Yann McLatchie, Sölvi Rögnvaldsson, Frank Weber, and I (Aki) write in a new preprint “Robust and efficient projection predictive inference”

The concepts of Bayesian prediction, model comparison, and model selection have developed significantly over the last decade. As a result, the Bayesian community has witnessed a rapid growth in theoretical and applied contributions to building and selecting predictive models. Projection predictive inference in particular has shown promise to this end, finding application across a broad range of fields. It is less prone to over-fitting than naïve selection based purely on cross-validation or information criteria performance metrics, and has been known to out-perform other methods in terms of predictive performance. We survey the core concept and contemporary contributions to projection predictive inference, and present a safe, efficient, and modular workflow for prediction-oriented model selection therein. We also provide an interpretation of the projected posteriors achieved by projection predictive inference in terms of their limitations in causal settings.

The main purpose of the is to present a workflow for projection predictive variable selection so that users may obtain reliable results in the least time-consuming way (sometimes there are safe shortcuts that can save enormous amount of wall clock and computing time). But it also discusses the use of the projected posterior in causal settings and gives some more background in general. All these have been implemented in the projpred R package (the most recent workflow supporting features added by Frank who has been doing awesome job in recent years improving projpred). While writing the introduction to the paper, we were happy to notice that projpred is currently the most downloaded R package for Bayesian variable selection!