论文标题
空间von-Mises Fisher回归方向数据
Spatial von-Mises Fisher Regression for Directional Data
论文作者
论文摘要
在几种现代应用中（例如气象，生物学，地球物理学，工程学等）通常会观察到空间变化的方向数据。但是，对于此类数据，只有几种方法可用于协方差依赖性统计分析。为了解决这一差距，我们提出了一种新型的广义线性模型来分析，以便使用Von Mises Fisher（VMF）分布式误差结构。使用依赖于笛卡尔和球形坐标之间转换的新型链路函数，我们会在外部协变量上回归VMF分布式的方向数据。该回归模型使我们能够量化外部因素对观察到的方向数据的影响。此外，我们使用自回归模型强加了空间依赖性，并适当考虑了结果的方向依赖性。这项新颖的规范提高了计算效率和灵活性。此外，综合的贝叶斯推论工具箱是彻底开发的，并应用于我们的分析中。随后，我们采用了我们的回归模型，这些模型在阿尔茨海默氏病神经影像学计划（ADNI）数据上，我们获得了对认知障碍与脑纤维方向之间关系的新见解，并通过模拟实验检查经验效果。实施我们提出的方法的代码可在GitHub上获得：https：//github.com/lanzhoubwh/spatial_vmf_regression。
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.
