  We consider the reconstruction of moving sources using partial measured data.
A two-step deterministic-statistical approach is proposed. In the first step,
an approximate direct sampling method is developed to obtain the locations of
the sources at different times. Such information is coded in the priors, which
is critical for the success of the Bayesian method in the second step. The
well-posedness of the posterior measure is analyzed in the sense of the
Hellinger distance. Both steps are based on the same physical model and use the
same set of measured data. The combined approach inherits the merits of the
deterministic method and Bayesian inversion as demonstrated by the numerical
examples.
