Heteroskedasticity-robust inference in Bayesian linear regression via the generalized method of moments

This study proposes a semiparametric approach to Bayesian linear regression using the Bayesian generalized method of moments. Unlike conventional methods, the proposed approach does not require specifying a probability distribution for the error term and avoids relying on the assumptions of homoskedasticity and normality. The primary advantage of this method is its ability to provide valid inference, particularly credible intervals with correct coverage, even in the presence of heteroskedasticity. Simulation studies show that both frequentist and Bayesian methods assuming homoskedasticity yield confidence or credible intervals with poor coverage under heteroskedasticity, whereas the proposed method consistently achieves accurate and reliable uncertainty quantification. A case study further demonstrates that failing to account for heteroskedasticity can lead to misleading conclusions. Overall, the proposed method offers a robust and practical alternative to conventional likelihood-based Bayesian linear regression, with potential extensions to more complex models involving linear components. (PsycInfo Database Record (c) 2026 APA, all rights reserved).