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In this paper, we focus on identifying differentially activated brain regionsusing a light sheet fluorescence microscopy - a recently developed techniquefor whole-brain imaging. Most existing statistical methods solve this problemby partitioning the brain regions into two classes: significantly andnon-significantly activated. However, for the brain imaging problem at thecenter of our study, such binary grouping may provide overly simplisticdiscoveries by filtering out weak but important signals, that are typicallyadulterated by the noise present in the data. To overcome this limitation, weintroduce a new Bayesian approach that allows classifying the brain regionsinto several tiers with varying degrees of relevance. Our approach is based ona combination of shrinkage priors - widely used in regression and multiplehypothesis testing problems - and mixture models - commonly used in model-basedclustering. In contrast to the existing regularizing prior distributions, whichuse either the spike-and-slab prior or continuous scale mixtures, our class ofpriors is based on a discrete mixture of continuous scale mixtures and devisesa cluster-shrinkage version of the Horseshoe prior. As a result, our approachprovides a more general setting for Bayesian sparse estimation, drasticallyreduces the number of shrinkage parameters needed, and creates a framework forsharing information across units of interest. We show that this approach leadsto more biologically meaningful and interpretable results in our brain imagingproblem, since it allows the discrimination between active and inactiveregions, while at the same time ranking the discoveries into clustersrepresenting tiers of similar importance.

A Horseshoe mixture model for Bayesian screening with an application to light sheet fluorescence microscopy in brain imaging