# Bayesian inference for diffusion driven mixed-effects models

arXiv: https://arxiv.org/abs/1507.06807 · HTML: https://mlsanity.com/paper/1507.06807/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2015.

## Built on by (most cited first, 10 of 10)

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- [Interpretable machine learning for high-dimensional trajectories of aging health](https://mlsanity.com/paper/2105.03410/) (2021)
- [Variational Sampling of Temporal Trajectories](https://mlsanity.com/paper/2403.11418/) (2024)
- [A Likelihood Approach for Inference of Population Heterogeneity in Particle Ensembles with Second-Order Langevin Dynamics](https://mlsanity.com/paper/2411.08692/) (2024)
- [Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows](https://mlsanity.com/paper/2605.05606/) (2026)
- [Learning stochastic multiscale models through normalizing flows](https://mlsanity.com/paper/2605.09718/) (2026)

## Abstract (arXiv)

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units, SDE driven mixed-effects models allow the quantification of between (as well as within) individual variation. Performing Bayesian inference for such models, using discrete time data that may be incomplete and subject to measurement error is a challenging problem and is the focus of this paper. We extend a recently proposed MCMC scheme to include the SDE driven mixed-effects framework. Fundamental to our approach is the development of a novel construct that allows for efficient sampling of conditioned SDEs that may exhibit nonlinear dynamics between observation times. We apply the resulting scheme to synthetic data generated from a simple SDE model of orange tree growth, and real data consisting of observations on aphid numbers recorded under a variety of different treatment regimes. In addition, we provide a systematic comparison of our approach with an inference scheme based on a tractable approximation of the SDE, that is, the linear noise approximation.