Neural demyelination and brain damage accumulated in white matter appear as hyperintense areas on T2-weighted MRI scans in the form of lesions. Modeling binary images at the population level, where each voxel represents the existence of a lesion, plays an important role in understanding aging and inflammatory diseases. We propose a scalable hierarchical Bayesian spatial model, called BLESS, capable of handling binary responses by placing continuous spike-and-slab mixture priors on spatially-varying parameters and enforcing spatial dependency on the parameter dictating the amount of sparsity within the probability of inclusion. The use of mean-field variational inference with dynamic posterior exploration, which is an annealing-like strategy that improves optimization, allows our method to scale to large sample sizes. Our method also accounts for underestimation of posterior variance due to variational inference by providing an approximate posterior sampling approach based on Bayesian bootstrap ideas and spike-and-slab priors with random shrinkage targets. Besides accurate uncertainty quantification, this approach is capable of producing novel cluster size based imaging statistics, such as credible intervals of cluster size, and measures of reliability of cluster occurrence. Lastly, we validate our results via simulation studies and an application to the UK Biobank, a large-scale lesion mapping study with a sample size of 40,000 subjects.

翻译：多发性硬化引起的神经脱髓鞘及脑白质损伤在T2加权MRI扫描中表现为高信号区域，即病灶。在群体水平上对每个体素代表病灶存在与否的二值图像进行建模，对于理解衰老和炎症性疾病具有重要作用。我们提出一种可扩展的分层贝叶斯空间模型（BLESS），该模型通过在空间变化参数上施加连续型尖峰-板混合先验，并对控制包含概率中稀疏程度的参数强制施加空间依赖性，从而能够处理二值响应变量。采用基于动态后验探索的均值场变分推断（一种类似退火的优化改进策略），使该方法可扩展至大样本量。针对变分推断导致的后验方差低估问题，我们结合基于贝叶斯自举思想的近似后验采样方法及具有随机收缩目标的尖峰-板先验，提供了解决方案。除精准的不确定性量化外，该方法还能生成基于簇尺寸的新型影像统计量，例如簇尺寸的置信区间及簇发生可靠度指标。最后，我们通过模拟研究及针对英国生物银行（UK Biobank）4万样本量的大规模病灶图谱研究验证了结果的有效性。