Abstract
In this presentation, we present in detail the seminal work of Wang et al. “Sum of Single Effects” (SuSiE) model (JRSSB 2021) — introducing a simple new approach to variable selection in linear regression, with a particular focus on quantifying uncertainty in which variables should be selected. We also introduce a corresponding new fitting procedure — Iterative Bayesian Stepwise Selection (IBSS) — which is a Bayesian analogue of stepwise selection methods. IBSS shares the computational simplicity and speed of traditional stepwise methods, but instead of selecting a single variable at each step, IBSS computes a distribution on variables that captures uncertainty in which variable to select. We provide a formal justification of this intuitive algorithm by showing that it optimizes a variational approximation to the posterior distribution under the SuSiE model. Finally, we will discuss extension of the SuSiE model to summary statistics regression and functional phenotypes.