Reconstructing the large scale density and velocity fields from surveys of
galaxy distances, is a major challenge for cosmography. The data is very noisy
and sparse. Estimated distances, and thereby peculiar velocities, are strongly
affected by the Malmquist-like lognormal bias. Two algorithms have been
recently introduced to perform reconstructions from such data: the Bias
Gaussian correction coupled with the Wiener filter (BGc/WF) and the HAMLET
implementation of the Hamiltonian Monte Carlo forward modelling. The two
methods are tested here against mock catalogs that mimic the Cosmicflows-3
data. Specifically the reconstructed cosmography and moments of the velocity
field (monopole, dipole) are examined. A comparison is made to the ``exact''
wiener filter as well - namely the Wiener Filter in the unrealistic case of
zero observational errors. This is to understand the limits of the WF method.
The following is found. In the nearby regime ($d\lesssim 40\mathrm{M}\mathrm{p}\mathrm{c}/h$ ) the
two methods perform roughly equally well. HAMLET does slightly better in the
intermediate regime ($40\lesssim d\lesssim 120\mathrm{M}\mathrm{p}\mathrm{c}/h$ ). The main
differences between the two appear in the most distant regime ($d\gtrsim 120\mathrm{M}\mathrm{p}\mathrm{c}/h$ ), close to the edge of the data. The HAMLET outperforms the BGc/WF
in terms of better and tighter correlations, yet in the distant regime the
HAMLET yields a somewhat biased reconstruction. Such biases are missing from
the BGc/WF reconstruction. In sum, both methods perform well and create
reliable reconstructions with significant differences apparent when details are
examined.