# A Moment-Based Generalization to Post-Prediction Inference

arXiv: https://arxiv.org/abs/2507.09119 · HTML: https://mlsanity.com/paper/2507.09119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2025.

## Built on by (most cited first, 1 of 1)

- [When Surveys Become Conversations: Adaptive Matrix Validation for AI-Assisted Interviews](https://mlsanity.com/paper/2606.24244/) (2026)

## Abstract (arXiv)

Artificial intelligence (AI) and machine learning (ML) are increasingly used to generate data for downstream analyses, yet naively treating these predictions as true observations can lead to biased results and incorrect inference. Wang et al. (2020) proposed a method, post-prediction inference, which calibrates inference by modeling the relationship between AI/ML-predicted and observed outcomes in a small, gold-standard sample. Since then, several methods have been developed for inference with predicted data. We revisit Wang et al. in light of these recent developments. We reflect on their assumptions and offer a simple extension of their method which relaxes these assumptions. Our extension (1) yields unbiased point estimates under standard conditions and (2) incorporates a simple scaling factor to preserve calibration variability. In extensive simulations, we show that our method maintains nominal Type I error rates, reduces bias, and achieves proper coverage.