Studies on diffusion tensor imaging (DTI) quantify the diffusion of water molecules in a brain voxel using an estimated 3 × 3 symmetric positive definite (p.d.) diffusion tensor matrix. Due to the challenges associated with modelling matrix‐variate responses, the voxel‐level DTI data are usually summarized by univariate quantities, such as fractional anisotropy. This approach leads to evident loss of information. Furthermore, DTI analyses often ignore the spatial association among neighbouring voxels, leading to imprecise estimates. Although the spatial modelling literature is rich, modelling spatially dependent p.d. matrices is challenging. To mitigate these issues, we propose a matrix‐variate Bayesian semiparametric mixture model, where the p.d. matrices are distributed as a mixture of inverse Wishart distributions, with the spatial dependence captured by a Markov model for the mixture component labels. Related Bayesian computing is facilitated by conjugacy results and use of the double Metropolis–Hastings algorithm. Our simulation study shows that the proposed method is more powerful than competing non‐spatial methods. We also apply our method to investigate the effect of cocaine use on brain microstructure. By extending spatial statistics to matrix‐variate data, we contribute to providing a novel and computationally tractable inferential tool for DTI analysis.

中文翻译：

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正定矩阵的空间贝叶斯半参数混合模型及其在扩散张量成像中的应用

扩散张量成像（DTI）的研究使用估计的3×3量化了脑素中水分子的扩散对称正定（pd）扩散张量矩阵。由于建模矩阵变量响应相关的挑战，体素级DTI数据通常用单变量来汇总，例如分数各向异性。这种方法导致明显的信息丢失。此外，DTI分析通常会忽略相邻体素之间的空间关联，从而导致估算结果不准确。尽管空间建模文献丰富，但对空间相关的pd矩阵进行建模仍具有挑战性。为了缓解这些问题，我们提出了矩阵-变量贝叶斯半参数混合模型，其中pd矩阵作为Wishart逆分布的混合分布，而马尔可夫模型捕获的空间相关性则用于混合成分标签。结合结果和双重Metropolis-Hastings算法的使用促进了相关的贝叶斯计算。我们的仿真研究表明，所提出的方法比竞争性非空间方法更强大。我们还将应用我们的方法来调查可卡因的使用对大脑微结构的影响。通过将空间统计信息扩展到矩阵变量数据，我们为DTI分析提供了一种新颖且易于计算的推理工具。