Bayesian inference for velocity-jump models for movement

Abstract: The velocity-jump model is a specific type of piecewise deterministic Markov process in which an individual's velocity is constant except at times that form the events of some point process. It represents an interpretable continuous-time version of the discrete-time `step and turn' models widely used in analysing wildlife telemetry. In this paper, I derive a reversible jump Markov chain Monte Carlo algorithm to carry out exact Bayesian inference for velocity-jump models by reconstructing the trajectories between observations, and illustrate its use in analysing real and simulated telemetry data. The method uses a proposal distribution for updating velocities that is constructed by approximating the movement model with a multivariate normal distribution and then conditioning that distribution on the data. The velocity-jump models considered can incorporate measurement error and Markov dependence between successive velocities.