Toward a kinetic-based probabilistic time geography

Abstract

Time geography represents a powerful framework for the quantitative analysis of individual movement. Time geography effectively delineates the space–time boundaries of possible individual movement by characterizing movement constraints. The goal of this paper is to synchronize two new ideas, probabilistic time geography and kinetic-based time geography, to develop a more realistic set of movement constraints that consider movement probabilities related to object kinetics. Using random-walk theory, the existing probabilistic time geography model characterizes movement probabilities for the space–time cone using a normal distribution. The normal distribution has a symmetric probability density function and is an appropriate model in the absence of skewness – which we relate to an object’s initial velocity. Moving away from a symmetric distribution for movement probabilities, we propose the use of the skew-normal distribution to model kinetic-based movement probabilities, where the degree and direction of skewness is related to movement direction and speed. Following a description of our model, we use a set of case-studies to demonstrate the skew-normal model: a random walk, a correlated random walk, wildlife data, cyclist data, and athlete movement data. Our results show that for objects characterized by random movement behavior, the existing model performs well, but for object movement with kinetic properties (e.g., athletes), the proposed model provides a substantial improvement. Future work will look to extend the proposed probabilistic framework to the space–time prism.

Keywords:

• time geography
• kinetics
• probability
• mobile objects
• personal movement models

Acknowledgements

The authors gratefully acknowledge the British Columbia Ministry of Environment for access to the Caribou telemetry data set. Also, we thank the University of Victoria Ultimate Frisbee Club for participating in ongoing data collection endeavors, including the athlete data used here. Thanks to H. Miller for discussions on a number of points related to kinetic time geography and to W. Othman for access to the code, and some tips, for computing the kinetic time geography boundaries. The constructive comments of four anonymous reviewers greatly improved the presentation of this manuscript.

Notes

1. 1. Here we assume, as in physics, that moving objects tend to continue their motion unless acted on by other forces. That is, it is most probable that the object does not change speed or direction.