I am a second year PhD student in the Oxford-Warwick Statistics Programme (OxWaSP). Currently, I am working under the supervision of Professor Bärbel Finkenstädt Rand on non-stationary and multivariate spectral analysis of time series, with application to circadian biomarkers for cancer chronotherapy and experiments on rodents to detect instances of sleep apnoea. Outside of my research interests I am a passionate footballer, a poker player and an electronic music producer.
The analysis of time series that show oscillatory and - more or less - periodic behaviour is a common task in many sciences. In particular, the nonstationary analysis of cyclical data that show regime shifts in periodicity, amplitude and phase is challenging as the timing and number of such changes is usually unknown. We propose a methodology for detecting such regime shifts using a Bayesian trans-dimensional Markov chain Monte Carlo algorithm which allows for model searches between parameters subspaces of different dimensionality. Our algorithm incorporates two model searches, namely the number of regimes and the harmonic model that captures the relevant frequencies along with their amplitudes and phases within each regime. We illustrate the use of the methodology for data from experiments on rodents to detect instances of sleep apnoea.
Moreover, we are hoping to develop statistical methodologies, in particular novel univariate and multivariate spectral analysis tools that are able to address in real time the non stationary nature of the incoming data as an individual’s circadian timing systems changes over time with the development of the disease and intermittent treatment courses.