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Activity Number: 346 - New Methods with Applications in Mental Health Statistics
Type: Contributed
Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
Sponsor: Mental Health Statistics Section
Abstract #304259 Presentation
Title: A Spatial Bayesian Semiparametric Mixture Model for Positive Definite Matrices with Applications to Diffusion Tensor Imaging
Author(s): Zhou Lan* and Brian Reich and Dipankar Bandyopadhyay
Companies: North Carolina State University and North Carolina State University and Virginia Commonwealth University
Keywords: Bayesian semiparametrics; Diffusion tensor imaging; Inverse Wishart distribution; Matrix-variate; Positive definite matrix; Spatial statistics
Abstract:

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.


Authors who are presenting talks have a * after their name.

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