Amortized Bayesian Multilevel Models
This work addresses a significant bottleneck for researchers and practitioners using Bayesian multilevel models by providing a faster, amortized inference method, though it is incremental as it builds on existing simulation-based inference techniques.
The paper tackles the computational challenges of estimating Bayesian multilevel models by proposing neural network architectures that leverage their probabilistic factorization, achieving near-instant posterior inference on unseen datasets and comparing favorably to Stan's gold-standard sampler in real-world case studies.
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.