Brownian Bridge Interpolation for Human Mobility?

The Brownian bridge is a method for probabilistically interpolating the location of a moving person, animal, or object between two measured points. This type of probabilistic interpolation is useful, because it represents the uncertainty of the interpolated points. It can be used to infer the probability of having visited a certain location, including possible exposure to disease. In the class of probabilistic interpolators, the Brownian bridge is attractive, because it has only a single adjustable parameter, the diffusion coefficient. This paper investigates the suitability of the Brownian bridge for interpolating human locations using mobility data from over 12 million people. One section looks at the consistency of the diffusion coefficient from person to person. As part of this, the paper presents, for the first time, a closed form solution for the maximum likelihood estimate of this parameter. The paper also presents statistical tests aimed at evaluating the accuracy of the Brownian bridge for interpolating human location.