# Simulation-based inference for stochastic nonlinear mixed-effects models with applications in systems biology

arXiv: https://arxiv.org/abs/2504.11279 · HTML: https://mlsanity.com/paper/2504.11279/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 62 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 23 of 23)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Sequential Neural Posterior and Likelihood Approximation](https://mlsanity.com/paper/2102.06522/) (2021)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation](https://mlsanity.com/paper/2208.13624/) (2022)
- [Partially Exchangeable Networks and Architectures for Learning Summary Statistics in Approximate Bayesian Computation](https://mlsanity.com/paper/1901.10230/) (2019)
- [Bayesian inference for diffusion driven mixed-effects models](https://mlsanity.com/paper/1507.06807/) (2015)
- [High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables](https://mlsanity.com/paper/1308.2302/) (2013)
- [Convolutional Neural Networks as Summary Statistics for Approximate Bayesian Computation](https://mlsanity.com/paper/2001.11760/) (2020)
- [Spectral Density-Based and Measure-Preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs](https://mlsanity.com/paper/1903.01138/) (2019)
- [ABC of the Future](https://mlsanity.com/paper/2112.12841/) (2021)
- [A Comprehensive Guide to Simulation-based Inference in Computational Biology](https://mlsanity.com/paper/2409.19675/) (2024)
- [Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings](https://mlsanity.com/paper/2403.07454/) (2024)
- [Model-based Clustering](https://mlsanity.com/paper/1807.01987/) (2018)
- [Particle Methods for Stochastic Differential Equation Mixed Effects Models](https://mlsanity.com/paper/1907.11017/) (2019)

## Built on by (most cited first, 2 of 2)

- [Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokinetics](https://mlsanity.com/paper/2604.17670/) (2026)
- [Amortized ratio-estimation importance sampling and localized simulation-based calibration for intractable likelihoods](https://mlsanity.com/paper/2609.39712/) (2026)

## Abstract (arXiv)

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.