Cookies on this website
We use cookies to ensure that we give you the best experience on our website. If you click 'Continue' we'll assume that you are happy to receive all cookies and you won't see this message again. Click 'Find out more' for information on how to change your cookie settings.

© Institute of Mathematical Statistics, 2020. We tackle modelling and inference for variable selection in regression problems with many predictors and many responses. We focus on detecting hotspots, that is, predictors associated with several responses. Such a task is critical in statistical genetics, as hotspot genetic variants shape the architecture of the genome by controlling the expression of many genes and may ini-tiate decisive functional mechanisms underlying disease endpoints. Existing hierarchical regression approaches designed to model hotspots suffer from two limitations: their discrimination of hotspots is sensitive to the choice of top-level scale parameters for the propensity of predictors to be hotspots, and they do not scale to large predictor and response vectors, for example, of dimensions 103 –105 in genetic applications. We address these shortcomings by introducing a flexible hierarchical regression framework that is tailored to the detection of hotspots and scalable to the above dimensions. Our pro-posal implements a fully Bayesian model for hotspots based on the horseshoe shrinkage prior. Its global-local formulation shrinks noise globally and, hence, accommodates the highly sparse nature of genetic analyses while be-ing robust to individual signals, thus leaving the effects of hotspots unshrunk. Inference is carried out using a fast variational algorithm coupled with a novel simulated annealing procedure that allows efficient exploration of multimodal distributions.

Original publication

DOI

10.1214/20-AOAS1332

Type

Journal article

Journal

Annals of Applied Statistics

Publication Date

01/01/2020

Volume

14

Pages

905 - 928