Amortized Variational Inference for Joint Posterior and Predictive Distributions in Bayesian Uncertainty Quantification

ArXi:2605.03710v1 Announce Type: cross Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior distribution of model parameters, and then propagating posterior samples through the predictive model via Monte Carlo simulation. This sequential workflow can be computationally demanding, particularly for high-fidelity models such as those governed by partial differential equations.