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

Finding parsimonious models through variable selection is a fundamental problem in many areas of statistical inference. Here, we focus on Bayesian regression models, where variable selection can be implemented through a regularizing prior imposed on the distribution of the regression coefficients. In the Bayesian literature, there are two main types of priors used to accomplish this goal: the spike-and-slab and the continuous scale mixtures of Gaussians. The former is a discrete mixture of two distributions characterized by low and high variance. In the latter, a continuous prior is elicited on the scale of a zero-mean Gaussian distribution. In contrast to these existing methods, we propose a new class of priors based on discrete mixture of continuous scale mixtures providing a more general framework for Bayesian variable selection. To this end, we substitute the observation-specific local shrinkage parameters (typical of continuous mixtures) with mixture component shrinkage parameters. Our approach drastically reduces the number of parameters needed and allows sharing information across the coefficients, improving the shrinkage effect. By using half-Cauchy distributions, this approach leads to a cluster-shrinkage version of the Horseshoe prior. We present the properties of our model and showcase its estimation and prediction performance in a simulation study. We then recast the model in a multiple hypothesis testing framework and apply it to a neurological dataset obtained using a novel whole-brain imaging technique

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

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 nonsignificantly 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

Imaging the dynamic recruitment of monocytes to the blood-brain barrier and specific brain regions during Toxoplasma gondii infection.

Brain infection by the parasite Toxoplasma gondii in mice is thought to generate vulnerability to predation by mechanisms that remain elusive. Monocytes play a key role in host defense and inflammation and are critical for controlling T. gondii However, the dynamic and regional relationship between brain-infiltrating monocytes and parasites is unknown. We report the mobilization of inflammatory (CCR2+Ly6Chi) and patrolling (CX3CR1+Ly6Clo) monocytes into the blood and brain during T. gondii infection of C57BL/6J and CCR2RFP/+CX3CR1GFP/+ mice. Longitudinal analysis of mice using 2-photon intravital imaging of the brain through cranial windows revealed that CCR2-RFP monocytes were recruited to the blood-brain barrier (BBB) within 2 wk of T. gondii infection, exhibited distinct rolling and crawling behavior, and accumulated within the vessel lumen before entering the parenchyma. Optical clearing of intact T. gondii-infected brains using iDISCO+ and light-sheet microscopy enabled global 3D detection of monocytes. Clusters of T. gondii and individual monocytes across the brain were identified using an automated cell segmentation pipeline, and monocytes were found to be significantly correlated with sites of T. gondii clusters. Computational alignment of brains to the Allen annotated reference atlas [E. S. Lein et al., Nature 445:168-176 (2007)] indicated a consistent pattern of monocyte infiltration during T. gondii infection to the olfactory tubercle, in contrast to LPS treatment of mice, which resulted in a diffuse distribution of monocytes across multiple brain regions. These data provide insights into the dynamics of monocyte recruitment to the BBB and the highly regionalized localization of monocytes in the brain during T. gondii CNS infection