Motivated by problems from neuroimaging in which existing approaches make use of "mass univariate" analysis which neglects spatial structure entirely, but the full joint modelling of all quantities of interest is computationally infeasible, a novel method for incorporating spatial dependence within a (potentially large) family of model-selection problems is presented. Spatial dependence is encoded via a Markov random field model for which a variant of the pseudo-marginal Markov chain Monte Carlo algorithm is developed and extended by a further augmentation of the underlying state space. This approach allows the exploitation of existing unbiased marginal likelihood estimators used in settings in which spatial independence is normally assumed thereby facilitating the incorporation of spatial dependence using non-spatial estimates with minimal additional development effort. The proposed algorithm can be realistically used for analysis of %smaller subsets of large image moderately sized data sets such as $2$D slices of whole $3$D dynamic PET brain images or other regions of interest. Principled approximations of the proposed method, together with simple extensions based on the augmented spaces, are investigated and shown to provide similar results to the full pseudo-marginal method. Such approximations and extensions allow the improved performance obtained by incorporating spatial dependence to be obtained at negligible additional cost. An application to measured PET image data shows notable improvements in revealing underlying spatial structure when compared to current methods that assume spatial independence.
翻译:由神经成形引起的问题,即现有方法使用完全忽视空间结构的“mas univariate univariate”分析,完全忽视空间结构,但所有利益量的全面联合建模在计算上是行不通的,这是将空间依赖纳入模型选择问题(可能很大)大家庭中的一种新颖方法。空间依赖通过Markov随机实地模型进行编码,为此,通过进一步扩大基础国家空间,开发并扩展了假边际马尔科诺夫链 Monte Carlo 算法的变式。这一方法允许利用在通常假定空间独立的环境中使用的现有不带偏见的边际概率估测算器,从而便利利用非空间估计数纳入空间依赖性,同时作出最低限度的额外发展努力。提议的算法可以现实地用于分析大型图像中度数据集的%最小子集,如3美元整张动态PET脑图像的2D切片或其他感兴趣区域。拟议方法的精确近似值,加上以扩大空间空间空间空间为基础的简单扩展,将获得类似结果,从而利用非空间独立的估计性估计性估计性估计性平面图像,从而得出了可测量性地平面图像的改进。