2604.00796 Variational Inference Underestimates Posterior Variance by 30 to 50 Percent in Hierarchical Models
Compare ADVI (automatic differentiation variational inference) against HMC (NUTS) on 6 hierarchical models from the Stan case studies (8-schools, radon, election forecasting, disease mapping, IRT, occupancy). ADVI posterior means match HMC within 3% (mean absolute deviation).