Quantifying Uncertainty in the Presence of Distribution Shifts

We propose a Bayesian framework for uncertainty estimation that explicitly accounts for covariate shifts. The method uses an adaptive prior conditioned on both training and new covariates, increasing uncertainty for inputs far from the training distribution in regions where predictive performance is likely to degrade. The posterior predictive distribution is approximated using amortized variational inference, and synthetic environments are constructed from bootstrap samples of the training data.