  Diffusion tensor imaging (DTI) is a prevalent neuroimaging tool in analyzing
the anatomical structure. The distinguishing feature of DTI is that the
voxel-wise variable is a 3x3 positive definite matrix other than a scalar,
describing the diffusion process at the voxel. Recently, several statistical
methods have been proposed to analyze the DTI data. This paper focuses on the
statistical inference of eigenvalues of DTI because it provides more
transparent clinical interpretations. However, the statistical inference of
eigenvalues is statistically challenging because few treat these responses as
random eigenvalues. In our paper, we rely on the distribution of the Wishart
matrix's eigenvalues to model the random eigenvalues. A hierarchical model
which captures the eigenvalues' randomness and spatial auto-correlation is
proposed to infer the local covariate effects. The Monte-Carlo
Expectation-Maximization algorithm is implemented for parameter estimation.
Both simulation studies and application to IXI data-set are used to demonstrate
our proposal. The results show that our proposal is more proper in analyzing
auto-correlated random eigenvalues compared to alternatives.
