Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging.
Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging.
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连续点参考数据的地统计建模已经被广泛应用于神经成像，因为它可以产生高效和有效的统计推断。然而，扩散张量成像(DTI)，一种表征大脑解剖结构的神经成像技术，产生了肯定的(P.D.)每个体素的矩阵。目前，针对P.D.的地统计学模型还很少。矩阵的提出是因为在P.D.之间引入了空间相关性。适当地使用矩阵是具有挑战性的。在本文中，我们使用空间Wishart过程，一个空间随机过程(随机场)，其中每个P.D.矩阵变量随机变量边缘服从Wishart分布，随机矩阵之间的空间相关性是由潜在的高斯过程引起的。这个过程在无数的空间位置集合上是有效的，并且几乎肯定是连续的，导致了一种合理的空间依赖建模方式。受可卡因使用者DTI数据的启发，我们提出了一个基于空间Wishart过程的空间矩阵-变量回归模型，问题是空间Wishart过程没有闭合的密度函数。因此，我们提出了一种近似方法来获得可行的Cholesky分解模型，我们证明了该模型与空间Wishart过程模型是渐近等价的。采用局部似然逼近方法，实现了快速计算。仿真研究和实际数据应用表明，与其他方法相比，Cholesky分解过程模型具有可靠的推理能力和更好的性能。
Geostatistical modeling for continuous point-referenced data has extensively been applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging technique characterizing the brain’s anatomical structure, produces a positive-definite (p.d.) matrix for each voxel. Currently, only a few geostatistical models for p.d. matrices have been proposed because introducing spatial dependence among p.d. matrices properly is challenging. In this paper, we use the spatial Wishart process, a spatial stochastic process (random field), where each p.d. matrix-variate random variable marginally follows a Wishart distribution, and spatial dependence between random matrices is induced by latent Gaussian processes. This process is valid on an uncountable collection of spatial locations and is almost-surely continuous, leading to a reasonable way of modeling spatial dependence. Motivated by a DTI data set of cocaine users, we propose a spatial matrix-variate regression model based on the spatial Wishart process.A problematic issue is that the spatial Wishart process has no closed-form density function. Hence, we propose an approximation method to obtain a feasible Cholesky decomposition model, which we show to be asymptotically equivalent to the spatial Wishart process model. A local likelihood approximation method is also applied to achieve fast computation. The simulation studies and real data application demonstrate that the Cholesky decomposition process model produces reliable inference and improved performance, compared to other methods.
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影响因子：
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