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:在本文中,我们的重点是利用光薄薄片荧光显微镜(一种最近开发的全脑成像技术)确定不同活跃的大脑区域。大多数现有的统计方法都通过将大脑区域分为两大类来解决这个问题:显著和非显著的激活。然而,对于我们研究中心大脑成像问题,这种二进制组可能通过过滤薄弱但重要的信号而提供过于简单化的发现,这些信号通常被数据中的噪音所混合。为了克服这一限制,我们采用了一种新的巴耶西亚方法,将大脑区域分为几个不同程度的级别,具有不同的重要性。我们的方法是以缩缩进前几个类别相结合的方式解决这个问题的:在回归和多重假设测试问题中广泛使用,而混合模型集成模型集成模式通常使用。相比之下,这种二进制组群群可能会通过过滤薄弱但重要的信号来提供过于简单化的发现。为了克服数据中的噪音,我们以前一类的前类的混合物是以离散混合物为基础,并设计出一个具有不同程度重要性的组合组合版本。作为结果,我们的方法基于一种缩缩缩前两个层次的分类,因此,我们的方法提供了一种更深层次的深度的层次的层次的分类,从而降低了对BAA级的模型进行解释。