Reconstructing dark matter distribution with peculiar velocities:
  Bayesian forward modelling with corrections for inhomogeneous Malmquist bias
  We present a forward-modelled velocity field reconstruction algorithm that
performs the reconstruction of the mass density field using only peculiar
velocity data. Our method consistently accounts for the inhomogeneous Malmquist
bias using analytic integration along the line-of-sight. By testing our method
on a simulation, we show that our method gives an unbiased reconstruction of
the velocity field. We show that not accounting for the inhomogeneous Malmquist
bias can lead to significant biases in the forward-modelled reconstructions. We
applied our method to a peculiar velocity data set consisting of the SFI++ and
2MTF Tully-Fisher catalogues and the A2 supernovae compilation, thus obtaining
a novel velocity reconstruction in the local Universe. Our velocity
reconstructions have a cosmological power spectrum consistent with the
theoretical expectation. Furthermore, we obtain a full description of the
uncertainties on reconstruction through samples of the posterior distribution.
We validate our velocity reconstruction of the local Universe by comparing it
to an independent reconstruction using the 2M++ galaxy catalogue, obtaining
good agreement between the two reconstructions. Using Bayesian model
comparison, we find that our velocity model performs better than the adaptive
kernel smoothed velocity with the same peculiar velocity data. However, our
velocity model does not perform as well as the velocity reconstruction from the
2M++ galaxy catalogue, due to the sparse and noisy nature of the peculiar
velocity tracer samples. The method presented here provides a way to include
peculiar velocity data in initial condition reconstruction frameworks.
