Bayesian reconstruction of dark matter distribution from peculiar velocities: accounting for inhomogeneous Malmquist bias

Abstract

We present a Bayesian 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 Bayesian 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.

Dark Energy Survey Year 3 results: Cosmology with moments of weak lensing mass maps

“…A growing number of studies, however, have investigated and highlighted the role of non-Gaussian statistics in improving cosmological constraints, as the lensing observables carry information beyond that probed by standard Gaussian statistics. Examples of non-Gaussian statistics investigated include higher-order moments [17,29,31,64,65,68,[83][84][85], peak counts [2,23,36,46,48,52,58,64,77,87,88], one-point probability distributions [11,14,79], Minkowski functionals [49,62,65,86], Betti numbers [25,63], persistent homology [38,39], scattering transform coefficients [18,19,80,81], wavelet phase harmonic moments [4], kNN and CDFs [7,10], map-level inference [13,67], and machine-learning methods [26,27,41,53,72].…”

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

“…However, a significant amount of the information contained in weak lensing mass maps lies in their non-Gaussian features, and these features are not fully captured by two-point statistics. Many recent studies, using a wide range of tools and statistics, have tried to extract the non-Gaussian information; examples include higherorder moments [19,39,41,83,84,86,[106][107][108], peak counts [4,27,49,60,62,68,77,83,97,111,112], onepoint probability distributions [12,16,100], Minkowski functionals [46,63,81,84,109], Betti numbers [32,82], persistent homology [52,53], scattering transform coefficients [21,102,103], wavelet phase harmonic moments * marcogatti29@gmail.com [5], kNN and CDFs [8,11], map-level inference [15,85], and machine-learning methods [34,35,56,70,89]. Many of these studies, however, are ...…”

Peculiar Velocity Reconstruction from Simulations and Observations Using Deep Learning Algorithms

“…It can be improved by introducing halo mass bias and density reconstruction into the velocity reconstruction process. Many approaches have been studied to improve the velocity reconstruction result and process (e.g., Crook et al 2010;Courtois et al 2012;Wang et al 2012;Lavaux 2016;Keselman & Nusser 2017;Sorce et al 2017;Yu & Zhu 2019;Zhu et al 2020;Boruah et al 2022;Valade et al 2023;Bayer et al 2023;Hoffman et al 2024). However, the analytical velocity reconstruction process is still complicated and computationally expensive.…”