# Bayesian correction for covariate measurement error: a frequentist evaluation and comparison with regression calibration

arXiv: https://arxiv.org/abs/1603.06284 · HTML: https://mlsanity.com/paper/1603.06284/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2016.

## Built on by (most cited first, 2 of 2)

- [Tree-Based Predictive Models for Noisy Input Data](https://mlsanity.com/paper/2603.07409/) (2026)
- [Bias-corrected Cox regression with AI-extracted covariates via calibration summary statistics](https://mlsanity.com/paper/2607.25868/) (2026)

## Abstract (arXiv)

Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration (RC), arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to RC, and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next we describe the closely related maximum likelihood and multiple imputation approaches, and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of RC and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey.