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This research introduces metabeta, a neural architecture that accelerates Bayesian inference for generalized linear mixed-effects models by two to three orders of magnitude compared to standard MCMC methods like NUTS. By accepting prior families as inputs at test time, the model achieves zero-shot generalization across diverse data types without retraining, offering a practical solution for analyzing hierarchical empirical data. The approach maintains rigorous statistical calibration while significantly reducing computational costs, making advanced Bayesian analysis more accessible for large-scale scientific applications.
Prior-Amortized In-Context Bayesian Inference for Generalized Linear Mixed-Effects Models
arXiv:2609.24422v1 Announce Type: new Abstract: Hierarchical data is ubiquitous in the empirical sciences and is most commonly analyzed with generalized linear mixed-effects models (GLMMs). Bayesian inference for GLMMs yields calibrated uncertainty but requires MCMC; the No-U-Turn Sampler (NUTS) is the gold standard but is slow and must restart from scratch for every new dataset, model and prior. We introduce metabeta, a pretrained neural network for prior-amortized in-context Bayesian inference over GLMMs. Unlike previous neural posterior estimators that fix the prior at training time, metabeta accepts prior families and hyperparameters as inputs at test time, enabling zero-shot generalization. Two set transformers and conditional normalizing flows mirror the posterior's two-level structure (global parameters shared across groups, local parameters per group). The model is trained on millions of realistic simulated datasets spanning continuous, binary, and count outcomes. By default, the flow posterior is refined by Independence Metropolis-Hastings against the unnormalized posterior, so its correctness rests on the sampler rather than the network; this yields tuning-free inference two to three orders of magnitude faster than NUTS. Alternatively, the flow can warm-start NUTS, giving nearly identical inference with substantially increased speed and stability. On controlled benchmarks with ground-truth parameters, metabeta matches NUTS in parameter recovery, calibration and out-of-sample prediction. On out-of-distribution real datasets, its posteriors closely match those of NUTS across all parameter types, and they remain faithful under misspecified likelihoods and priors, out-of-distribution predictors, collinear designs, and data-poor regimes. The model is open-source and open-weights and thus immediately deployable.
Abstract:Hierarchical data is ubiquitous in the empirical sciences and is most commonly analyzed with generalized linear mixed-effects models (GLMMs). Bayesian inference for GLMMs yields calibrated uncertainty but requires MCMC; the No-U-Turn Sampler (NUTS) is the gold standard but is slow and must restart from scratch for every new dataset, model and prior. We introduce metabeta, a pretrained neural network for prior-amortized in-context Bayesian inference over GLMMs. Unlike previous neural posterior estimators that fix the prior at training time, metabeta accepts prior families and hyperparameters as inputs at test time, enabling zero-shot generalization. Two set transformers and conditional normalizing flows mirror the posterior's two-level structure (global parameters shared across groups, local parameters per group). The model is trained on millions of realistic simulated datasets spanning continuous, binary, and count outcomes. By default, the flow posterior is refined by Independence Metropolis-Hastings against the unnormalized posterior, so its correctness rests on the sampler rather than the network; this yields tuning-free inference two to three orders of magnitude faster than NUTS. Alternatively, the flow can warm-start NUTS, giving nearly identical inference with substantially increased speed and stability. On controlled benchmarks with ground-truth parameters, metabeta matches NUTS in parameter recovery, calibration and out-of-sample prediction. On out-of-distribution real datasets, its posteriors closely match those of NUTS across all parameter types, and they remain faithful under misspecified likelihoods and priors, out-of-distribution predictors, collinear designs, and data-poor regimes. The model is open-source and open-weights and thus immediately deployable.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2609.24422 [cs.LG]
(or arXiv:2609.24422v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.24422 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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