We present dynamic spatial modelling and computational
methods for the analysis of collections of objects moving in a
spatially inhomogeneous force field under the influence of covariates.
Core motivating examples come from movement ecology and cell motility,
where multiple animals are tracked moving in 2-D or 3-D largely driven
by the external environmental characteristics. Interest lies in
identifying the role of different covariates in guiding the motion,
both in terms of the shape of their implied field, as well as their
overall presence or absence of influence. Models are based on
discrete-time, dynamic state-space models for locations and
directional velocities of each of a set of animals, combined with a
latent force-field over the temporal domain that drives changes in
velocities. We extend models for the force fields using dynamic
Bayesian radial basis function regression to define a potential
surface varying in space but also in the space of covariates, with the
force field given by the gradient of the potential in 3-D.
Corresponding variable selection priors allow us to detect which
covariates play a role in shaping the motion, and provide a basis for
understanding their precise functional form. We exemplify the work on
two examples: a 3-D dataset from in-vivo immune cell motility, and a
GPS tracking dataset from toucans in central America.
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