Bayesian Methods in Brain Connectivity Change Point Detection with EEG Data and Genetic Algorithm

Human brain is processing a great amount of information everyday, and our brain regions are organized optimally for this information processing. There have been increasing number of studies focusing on functional or effective connectivity in human brain regions in the last decade. In this dissertation, Bayesian methods in Brain connectivity change point detection are discussed. First, a review of state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data is carried out, three methods are reviewed and compared. Second, the Bayesian connectivity change point model is extended to change point analysis in electroencephalogram (EEG) data, and the ability of EEG measures of frontal and temporo-parietal activity during mindfulness therapy to track response to dysfunctional anxiety patients\u27 treatment is tested successfully. Then an optimized method for Bayesian connectivity change point model with genetic algorithm (GA) is proposed and proved to be more efficient in change point detection. And due to the good parallel performance of GA, the change point detection method can be parallelized in GPU or multi-processor computers as a future work. Furthermore, a more advanced Bayesian bi-cluster connectivity change point model is developed to simultaneously detect change point of each subject within a group, and cluster subjects into different groups according to their change point distribution and connectivity dynamics. The method is also validated on experimental datasets. After discussing brain change point detection, a review of Bayesian analysis of complex mutations in HBV HCV and HIV studies is also included as part of my Ph.D. work. Finally, conclusions are drawn and future work is discussed

Fast spatial inference in the homogeneous Ising model

The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction are intractable. We provide accurate approximations that make it possible to calculate these quantities numerically. Simulation studies indicate good performance when compared to Markov Chain Monte Carlo methods and at a tiny fraction of the time. The methodology is also used to perform Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment.Comment: 18 pages, 1 figure, 3 table