Effect of sampling on the descriptive distributions of correlated random walks

Abstract

Random walks are commonly used to model movement throughout the sciences, from the motion of particles and molecules to the observed behaviour of animals and crowds. The correlated random walk, which assumes a level of persistence between movement directions, has become ubiquitous in the analysis and modelling of movement in recent times. Whilst many properties of the correlated random walk are known, there are still many which are not fully understood and, therefore, under utilised in movement data analysis. Here we consider the effect that sub-sampling has on the descriptive distributions of correlated random walks. Our work demonstrates the connection between the distributions of turning angles and step-lengths that characterise a correlated random walk, along with the resulting distributions found after sub-sampling. We provide examples for where this approach could aid in movement analysis as well as determining future ways the work could be extended.