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.

翻译：贝叶斯预测、模型比较和模型选择的概念在过去十年中得到了显著发展。因此，贝叶斯领域在构建和选择预测模型的理论与应用贡献方面经历了快速增长。其中，投影预测推断在这一方向上展现出潜力，并在广泛领域中得到应用。与纯粹基于交叉验证或信息准则性能指标的简单选择方法相比，它更不易过拟合，且在预测性能方面已知优于其他方法。我们综述了投影预测推断的核心概念及当代贡献，并提出了一种安全、高效且模块化的工作流程，用于其中面向预测的模型选择。此外，我们还对投影预测推断所获得的投影后验在因果设定下的局限性进行了解释。