Cutset Sampling for Bayesian Networks

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the networks graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks

Distances and parallax bias in Gaia DR2

We derive Bayesian distances for all stars in the RV sample of Gaia DR2, and use the statistical method of Schoenrich, Binney & Asplund(2012) to validate the distances and test the Gaia parallaxes. In contrast to other methods, which rely on special sources, our method directly tests the distances to all stars in our sample. We find clear evidence for a near-linear trend of distance bias f with distance s, proving a parallax offset delta p. On average, we find delta p = -0.054 mas (parallaxes in Gaia DR2 need to be increased) when accounting for the parallax uncertainty under-estimate in the Gaia set (delta p = -0.048 mas on the raw parallax errors) with negligible formal error and a systematic uncertainty of about 0.006 mas. The value is in concordance with results from asteroseismic measurements, but differs from the much lower bias found on quasar samples. We further use our method to compile a comprehensive set of quality cuts in colour, apparent magnitude, and astrometric parameters. Last, we find that for this sample delta p appears to strongly depend on the parallax uncertainty sigma_p (when including the additional 0.043 mas) with a statistical confidence far in excess of 10\sigma and a proportionality factor close to 1, though the dependence varies somewhat with sigma_p. Correcting for the sigma_p dependence also resolves otherwise unexplained correlations of the offset with the number of observation periods n_{vis} and ecliptic latitude. Every study using Gaia DR2 parallaxes/distances should investigate the sensitivity of their results on the parallax biases described here and - for fainter samples - in the DR2 astrometry paper.Comment: 14 pages, 13 figures, accepted in MNRAS. The derived distances, as well as stellar positions and kinematics are found at https://zenodo.org/record/255780