Bayesian Inference in Astrophysics: Applications to Gravitational-Wave Memory and Quasi-Periodic Oscillations

In this thesis, I explore how Bayesian inference, a key statistical technique in astrophysics, can be used to analyse some of the most energetic phenomena. First, I show that we can use inference to find small deviations in the models of gravitational waves, specifically the gravitational-wave memory effect. Gravitational waves are sourced in the collision of black holes and finding the memory effect is an important test of prevalent theories. I also show that inference is a useful tool to develop and evaluate models for x-ray signals, specifically to search for oscillatory behaviour.