面向方向数据的空间 von-Mises Fisher 回归
Spatial von-Mises Fisher Regression for Directional Data
AI总结：
提出基于 vMF 分布和自回归模型的空间方向数据广义线性回归方法，结合贝叶斯推断，揭示脑神经纤维走向与认知障碍关系。
摘要：
空间变化的方向数据在气象学、生物学、地球物理学、工程学等现代应用中经常被观测到。然而，针对此类数据的协变量依赖性统计分析方法寥寥无几。为填补这一空白，我们提出了一种新型广义线性模型，利用 von Mises Fisher (vMF) 分布的误差结构对此类数据进行分析。通过一种依赖于笛卡尔坐标与球面坐标之间转换的新型链接函数，我们将 vMF 分布的方向数据对外部协变量进行回归。该回归模型使我们能够量化外部因素对观测到方向数据的影响。此外，我们使用自回归模型施加空间依赖性，适当地考虑了结果中的方向依赖性。这种新型设定带来了计算效率和灵活性。此外，我们全面开发了一个综合的贝叶斯推断工具箱，并将其应用于我们的分析中。随后，将我们的回归模型应用于阿尔茨海默病神经影像学计划 (ADNI) 数据，我们获得了关于认知障碍与脑神经纤维走向之间关系的新见解，同时通过模拟实验检验了实证有效性。用于实现我们提出方法的代码可在 GitHub 上获取：https://github.com/lanzhouBWH/Spatial_VMF_Regression。
英文摘要：
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.
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