highly efficient and scalable algorithms and developing a powerful tool that astrophysicists can integrate in their current research processes. The second sub-component will attempt to solve the problem of the inconsistent Hubble constant measurements by providing a probabilistic estimation of this physical quantity of interest. This involves developing flexible and scalable methods to model astronomical time series. The novelty of the research methodology resides in the design of state-of-the-art modelling and computational techniques to draw new insights from complex data. The immediate impact of this research will be on statistical analysis of astronomical data, but the developed methods are conceived to be highly generalizable and will be applicable to many different fields. This project falls within the EPSRC "Statistics and Applied Probability research area. This project is supervised by Prof. David van Dyk (Imperial College London), and a number of astrophysicists from the Harvard-Smithsonian Center for Astrophysics are also involved.

The primary CDT impact will be training 75 PhD graduates as the next generation of leaders in statistics and statistical machine learning. These graduates will lead in industry, government, health care, and academic research. They will bridge the gap between academia and industry, resulting in significant knowledge transfer to both established and start-up companies. Because this cohort will also learn to mentor other researchers, the CDT will ultimately address a UK-wide skills gap. The students will also be crucial in keeping the UK at the forefront of methodological research in statistics and machine learning.
After graduating, students will act as multipliers, educating others in advanced methodology throughout their career. There are a range of further impacts:
- The CDT has a large number of high calibre external partners in government, health care, industry and science. These partnerships will catalyse immediate knowledge transfer, bringing cutting edge methodology to a large number of areas. Knowledge transfer will also be achieved through internships/placements of our students with users of statistics and machine learning.
- Our Women in Mathematics and Statistics summer programme is aimed at students who could go on to apply for a PhD. This programme will inspire the next generation of statisticians and also provide excellent leadership training for the CDT students.
- The students will develop new methodology and theory in the domains of statistics and statistical machine learning. It will be relevant research, addressing the key questions behind real world problems. The research will be published in the best possible statistics journals and machine learning conferences and will be made available online. To maximize reproducibility and replicability, source code and replication files will be made available as open source software or, when relevant to an industrial collaboration, held as a patent or software copyright.