Abstract
We consider how to specify prior distributions for top-level scale parameters in a sparse hierarchical regression model with many predictors and many responses. Our model borrows information across responses through a parameter that captures the “propensity” of a predictor to be a hotspot, i.e., to influence several responses at once. It can detect associations between p = 10E4 − 10E6 predictors (e.g., genetic variants) and q = 10E2 − 104 responses (e.g., molecular expression levels), but for very large q, inference can be sensitive to the variance of the hotspot “propensity”. While this sensitivity can be cast as a general problem of specifying prior distributions in variance components, we show that it is also caused by a lack of adjustment for the number of responses considered. To solve this problem, we introduce a control parameter which depends on q as part of a global-local hotspot prior variance based on the Horseshoe prior. Our proposal shrinks noise globally and hence adapts to the sparse context of eQTL analyses, while being robust to individual signals, thus leaving the effects of hotspot genetic variants unshrunk. It can therefore detect important pleiotropic effects, of particular interest for current research in genetics. Inference is carried out using an annealed Variational Bayes procedure, which allows fast and efficient exploration of multimodal distributions. If time will permit, we will also illustrate an extension to include annotation to help the detection of important associations while retaining the computational advantages of the Variational Bayes formulation. We illustrate the benefits of proposed models on simulated data sets and two real examples that aim to detect hotspots pleiotropic effects in eQTL experiments.
This is a joint work with Ruffieux Helene (EPFL) and Sylvia Richardson (MRC-BSU).
Junior talk
The junior talk will be given by David Swanson on “Parametric cluster of cluster assignments for multi-omic data integration."