  We consider the subsonic moving point source problem for the scalar wave
equation in $\pmb{R}^3$, proving a regularity result for the direct problem,
and uniqueness and stability results for the inverse problem. We then present
and investigate numerically a Bayesian framework for the inference of the
source trajectory and intensity from wave field measurements. The framework
employs Gaussian process priors, the pre-conditioned Crank-Nicholson scheme
with Markov Chain Monte Carlo sampling, and conditioning on functionals to
include prior information on the source trajectory.
