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

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities. These tracking data can be used to calibrate mathematical models describing the motility of individual entities. The challenges in calibrating models for single-agent motion derive from the intrinsic characteristics of experimental data, collected at discrete time steps and with measurement noise. We consider the motion of individual agents that can be described by velocity-jump models in one spatial dimension. These agents transition between a network of n states, in which each state is associated with a fixed velocity and fixed rates of switching to every other state. Exploiting approximate solutions to the resultant stochastic process, we develop a Bayesian inference framework to calibrate these models to discrete-time noisy data. We first demonstrate that the framework can be used to effectively recover the model parameters of data simulated from two-state and three-state models. Finally, we explore the question of model selection first using simulated data and then using experimental data tracking mRNA transport inside Drosophila neurons. Overall, our results demonstrate that the framework is effective and efficient in calibrating and selecting between velocity-jump models, and it can be applied to a range of motion processes.