Inferring Parameter Distributions in Heterogeneous Motile Particle Ensembles: A Likelihood Approach for Second Order Langevin Models

TL;DR

This paper introduces a maximum likelihood method to infer parameters and heterogeneity in second order Langevin models from trajectory data, improving accuracy especially for short trajectories and enabling uncertainty quantification.

Contribution

It presents a novel likelihood approximation technique for non-linear second order Langevin models that accounts for population heterogeneity in motile particles.

Findings

Likelihood approach outperforms alternatives for short trajectories

Method quantifies heterogeneity and uncertainty

Enables data-driven inference of active particle dynamics

Abstract

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 new 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.