The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes mixed-effects models widely applied in fields such as biology, pharmacokinetics, and sociology. In this work, we propose a novel methodology for scalable Bayesian inference in hierarchical mixed-effects models. Our framework first constructs amortized approximations of the likelihood and the posterior distribution, which are then rapidly refined for each individual dataset, to ultimately approximate the parameters posterior across many individuals. The framework is easily trainable, as it uses mixtures of experts but without neural networks, leading to parsimonious yet expressive surrogate models of the likelihood and the posterior. We demonstrate the effectiveness of our methodology using challenging stochastic models, such as mixed-effects stochastic differential equations emerging in systems biology-driven problems. However, the approach is broadly applicable and can accommodate both stochastic and deterministic models. We show that our approach can seamlessly handle inference for many parameters. Additionally, we applied our method to a real-data case study of mRNA transfection. When compared to exact pseudomarginal Bayesian inference, our approach proved to be both fast and competitive in terms of statistical accuracy.

翻译：多实验数据分析（如多个个体的观测）通常采用混合效应模型进行处理，该模型通过分层表示来考虑个体间的变异。这使得混合效应模型在生物学、药代动力学和社会学等领域得到广泛应用。本文提出了一种新颖的、适用于分层混合效应模型的可扩展贝叶斯推断方法。我们的框架首先构建似然函数和后验分布的摊销近似，随后针对每个独立数据集进行快速优化，最终实现对多个个体间参数后验分布的近似。该框架易于训练，因为它采用了专家混合方法但无需神经网络，从而构建出简约且表达能力强的似然函数与后验分布代理模型。我们通过具有挑战性的随机模型（例如系统生物学问题中出现的混合效应随机微分方程）验证了本方法的有效性。然而，该方法具有广泛适用性，能够同时兼容随机模型与确定性模型。我们证明了该方法可以无缝处理多参数推断问题。此外，我们将本方法应用于mRNA转染的真实数据案例研究。与精确的伪边际贝叶斯推断相比，我们的方法在计算速度上表现出显著优势，同时在统计准确性方面也具备竞争力。