Wegmann Bertil, Eklund Anders, Villani Mattias
Division of Statistics and Machine Learning, Department of Computer and Information Science, Linköping University, Linköping, Sweden.
Division of Medical Informatics, Department of Biomedical Engineering, Linköping University, Linköping, Sweden.
Front Neurosci. 2017 Oct 20;11:586. doi: 10.3389/fnins.2017.00586. eCollection 2017.
It is well-known that data from diffusion weighted imaging (DWI) follow the Rician distribution. The Rician distribution is also relevant for functional magnetic resonance imaging (fMRI) data obtained at high temporal or spatial resolution. We propose a general regression model for non-central χ (NC-χ) distributed data, with the heteroscedastic Rician regression model as a prominent special case. The model allows both parameters in the Rician distribution to be linked to explanatory variables, with the relevant variables chosen by Bayesian variable selection. A highly efficient Markov chain Monte Carlo (MCMC) algorithm is proposed to capture full model uncertainty by simulating from the joint posterior distribution of all model parameters and the binary variable selection indicators. Simulated regression data is used to demonstrate that the Rician model is able to detect the signal much more accurately than the traditionally used Gaussian model at low signal-to-noise ratios. Using a diffusion dataset from the Human Connectome Project, it is also shown that the commonly used approximate Gaussian noise model underestimates the mean diffusivity (MD) and the fractional anisotropy (FA) in the single-diffusion tensor model compared to the Rician model.
众所周知，扩散加权成像（DWI）数据服从莱斯分布。莱斯分布也与在高时间或空间分辨率下获得的功能磁共振成像（fMRI）数据相关。我们提出了一种针对非中心χ（NC-χ）分布数据的通用回归模型，其中异方差莱斯回归模型是一个突出的特殊情况。该模型允许莱斯分布中的两个参数都与解释变量相关联，相关变量通过贝叶斯变量选择来确定。提出了一种高效的马尔可夫链蒙特卡罗（MCMC）算法，通过从所有模型参数和二元变量选择指标的联合后验分布中进行模拟，来捕捉完整的模型不确定性。模拟回归数据用于证明，在低信噪比下，莱斯模型比传统使用的高斯模型能够更准确地检测信号。使用来自人类连接组计划的扩散数据集还表明，与莱斯模型相比，常用的近似高斯噪声模型在单扩散张量模型中低估了平均扩散率（MD）和分数各向异性（FA）。
