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 moderately sized data sets such as 2D slices of whole 3D 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.

受神经成像问题的启发，其中现有方法利用“质量单变量”分析完全忽略空间结构，但所有感兴趣量的完整联合建模在计算上是不可行的，这是一种将空间依赖性纳入（可能很大）的新方法提出了一系列模型选择问题。空间相关性通过马尔可夫随机场模型进行编码，通过进一步扩展底层状态空间，开发并扩展了伪边际马尔可夫链蒙特卡罗算法的变体。这种方法允许利用在通常假设空间独立性的环境中使用的现有无偏边际似然估计量，从而以最小的额外开发工作促进使用非空间估计结合空间依赖性。所提出的算法可以实际用于分析中等大小的数据集，例如整个 3D 动态 PET 脑图像的 2D 切片或其他感兴趣区域。对所提出方法的原则性近似以及基于增强空间的简单扩展进行了研究，并显示其提供了与完整伪边际方法相似的结果。这种近似和扩展允许以可忽略的额外成本获得通过结合空间依赖性获得的改进性能。