A Pseudo-Bayesian Model Averaging method for Predictive Ensembling in the Presence of Measurement Error

A. Forte Deltell, J. Martínez-Minaya, J. Piqueras Marqués

Bayesian Model Averaging (BMA) is widely used to identify relevant predictors and combine plausible models. However, it typically assumes error-free predictors, which leads to overconfident uncertainty estimates and suboptimal model weights when measurement error is present. We propose a Metropolis–Hastings algorithm for linear meta-model construction that incorporates measurement error through a hierarchical latent variable framework. Instead of relying on marginal likelihoods, our approach uses a pseudo-likelihood based on leave-one-out cross-validation (LOO-CV) to calculate predictive weights. This yields key advantages: a purely predictive focus, robustness to prior specification, and reduced penalization of complex models. The method is validated on simulated data under controlled measurement error scenarios, assessing predictive accuracy, interval calibration, and model selection performance.

Keywords: Measurement Uncertainty, MCMC, Model selection, Bayesian Model Averaging

Bayesian Methods
September 4, 2026  11:10 AM
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