Title: A semiparametric mixture model for positive-definite matrices with applications to neuroimaging
Authors: Dipankar Bandyopadhyay - Virginia Commonwealth University (United States) [presenting]
Brian Reich - North Carolina State University (United States)
Zhou Lan - Yale School of Medicine (United States)
Abstract: Studies on diffusion tensor imaging (DTI) quantifies the diffusion of water molecules in a brain voxel, using an estimated 3x3 symmetric positive definite (p.d.) diffusion tensor matrix. Due to the challenges associated with modeling matrix-variate responses, the voxel-level DTI data is usually summarized by univariate quantities, such as the fractional anisotropy (FA). This leads to evident loss of information. Furthermore, DTI analyses often ignore the spatial associationamong neighboring voxels, leading to imprecise estimates. Although the spatial modeling literature is abundant, modeling spatially dependent p.d. matrices is challenging. To mitigate these issues, we propose a matrix-variate Bayesian semiparametric mixture model, where the p.d. matrices are distributed as a mixture of inverse Wishart distributions, with the spatial dependence captured by a Markov model for the mixture component labels. Related Bayesian computing is facilitated by conjugacy results, and the implementation of the double Metropolis-Hastings algorithm. The simulation study shows that the proposed method is more powerful than the non-spatial methods. We also apply our method to investigate the effect of cocaine use on brain microstructure. By extending spatial statistics to matrix-variate data, we contribute to providing a novel and computationally tractable inferential tool for DTI analysis.