BibTeX

@article{2408.13230v3,
Author        = {Daniel Habermann and Marvin Schmitt and Lars Kühmichel and Andreas Bulling and Stefan T. Radev and Paul-Christian Bürkner},
Title         = {Amortized Bayesian Multilevel Models},
Eprint        = {2408.13230v3},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.ML},
Abstract      = {Multilevel models (MLMs) are a central building block of the Bayesian
workflow. They enable joint, interpretable modeling of data across hierarchical
levels and provide a fully probabilistic quantification of uncertainty. Despite
their well-recognized advantages, MLMs pose significant computational
challenges, often rendering their estimation and evaluation intractable within
reasonable time constraints. Recent advances in simulation-based inference
offer promising solutions for addressing complex probabilistic models using
deep generative networks. However, the utility and reliability of deep learning
methods for estimating Bayesian MLMs remains largely unexplored, especially
when compared with gold-standard samplers. To this end, we explore a family of
neural network architectures that leverage the probabilistic factorization of
multilevel models to facilitate efficient neural network training and
subsequent near-instant posterior inference on unseen datasets. We test our
method on several real-world case studies and provide comprehensive comparisons
to Stan's gold standard sampler, where possible. Finally, we provide an
open-source implementation of our methods to stimulate further research in the
nascent field of amortized Bayesian inference.},
Year          = {2024},
Month         = {Aug},
Url           = {http://arxiv.org/abs/2408.13230v3},
File          = {2408.13230v3.pdf}
}