In this paper, we focus on identifying differentially activated brain regions using a light sheet fluorescence microscopy - a recently developed technique for whole-brain imaging. Most existing statistical methods solve this problem by partitioning the brain regions into two classes: significantly and non-significantly activated. However, for the brain imaging problem at the center of our study, such binary grouping may provide overly simplistic discoveries by filtering out weak but important signals, that are typically adulterated by the noise present in the data. To overcome this limitation, we introduce a new Bayesian approach that allows classifying the brain regions into several tiers with varying degrees of relevance. Our approach is based on a combination of shrinkage priors - widely used in regression and multiple hypothesis testing problems - and mixture models - commonly used in model-based clustering. In contrast to the existing regularizing prior distributions, which use either the spike-and-slab prior or continuous scale mixtures, our class of priors is based on a discrete mixture of continuous scale mixtures and devises a cluster-shrinkage version of the Horseshoe prior. As a result, our approach provides a more general setting for Bayesian sparse estimation, drastically reduces the number of shrinkage parameters needed, and creates a framework for sharing information across units of interest. We show that this approach leads to more biologically meaningful and interpretable results in our brain imaging problem, since it allows the discrimination between active and inactive regions, while at the same time ranking the discoveries into clusters representing tiers of similar importance.

翻译：本文聚焦于利用光片荧光显微镜——一种近期发展的全脑成像技术——识别差异性激活的脑区。现有统计方法大多通过将脑区划分为显著激活和非显著激活两类来解决该问题。然而，针对本研究核心的脑成像问题，这种二元分组可能因过滤掉数据噪声中通常掺杂的微弱但重要信号，而得出过于简化的发现。为突破这一局限，我们引入一种新的贝叶斯方法，能够将脑区按不同程度的相关性划分为多个层级。该方法结合了回归与多重假设检验中广泛使用的收缩先验，以及基于模型的聚类中常用的混合模型。与现有使用尖峰-板先验或连续尺度混合的正则化先验分布不同，我们的先验类基于连续尺度混合的离散混合，并设计了马蹄铁先验的聚类收缩版本。因此，该方法为贝叶斯稀疏估计提供了更通用的框架，大幅减少了所需收缩参数的数量，并建立了跨兴趣单元的信息共享机制。我们证明，该方法在脑成像问题中能产生更具生物学意义和可解释性的结果，因为它不仅能区分活跃与非活跃区域，同时还能将发现聚类为具有相似重要性的层级。