Abstract:
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Diffusion tensor imaging (DTI), a popular magnetic resonance imaging technique, is used to characterize structural changes in the brain. DTI quantify the diffusion of water molecules via a voxel-level positive definite matrix. Because statistical analysis for DTI data is challenging due to modeling matrix-variate positive definite matrices, matrix-variate information is often summarized to a univariate quantity, such as the fractional anisotropy, leading to loss of information. To mitigate these issues, we propose a matrix-variate semiparametric mixture model under a Bayesian paradigm, where the positive definite matrices are distributed as a mixture of inverse Wishart distributions with the spatial dependence captured by a Markov model for the mixture component labels. The nice conjugacy and double Metropolis-Hastings algorithm result in a fast and elegant Bayesian computing. The simulation results show that our method is powerful and robust. We apply this method to the cocaine users data and investigate the effect of cocaine use on brain structure. Our work provides a novel statistical inference tool in DTI analysis and extends classic spatial statistics to matrix-variate data.
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