Spike‐and‐Slab Priors and Their Applications

Abstract

Over the last decades, high‐dimensional datasets, notably with large p , small n , have become commonplace in a wide range of applications in several fields, such as medicine, genomics, ecology, astronomy, finance, image processing, and social networks. At the same time, Bayesian variable selection methods have experienced substantial development. Specifically, the spike‐and‐slab mixture priors have been an important tool for most high‐dimensional variable selection and shrinkage methods in the Bayesian framework. Thus, in this article, we briefly review discrete and continuous spike‐and‐slab priors in linear settings, as well as their extensions to a wide variety of statistical problems. Our focus, however, will be on the variable selection and parameter estimation in linear regression models with compositional covariates via the spike‐and‐slab LASSO procedure.