Spatial von-Mises Fisher Regression for Directional Data

TL;DR

This paper introduces a novel Bayesian spatial regression model for directional data using von Mises Fisher distribution, enabling analysis of covariate effects and spatial dependence with applications in neuroscience.

Contribution

It proposes a new generalized linear model with a specialized link function and spatial autoregression for directional data, along with a comprehensive Bayesian inference framework.

Findings

Applied to ADNI data revealing relationships between brain fiber orientations and cognitive impairment

Demonstrated computational efficiency and flexibility of the proposed model

Validated through simulation experiments showing accurate inference

Abstract

Spatially varying directional data are routinely observed in several modern applications such as meteorology, biology, geophysics, engineering, etc. However, only a few approaches are available for covariate-dependent statistical analysis for such data. To address this gap, we propose a novel generalized linear model to analyze such that using a von Mises Fisher (vMF) distributed error structure. Using a novel link function that relies on the transformation between Cartesian and spherical coordinates, we regress the vMF-distributed directional data on the external covariates. This regression model enables us to quantify the impact of external factors on the observed directional data. Furthermore, we impose the spatial dependence using an autoregressive model, appropriately accounting for the directional dependence in the outcome. This novel specification renders computational efficiency and flexibility. In addition, a comprehensive Bayesian inferential toolbox is thoroughly developed and applied to our analysis. Subsequently, employing our regression model on the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, we gain new insights into the relationship between cognitive impairment and the orientations of brain fibers, along with examining empirical efficacy through simulation experiments. The code for implementing our proposed method is available on GitHub: https://github.com/lanzhouBWH/Spatial_VMF_Regression.