论文标题

带有空间全局尖峰和斜杠的贝叶斯图像在影片上的回归先验

Bayesian Image-on-Scalar Regression with a Spatial Global-Local Spike-and-Slab Prior

论文作者

Zeng, Zijian, Li, Meng, Vannucci, Marina

论文摘要

在本文中,我们提出了一个新型的空间全局 - 本地尖峰和slab选择。我们考虑了用于图像平滑的贝叶斯分层高斯过程模型,该模型在处理图像内依赖性之前使用灵活的逆宽道过程,并提出了一般的全球空间空间选择,该过程扩展了一类丰富的选择的选择先验。与现有构造不同,我们通过引入“参与率”参数来衡量单个协变量影响观察到的图像的概率,从而实现同时的全局(即,在协变量级别)和局部(即在像素/体素级级别上)选择。这与坚硬的策略一起导致在两个级别的选择之间的依赖性,在本地层面引入额外的稀疏性,并允许以基于模型的方式通过本地选择来告知全局选择。我们设计了一个有效的Gibbs采样器,可以推断大型图像数据。我们在模拟数据上显示参数可解释并导致有效的选择。最后,我们通过使用自闭症脑成像数据交换(ABIDE)研究的数据来证明所提出的模型的性能。据我们所知,所提出的模型构建是贝叶斯文献中的第一个同时实现图像平滑,参数估计和两级变量的选择。

In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart process prior to handle within-image dependency, and propose a general global-local spatial selection prior that extends a rich class of well-studied selection priors. Unlike existing constructions, we achieve simultaneous global (i.e, at covariate-level) and local (i.e., at pixel/voxel-level) selection by introducing `participation rate' parameters that measure the probability for the individual covariates to affect the observed images. This along with a hard-thresholding strategy leads to dependency between selections at the two levels, introduces extra sparsity at the local level, and allows the global selection to be informed by the local selection, all in a model-based manner. We design an efficient Gibbs sampler that allows inference for large image data. We show on simulated data that parameters are interpretable and lead to efficient selection. Finally, we demonstrate performance of the proposed model by using data from the Autism Brain Imaging Data Exchange (ABIDE) study. To the best of our knowledge, the proposed model construction is the first in the Bayesian literature to simultaneously achieve image smoothing, parameter estimation and a two-level variable selection for image-on-scalar regression.

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