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Title: Wavelet spectra for multivariate point processes Authors:  Ed Cohen - Imperial College London (United Kingdom) [presenting]
Alex Gibberd - Lancaster University (United Kingdom)
Abstract: Humans are harvesting vast event datasets that manifest themselves as a list of times at which particular events of interest occur. Often these are multivariate in nature, with events being of different types or arriving on multiple channels. A key question is to what extent the data-generating point processes are correlated and to track non-stationary correlation structure. Wavelets provide the flexibility to analyse stochastic processes at different scales in a time-localised manner and have had a profound impact in statistics, particularly in time series analysis. We apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across component processes. To provide statistical tractability, a temporally smoothed wavelet periodogram is developed and distributional results are extended to wavelet coherence; a time-scale measure of inter-process correlation. This statistical framework is further used to construct a test for stationarity in multivariate point-processes. The methodology is applied to neural spike train data, where it is shown to detect and characterise time-varying dependency patterns.