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Diffusion MRI is a neuroimaging technique measuring the anatomical structure of tissues. Using diffusion MRI to construct the connections of tissues, known as fiber tracking, is one of the most important uses of diffusion MRI. Many techniques are available recently but few properly quantify statistical uncertainties. In this paper, we propose a directed acyclic graph auto-regressive model of positive definite matrices and apply a probabilistic fiber tracking algorithm. We use both real data analysis and numerical studies to demonstrate our proposal.
Diffusion tensor imaging (DTI) is a popular magnetic resonance imaging technique used to characterize microstructural changes in the brain. DTI studies quantify the diffusion of water molecules in a voxel using an estimated 3x3 symmetric positive def
Geostatistical modeling for continuous point-referenced data has been extensively applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging characterizing the brain
In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive definite matr
Estimation of the long-term health effects of air pollution is a challenging task, especially when modelling small-area disease incidence data in an ecological study design. The challenge comes from the unobserved underlying spatial correlation struc
Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time tha