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Abstract:
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This project is motivated by the observation that many biological and physical signals exhibit an almost periodic behavior. For example, the electrocardiogram (ECG), machinery, telecommunication, or econometric signals. The goal of this project is to investigate the class of non-stationary models and identify a subclass that can capture this almost periodic behavior in brain electrical signals collected from a designed experiment. We will generalize these models to include a fixed effect and random effect components. The purpose of the fixed effect is to allow for direct comparison between the different stimulus types and different populations; the purpose of the random effect will be to model the variation of the brain response across many repeated presentations of each stimulus. We will examine the limitations of the existing models and propose new generalizations that are well suited for brain electrical signals. Moreover, we will develop a procedure for performing statistical inference and examine its behavior in various numerical experiments. This is joint work with A. Dudek (AGH, Poland), A. Napolitano (Univ Parthenope, Italy) and H. Ombao (KAUST, Saudi Arabia).
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