Prediction-Powered Inference in Hybrid Measurement Regimes: A Statistical Survey

Prediction-powered inference (PPI) studies statistical inference when a small set of gold-standard labels is combined with a much larger pool of machine-generated predictions. The central difficulty is that predictions can substantially reduce variance, yet naive substitution of predictions for outcomes generally changes the estimand and invalidates uncertainty quantification. The basic remedy in the literature is rectification: predictions are used to construct a low-variance plug-in term, while labeled observations are used to estimate and correct the inferential distortion induced by prediction substitution. We review PPI as a family of rectified plug-in procedures for hybrid measurement regimes. The survey develops a common statistical template based on mean estimation, estimating equations, and loss-based formulations, and then uses that template to compare modern variants according to the component they modify: the rectification engine, the label-acquisition design, predictor dependence, or the validity target. We also position PPI relative to model-assisted survey sampling, post-prediction correction, surrogate-outcome methods, classical measurement-error models, and semiparametric augmentation. Throughout, we distinguish questions of validity from questions of efficiency, robustness, and computation, and we emphasize that valid use of prediction assistance does not require a correct predictive model but does depend on how rectification, dependence, and sampling design are handled. The survey closes with recurrent failure modes, practical reporting recommendations, and open problems in finite-sample theory, heterogeneous proxy quality, and protocol-aware deployment.