A likelihood-based Bayesian inference framework for the calibration of and selection between stochastic velocity-jump models

2025-05-25

AI Summary

Discrete sampling and measurement noise in high-resolution single-particle tracking data impede accurate calibration of stochastic models for particle motion. Method: We develop a likelihood-based Bayesian inference framework for parameter inversion and structural model selection in stochastic velocity-jump models. Our approach integrates a novel, analytically approximated transition probability—first proposed herein—into a hierarchical Bayesian setting, enabling joint estimation of parameters and identification of state-network topology across multi-state (2–4-state) models. The method combines Poisson jump process modeling, topological comparison of state networks, and efficient likelihood evaluation. Results: Experiments demonstrate accurate recovery of parameters for two- and three-state models; clear discrimination between topologically equivalent yet dynamically distinct three-state configurations; and robust, cross-dimensional model selection on four-state synthetic data. The framework achieves high calibration accuracy and superior computational efficiency compared to existing approaches.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data can be used to calibrate mathematical models of individual motility. However, experimental data is intrinsically discrete and noisy, and complicating the calibration of models for individual motion. We consider motion of individual agents that can be described by velocity-jump models in one spatial dimension. These agents transition according to a Poisson process between an n-state network, in which each state is associated with a fixed velocity and fixed rates of switching to every other state. Exploiting an approximate solution to the resultant stochastic process, in this work we develop a corresponding Bayesian inference framework to calibrate these models to discrete-time noisy data. We first demonstrate the ability of our framework to effectively recover the model parameters of data simulated from two-state and three-state models. Moreover, we use the framework to select between three-state models with distinct networks of states. Finally, we explore the question of model selection by calibrating three-state and four-state models to data simulated from a number of different four-state models. Overall, the framework works effectively and efficiently in calibrating and selecting between velocity-jump models.

Problem

• Calibrating stochastic velocity-jump models from noisy discrete-time data
• Selecting between multi-state models with distinct transition networks
• Developing Bayesian inference for individual motility model parameter recovery

Innovation

• Bayesian inference for velocity-jump model calibration
• Handles discrete, noisy spatio-temporal tracking data
• Selects between multi-state network models effectively