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.