| Summary: | Advances in experimental techniques allow the collection of high-space-andtime resolution data that track individual motile entities over time. This poses
the question of how to use these data to efficiently and effectively calibrate
motion models. However, typical mathematical models often overlook the inherent aspects of data collection, such as the discreteness and the experimental noise
of the measured locations. In this paper, we focus on velocity-jump models suitable to describe single-agent motion in one spatial dimension, characterised by
successive Markovian transitions between a finite network of n states, each with
a specified velocity and a fixed rate of switching to every other state. Since the
problem of finding the exact distributions of discrete-time noisy data is generally intractable, we derive a series of approximations for the data distributions
and compare them to in-silico data generated by the models using four example
network structures. These comparisons suggest that the approximations are accurate given sufficiently infrequent state switching, or equivalently, a sufficiently
high data collection frequency. Moreover, for infrequent switching, the PDFs
comparisons highlight the importance of accounting for the correlation between
subsequent measured locations, due to the likely permanence in the state visited in the previous measurement. The approximate distributions computed can
be used for fast parameter inference and model selection between a range of
velocity-jump models using single-agent tracking data.
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