Bayesian comparison of Langevin dynamics for cell motility from positional observation

2026-08-01

AI Summary

Existing approaches lack a unified framework for evidence-based comparison of second-order Langevin dynamics models using only positional observations. This work proposes a Bayesian model comparison method that integrates exact incremental likelihoods from linear Gaussian models with approximate likelihoods for nonlinear dynamics, enabling, for the first time, a unified Bayesian evidence comparison across multiple classes of second-order stochastic dynamical models based solely on position trajectories. The method is validated on synthetic data and applied to trajectories of *Dictyostelium discoideum* cells, accurately recovering the ground-truth generative model under fine-grained temporal sampling. The selected model successfully reproduces key statistical features of experimental trajectories, revealing the decisive influence of temporal resolution on model selection.

Abstract

We develop a Bayesian framework for model comparison of second-order Langevin dynamics from position-only trajectories. While approximate increment likelihoods for nonlinear position-only inference have been formulated previously, a unified evidence-based framework for comparing multiple second-order models under positional observation has remained lacking. Here we address this problem by combining exact increment likelihoods for linear Gaussian models with a previously proposed approximate likelihood for nonlinear dynamics. Synthetic-data benchmarks show reliable recovery of the generating model at fine sampling intervals and progressive loss of identifiability under coarse temporal sampling. Application to Dictyostelium discoideum trajectories demonstrates that the statistically supported model depends strongly on temporal resolution. Moreover, the selected models reproduce key statistical properties of the experimental trajectories, providing additional support for the model-comparison results. Our framework therefore offers a practical approach to evidence-based comparison of partially observed stochastic dynamics.

Problem

• Langevin dynamics
• model comparison
• position-only observation
• Bayesian inference
• cell motility

Innovation

• Bayesian model comparison
• Langevin dynamics
• position-only inference
• stochastic dynamics
• temporal resolution