We address efficient Bayesian inference in multilevel models, where group-specific latent variables are drawn from a shared hyperprior. In standard approaches, inferring the posterior for a new group requires revisiting all previous groups, incurring growing computational cost due to increased data volume and latent dimensionality. We propose replacing past groups with a set of weighted virtual observations of latent variables that preserve the prior over new groups, enabling fast, scalable inference. We provide theoretical analysis, empirical validation on case studies, and a reference implementation compatible with common probabilistic programming languages and inference algorithms.
David Tolpin (Sat,) studied this question.