Open Access

Table 1

Comparison of the different dust inference methods with the one performed in this paper.

This paper Sale &Magorrian (2018) Rezaei Kh et al. (2018b) Lallement et al. (2018) Green et al. (2018)
Parallax uncertainty Smoothing only Marginalization by sampling Neglected Neglected Proper uncertainty handling
           
Max distance 5 kpc 6 kpc 3 kpc
           
Max voxel resolution 2.3 pc Not applicable About 200 pc 5 pc 16.4 pc/0.063 pc
           
Number of data points 3.7 million 6349 21 000 71 357 806 million
           
Power spectrum inference Yes No No No No
           
Correlations 3D 3D 2D map only 3D 1D correlations only
           
Positiveness Yes Only of reddening No Yes Yes
           
Statistical method Variational Bayes Expectation propagation Analytic Maximum posterior Hamiltonian Monte Carlo
           
Data sets Gaia DR2 Synthetic Gaia data APOGEE Gaia DR1 + APOGEE + 2MASS Pan-STARRS + 2MASS

Notes. The first row indicates how the parallax uncertainty of the stars was treated. Hereby smoothing refers to weighting a voxel in the line of sight by the survival function of the star radial distance, as is described in Eq. (7). The distance of the furthest point in the reconstruction is given in the second row. The dimensions of the smallest voxel are given in the third row. For the reconstruction of Sale & Magorrian (2018) the concept of voxel resolution is not readily applicable; Sale & Magorrian (2018) use 140 inducing points spanning a region for which one could evaluate theposterior mean at any point. The resolution for Green et al. (2018) contains two values because the resolution is different in radial and angular directions. The fourth row provides the number of data points used. The fifth row indicates whether or not the power spectrum is inferred. The sixth row states which kind of correlations are assumed for the reconstruction. Whether or not positivity of dust density is enforced can be read in the seventh row. The second-to-last row states the method with which the posterior summary statistics was calculated from the non-normalized log posterior. In the last row the data sets used for the reconstruction are listed.

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