Hierarchical data with multiple observations per group is ubiquitous in empirical sciences and is often analyzed using mixed-effects regression. In such models, Bayesian inference gives an estimate of uncertainty but is analytically intractable and requires costly approximation using Markov Chain Monte Carlo (MCMC) methods. Neural posterior estimation shifts the bulk of computation from inference time to pre-training time, amortizing over simulated datasets with known ground truth targets. We propose metabeta, a neural network model for Bayesian mixed-effects regression. Using simulated and real data, we show that it reaches stable and comparable performance to MCMC-based parameter estimation at a fraction of the usually required time, enabling new use cases for Bayesian mixed-effects modeling.

翻译：在实证科学中，具有每组多个观测值的分层数据普遍存在，通常使用混合效应回归进行分析。在此类模型中，贝叶斯推断能够提供不确定性估计，但其解析形式难以处理，需要借助计算成本高昂的马尔可夫链蒙特卡洛（MCMC）方法进行近似。神经后验估计将大部分计算从推断阶段转移到预训练阶段，通过在已知真实目标的模拟数据集上进行摊销来实现。我们提出了metabeta，一种用于贝叶斯混合效应回归的神经网络模型。通过使用模拟数据和真实数据，我们证明该模型仅需通常所需时间的一小部分，即可达到与基于MCMC的参数估计相当且稳定的性能，从而为贝叶斯混合效应建模开辟了新的应用场景。