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Galaxy peculiar velocities are excellent cosmological probes provided thatbiases inherent to their measurements are contained before any study. Thispaper proposes a new algorithm based on an object point process model whoseprobability density is built to statistically reduce the effects of Malmquistbiases and uncertainties due to lognormal errors in radial peculiar velocitycatalogs. More precisely, a simulated annealing algorithm permits maximizingthe probability density describing the point process model. The resultingconfigurations are bias-minimized catalogs. Tests are conducted on syntheticcatalogs mimicking the second and third distance modulus catalogs of theCosmicflows project from which peculiar velocity catalogs are derived. Byreducing the local peculiar velocity variance in catalogs by an order ofmagnitude, the algorithm permits recovering the expected one while preservingthe small-scale velocity correlation. It also permits retrieving the expectedclustering. The algorithm is then applied to the observational catalogs. Thelarge-scale structure reconstructed with the Wiener-filter technique applied tothe bias-minimized observational catalogs matches with great success the localcosmic web as depicted by redshift surveys of local galaxies. These newbias-minimized versions of peculiar velocity catalogs can be used as a startingpoint for several studies from possibly estimating the most probable Hubbleconstant, H0, value to the production of simulations constrained to reproducethe local Universe.

Statistically bias-minimized peculiar velocity catalogs from Gibbs point processes and Bayesian inference