Advances in projection predictive inference

TL;DR

This paper surveys the development and application of projection predictive inference in Bayesian modeling, highlighting its advantages in avoiding overfitting and improving predictive accuracy across various fields.

Contribution

It provides a comprehensive overview of projection predictive inference, introduces a modular workflow for model selection, and discusses its limitations in causal inference contexts.

Findings

Projection predictive inference reduces overfitting compared to naive methods.

It outperforms other model selection techniques in predictive tasks.

A modular workflow for prediction-oriented model selection is proposed.

Abstract

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 na\"ive 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.