The setting for most of my research is the field of gravitational-wave (GW) astronomy, which has exploded in scientific relevance and public attention since the first direct detection of GWs by the LIGO detectors in 2015. As a theorist in this field, I apply modern computational and statistical techniques to the two-sided problem of source modelling (describing astrophysical GW sources using general relativity) and data analysis (extracting and measuring GW signals in detector data). My recent focus is on binaries with extreme mass ratios, which will be important sources for the near-future space-based detector LISA. I am also broadly interested in machine learning for science, as well as more fundamental topics in applied and computational statistics.