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Title: Bayesian analysis of nonstationary periodic time series Authors:  Beniamino Hadj-Amar - Rice University (United States) [presenting]
Mark Fiecas - University of Minnesota (United States)
Barbel Finkenstadt - University of Warwick (United Kingdom)
Francis Levi - Warwick Medical School - University of Warwick (United Kingdom)
Robert Huckstepp - School of Life Sciences - University of Warwick (United Kingdom)
Abstract: Statistical methodology for identifying periodicities in cyclical phenomenon allows us to gain insight into the sources of variability that drive such a phenomenon. Non-stationary behavior seems to be the norm rather than the exception in physiological time series as time-varying periodicities, and other forms of rich dynamical patterns are commonly observed. We address these challenges and present two novel Bayesian methodologies for the automated analysis of these types of data. First, we propose to approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Second, we present a non-parametric HMM where the states are defined through the spectral properties of a periodic regime. This approach further quantifies the probabilistic mechanism governing the transitions and recurrence of distinct periodic patterns. We show that the proposed methodologies are successfully applied in several applications that are relevant to e-Health and sleep research.