Valid standard errors for misspecified Bayesian models

Giordano and Broderick (2024) introduced infinitesimal jackknife (IJ) standard errors for Bayesian estimators (posterior means). Just like resampling standard errors, IJ standard errors are robust to model misspecification and can be adapted to account for clustering. Importantly, IJ standard errors do not require resampling but can be obtained from a single MCMC run. Standard Bayesian quantile regression, as implemented in bayes: qreg bayes: qreg bayes: qreg bayes: qreg, is generally misspecified. This is because the motivation for the asymmetric Laplace (AL) likelihood is merely that its maximum coincides with the classical quantile regression estimator of Koenker and Bassett (1978). There is no reason to believe that the AL distribution is a plausible data-generating mechanism. For example, the shape of the distribution depends on the quantile you are interested in. While point estimation is consistent, credible intervals often have poor frequentist coverage. We therefore propose using IJ standard errors for Bayesian quantile regression and show, via simulations, that they have good frequentist properties, both for independent and clustered data. If made available as an option in bayes: bayes: bayes: bayes: and bayesmh bayesmh bayesmh bayesmh, IJ standard errors may soon become as popular for Bayesian inference as the vce(robust) vce(robust) vce(robust) vce(robust) option for frequentist inference.