Bayesian nonparametric methods for spectral analysis of complex brain signals

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Complex multiple time series are often recorded in several applied areas of research such as neuroscience, environmetrics, and econometrics. This project develops Bayesian nonparametric methods and related computational tools for frequency-domain analysis of multiple time series. In particular, the statistical approaches that will be developed in this project are motivated by the need to analyze brain signals recorded in clinical and non-clinical studies including electroencephalograms, fMRI data, and magnetoencephalograms.A novel and flexible mixture modeling framework will be used to represent the spectral characteristics of multiple time series. Computationally efficient algorithms will be implemented, tested and used to analyze complex and large-dimensional brain signals. These algorithms will make use of a variety of computational methods for inference in Bayesian nonparametric models. The models and methods that will be developed have the following key features: (i) they will provide flexible representations of the spectral densities of multiple signals as well as computational feasibility (ii) they will allow researchers to investigate clustering patterns of multiple time series with similar spectral characteristics, and (iii) they will incorporate hierarchical settings that can appropriately accommodate neuroscience data sets involving multiple trials, multiple subjects and/or relevant covariates. The research project has the potential of impacting data-intensive neuroscience research that requires the analysis of several complex brain signals.