Testing Bayesian reconstruction methods from peculiar velocities. Issue 2 (15th December 2022) - Valade, Aurélien; Libeskind, Noam I; Hoffman, Yehuda; Pfeifer, Simon
ABSTRACT: Reconstructing the large-scale density and velocity fields from surveys of galaxy distances is a major challenge for cosmography. The data are 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 catalogues 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' WF as well, namely, the WF 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 ($d \lesssim 40 \, h^{-1}\, {\rm Mpc}$ ), the two methods perform roughly equally well. Hamlet shows more contrast in the intermediate regime ($40 \lesssim d \lesssim 120 \, h^{-1}\, {\rm Mpc}$ ). The main differences between the two appear in the most distant regime ($d \gtrsim 120 \, h^{-1}\, {\rm Mpc}$ ), close to the edge of the data. Hamlet outperforms the BGc/WF in terms of contrast and tighter correlations of the density and velocity fields. Yet, close to the edge of the data, Hamlet yields a slightly biased reconstruction, which affects the multipoles of the velocity field. 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.