Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging

Area of Science:

• Neuroimaging
• Geostatistics
• Statistical modeling

Background:

• Diffusion tensor imaging (DTI) generates positive-definite matrices, posing challenges for traditional geostatistical modeling.
• Existing geostatistical models for DTI data are limited due to the difficulty in properly introducing spatial dependence among matrices.

Purpose of the Study:

• To propose a novel spatial matrix-variate regression model for DTI data using the spatial Wishart process.
• To address the lack of a closed-form density function for the spatial Wishart process by developing an approximation method.

Main Methods:

• Utilized the spatial Wishart process, a spatial stochastic process with latent Gaussian processes to induce spatial dependence.
• Developed a feasible Cholesky decomposition model as an approximation to the spatial Wishart process.
• Applied a local likelihood approximation for efficient computation.

Main Results:

• The proposed Cholesky decomposition model is asymptotically equivalent to the spatial Wishart process.
• Simulation studies and real DTI data application demonstrated reliable inference.
• The Cholesky decomposition model showed improved performance compared to existing methods.

Conclusions:

• The developed Cholesky decomposition model provides a valid and efficient approach for geostatistical modeling of DTI data.
• This method enhances the analysis of brain anatomical structure from DTI neuroimaging.
• The model shows promise for applications in understanding neurological conditions, such as in cocaine users.