Optimal spectral tracking--adapting to dynamic regime change.

Real world data do not always obey the statistical restraints imposed upon them by sophisticated analysis techniques. In spectral analysis for instance, an ergodic process--the interchangeability of temporal for spatial averaging--is assumed for a repeat-trial design. Many evolutionary scenarios, such as learning and motor consolidation, do not conform to such linear behaviour and should be approached from a more flexible perspective. To this end we previously introduced the method of optimal spectral tracking (OST) in the study of trial-varying parameters. In this extension to our work we modify the OST routines to provide an adaptive implementation capable of reacting to dynamic transitions in the underlying system state. In so doing, we generalise our approach to characterise both slow-varying and rapid fluctuations in time-series, simultaneously providing a metric of system stability. The approach is first applied to a surrogate dataset and compared to both our original non-adaptive solution and spectrogram approaches. The adaptive OST is seen to display fast convergence and desirable statistical properties. All three approaches are then applied to a neurophysiological recording obtained during a study on anaesthetic monitoring. Local field potentials acquired from the posterior hypothalamic region of a deep brain stimulation patient undergoing anaesthesia were analysed. The characterisation of features such as response delay, time-to-peak and modulation brevity are considered.