When do trajectories matter? Identifiability analysis for stochastic transport phenomena

2026-04-16

AI Summary

This study investigates whether parameters in stochastic transport models can be uniquely identified from aggregate count data alone and examines the value of individual trajectory data in mitigating structural non-identifiability. By integrating lattice-based random walk models with both population counts and individual trajectories, the work employs multiscale modeling, mean-field PDE approximations, likelihood-based inference, and identifiability analysis to systematically uncover the inherent limitations of count-only data. The findings demonstrate that incorporating trajectory information substantially enhances parameter identifiability and estimation accuracy, offering theoretical guidance for optimal experimental design. The impact of various trajectory sampling strategies on practical identifiability is quantified, and all algorithms are made publicly available to support reproducible research.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Security and Privacy: Large-scale security measurements

Abstract

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across a range of scales, including count data collected across a series of fixed sampling regions to characterize population-level dispersal, as well as individual trajectory data to examine at the motion of individuals within a diffusive population. In this work we consider a lattice-based random walk model and examine the extent to which model parameters can be determined by collecting count data and/or trajectory data. Our analysis combines agent-based stochastic simulations, mean-field partial differential equation approximations, likelihood-based estimation, identifiability analysis, and model-based prediction. These combined tools reveal that working with count data alone can sometimes lead to challenges involving structural non-identifiability that can be alleviated by collecting trajectory data. Furthermore, these tools allow us to explore how different experimental designs impact inferential precision by comparing how different trajectory data collection protocols affects practical identifiability. Open source implementations of all algorithms used in this work are available on GitHub.

Problem

• stochastic transport
• identifiability
• trajectory data
• count data
• diffusion models

Innovation

• identifiability analysis
• stochastic transport
• trajectory data
• count data
• random walk model