Approximate Solutions of a General Stochastic Velocity-Jump Model Subject to Discrete-Time Noisy Observations

Area of Science:

• Mathematical Biology
• Statistical Physics
• Dynamical Systems

Background:

• High-resolution spatio-temporal data from tracking motile entities are increasingly common.
• Mathematical models are crucial for characterizing observed motion patterns.
• Velocity-jump models offer a framework for describing agent movement with state transitions.

Purpose of the Study:

• To derive solutions for velocity-jump models of single-agent motion in one dimension.
• To address challenges posed by noisy, discrete-time observations of hidden agent states.
• To develop accurate approximations for data distributions in these models.

Main Methods:

• Modeling single-agent motion using velocity-jump processes with Markovian transitions.
• Developing approximations for data distributions under noisy, unobserved state conditions.
• Simulating model structures to generate empirical distributions for comparison.

Main Results:

• Derived a series of approximations for data distributions in velocity-jump models.
• Verified the accuracy of approximations against simulated empirical distributions.
• Approximations are accurate when state switching is infrequent relative to imaging frequency.

Conclusions:

• The derived approximations provide accurate methods for analyzing velocity-jump models with hidden states.
• These approximations facilitate fast forward predictions and inform experimental design.
• The computed distributions serve as likelihoods for inference and model selection in agent-based modeling.