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

@article{Lan2021GeostatisticalMO, title={Geostatistical modeling of positive definite matrices: An application to diffusion tensor imaging.}, author={Zhou Lan and Brian J. Reich and Joseph Guinness and Dipankar Bandyopadhyay and Liangsuo Ma and F. Gerard Moeller}, journal={Biometrics}, year={2021} }

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 technique characterizing the brain's anatomical structure, produces a positive definite (p.d.) matrix for each voxel. Currently, only a few geostatistical models for p.d. matrices have been proposed because introducing spatial dependence among p.d. matrices properly is… Expand

#### One Citation

Statistical Inference of Auto-correlated Eigenvalues with Applications to Diffusion Tensor Imaging

- Mathematics
- 2021

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 3× 3 positive definite… Expand

#### References

SHOWING 1-10 OF 50 REFERENCES

A spatial Bayesian semiparametric mixture model for positive definite matrices with applications in diffusion tensor imaging

- Mathematics
- 2019

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… Expand

Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging

- Mathematics, Medicine
- Journal of the American Statistical Association
- 2009

The intrinsic regression model, which is a semiparametric model, uses a link function to map from the Euclidean space of covariates to the Riemannian manifold of positive-definite matrices, and develops an estimation procedure to calculate parameter estimates and establish their limiting distributions. Expand

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

- Computer Science, Medicine
- Journal of the American Statistical Association
- 2016

A class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets are developed and it is established that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. Expand

Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging

- Mathematics
- 2009

The statistical analysis of covariance matrices occurs in m any important applications, e.g. in diffusion tensor imaging or longitudinal data analysis. We consider the situation where it is of… Expand

A hitchhiker's guide to diffusion tensor imaging

- Computer Science, Medicine
- Front. Neurosci.
- 2013

A straightforward hitchhiker's guide that will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI. Expand

A Bayesian Spatial Model to Predict Disease Status Using Imaging Data From Various Modalities

- Computer Science, Medicine
- Front. Neurosci.
- 2018

A Bayesian hierarchical model is proposed to predict disease status, which is able to incorporate information from both functional and structural brain imaging scans, and identifies key regions contributing to accurate prediction including caudate, putamen, and fusiform gyrus as well as several sensory system regions. Expand

Local Polynomial Regression for Symmetric Positive Definite Matrices.

- Mathematics, Medicine
- Journal of the Royal Statistical Society. Series B, Statistical methodology
- 2012

An intrinsic local polynomial regression estimate is developed for the analysis of symmetric positive definite (SPD) matrices as responses that lie in a Riemannian manifold with covariate in Euclidean space and is used to detect diagnostic differences between diffusion tensors along fiber tracts in a study of human immunodeficiency virus. Expand

Accounting for Spatial Dependence in the Analysis of SPECT Brain Imaging Data

- Mathematics
- 2007

The size and complexity of brain imaging databases confront statistical analysts with a variety of issues when assessing brain activation differences between groups of subjects. Detecting small group… Expand

Nonstationary multivariate process modeling through spatially varying coregionalization

- Mathematics
- 2004

Models for the analysis of multivariate spatial data are receiving increased attention these days. In many applications it will be preferable to work with multivariate spatial processes to specify… Expand

Mapping the Voxel-Wise Effective Connectome in Resting State fMRI

- Physics, Medicine
- PloS one
- 2013

This work depicted the voxel-wise hubs of incoming and outgoing information, called Granger causality density (GCD), as a complement to previous repertoire of functional and anatomical connectomes, and could open the way to a new description of global organization and information influence of brain function. Expand