Normalizing-flow variational posteriors for NNGP-based spatial variational inference

Develop normalizing-flow-based variational posteriors for Nearest Neighbor Gaussian Process (NNGP)-based Bayesian spatial linear mixed effects models, using sequences of invertible mappings to transform simple base distributions into expressive variational distributions that capture complex posterior correlations.

Background

The proposed spVarBayes methods rely on Gaussian variational families (including mean-field and NNGP-structured precision) that, while scalable and accurate for means, may underestimate uncertainty or miss complex dependencies in the posterior, especially under independence assumptions.

The authors point to normalizing flows as a promising open direction to construct more flexible variational posteriors in spatial models, potentially overcoming limitations of Gaussian families by learning rich transformations while maintaining tractability and scalability.