# A Likelihood Approach for Inference of Population Heterogeneity in Particle Ensembles with Second-Order Langevin Dynamics

arXiv: https://arxiv.org/abs/2411.08692 · HTML: https://mlsanity.com/paper/2411.08692/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 83 references that are in the map.
- First posted on arXiv 13 Nov 2024.

## Builds on (most cited first, 6 of 6)

- [Bayesian inference for diffusion driven mixed-effects models](https://mlsanity.com/paper/1507.06807/) (2015)
- [Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing](https://mlsanity.com/paper/2001.02466/) (2020)
- [Flocking and turning: a new model for self-organized collective motion](https://mlsanity.com/paper/1403.1202/) (2014)
- [A Renormalization Group Approach to Connect Discrete- and Continuous-Time Descriptions of Gaussian Processes](https://mlsanity.com/paper/2101.06482/) (2021)
- [Parameter estimation for partially observed second-order diffusion processes](https://mlsanity.com/paper/2406.14738/) (2024)
- [Likelihood estimation for stochastic differential equations with mixed effects](https://mlsanity.com/paper/2408.17257/) (2024)

## Abstract (arXiv)

The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time-discrete trajectory data provided by experiments. In many cases, second-order Langevin models are needed to adequately capture the motility. Additionally, population heterogeneity needs to be taken into account when analyzing data from several individual organisms. In this work, we describe a maximum likelihood approach to infer dynamical, stochastic models and, simultaneously, estimate the heterogeneity in a population of motile active particles from discretely sampled, stochastic trajectories. To this end, we propose a method to approximate the likelihood for non-linear second-order Langevin models. We show that this maximum likelihood ansatz outperforms alternative approaches, especially for short trajectories. Additionally, we demonstrate how a measure of uncertainty for the heterogeneity estimate can be derived. We thereby pave the way for the systematic, data-driven inference of dynamical models for actively driven entities based on trajectory data, deciphering temporal fluctuations and inter-particle variability.