Membership Lists for 431 Open Clusters in Gaia DR2 Using Extreme Deconvolution Gaussian Mixture Models

Open clusters are groups of stars that form at the same time, making them an ideal laboratory to test theories of star formation, stellar evolution, and dynamics in the Milky Way disk. However, the utility of an open cluster can be limited by the accuracy and completeness of its known members. Here, we employ a “top-down” technique, Extreme Deconvolution Gaussian Mixture Models (XDGMMs), to extract and evaluate known open clusters from Gaia DR2 by fitting the distribution of stellar parallax and proper motion along a line of sight. Extreme deconvolution techniques can recover the intrinsic distribution of astrometric quantities, accounting for the full covariance matrix of the errors; this allows open cluster members to be identified even when presented with relatively uncertain measurement data. To date, open cluster studies have only applied extreme deconvolution to specialized searches for individual systems. We use XDGMMs to characterize the open clusters reported by Ahumada & Lapasset and are able to recover 420 of the 426 open clusters therein (98.1%). Our membership list contains the overwhelming majority (>95%) of previously known cluster members. We also identify a new, significant, and relatively faint cluster member population and validate their membership status using Gaia eDR3. We report the fortuitous discovery of 11 new open cluster candidates within the lines of sight we analyzed. We present our technique, as well as its advantages and challenges, and publish our membership lists and updated cluster parameters.

Sparse covariance estimation in logit mixture models

This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correlations between all random coefficients), or a restricted diagonal matrix (allowing no correlations at all). Our objective is to find optimal subsets of correlated coefficients for which we estimate covariances. We propose a new estimator, called MISC, that uses a mixed-integer optimization (MIO) program to find an optimal block diagonal structure specification for the covariance matrix, corresponding to subsets of correlated coefficients, for any desired sparsity level using Markov Chain Monte Carlo (MCMC) posterior draws from the unrestricted full covariance matrix. The optimal sparsity level of the covariance matrix is determined using out-of-sample validation. We demonstrate the ability of MISC to correctly recover the true covariance structure from synthetic data. In an empirical illustration using a stated preference survey on modes of transportation, we use MISC to obtain a sparse covariance matrix indicating how preferences for attributes are related to one another.

Multivariate Ensemble Sensitivity Analysis for Super Typhoon Haiyan (2013)

Ensemble sensitivity is often a diagonal approximation to the multivariate regression, leading to a simple univariate regression. Comparatively, the multivariate ensemble sensitivity retains the full covariance matrix when computing the multivariate regression. The performances of both univariate and multivariate ensemble sensitivities in multiscale flows have not been thoroughly examined, and the demonstration of the latter in realistic applications has been sparse. A high-resolution ensemble forecast of Typhoon Haiyan (2013) is used to examine the performances of the two ensemble sensitivities. Compared to the multivariate sensitivity, the univariate sensitivity overestimates the forecast metric, especially at higher levels. To increase the predicted Haiyan’s intensity, multivariate ensemble sensitivity gives initial perturbations characterized by a warming area around the center of the storm, an increased moisture area around the eyewall, a stronger primary circulation around the radius of maximum wind, and stronger inflow at low levels and stronger outflow at high levels. Perturbed initial condition experiments verify that the predicted response from the multivariate sensitivity is more accurate than that from the univariate sensitivity. Therefore, the ability of multivariate sensitivity to provide more accurate predicted responses than the univariate sensitivity has been demonstrated in a realistic multiscale flow application.

AUTOMATIC CAMERA SYSTEM CALIBRATION WITH A CHESSBOARD ENABLING FULL IMAGE COVERAGE

<p><strong>Abstract.</strong> Geometric camera calibration is a mandatory prerequisite for many applications in computer vision and photogrammetry. Especially when requiring an accurate camera model the effort for calibration can increase dramatically. For the calibration of the stereo-camera used for optical navigation a new chessboard based approach is presented. It is derived from different parts of existing approaches which, taken separately, are not able to meet the requirements. Moreover, the approach adds one novel main feature: It is able to detect all visible chessboard fields with the help of one or more fiducial markers simply sticked on a chessboard (AprilTags). This allows a robust detection of one or more chessboards in a scene, even from extreme perspectives. Except for the acquisition of the calibration images the presented approach enables a fully automatic calibration. Together with the parameters of the interior and relative orientation the full covariance matrix of all model parameters is calculated and provided, allowing a consistent error propagation in the whole processing chain of the imaging system. Even though the main use case for the approach is a stereo camera system it can be used for a multi-camera system with any number of cameras mounted on a rigid frame.</p>

With and without spectroscopy: Gaia DR2 proper motions of seven ultra-faint dwarf galaxies

Aims. We present mean absolute proper motion measurements for seven ultra-faint dwarf galaxies orbiting the Milky Way, namely Boötes III, Carina II, Grus II, Reticulum II, Sagittarius II, Segue 2, and Tucana IV. For four of these dwarfs our proper motion estimate is the first ever provided. Methods. The adopted astrometric data come from the second data release of the Gaia mission. We determine the mean proper motion for each galaxy starting from an initial guess of likely members, based either on radial velocity measurements or using stars on the horizontal branch identified in the Gaia (GBP – GRP, G) colour-magnitude diagram in the field of view towards the UFD. We then refine their membership iteratively using both astrometry and photometry. We take into account the full covariance matrix among the astrometric parameters when deriving the mean proper motions for these systems. Results. Our procedure provides mean proper motions with typical uncertainties of ∼0.1 mas yr−1, even for galaxies without prior spectroscopic information. In the case of Segue 2 we find that using radial velocity members only leads to biased results, presumably because of the small number of stars with measured radial velocities. Conclusions. Our procedure allows the number of member stars per galaxy to be maximized regardless of the existence of prior spectroscopic information, and can therefore be applied to any faint or distant stellar system within reach of Gaia.

Numerical Reconstruction of the Covariance Matrix of a Spherically Truncated Multinormal Distribution

We relate the matrixSBof the second moments of a spherically truncated normal multivariate to its full covariance matrixΣand present an algorithm to invert the relation and reconstructΣfromSB. While the eigenvectors ofΣare left invariant by the truncation, its eigenvalues are nonuniformly damped. We show that the eigenvalues ofΣcan be reconstructed from their truncated counterparts via a fixed point iteration, whose convergence we prove analytically. The procedure requires the computation of multidimensional Gaussian integrals over an Euclidean ball, for which we extend a numerical technique, originally proposed by Ruben in 1962, based on a series expansion in chi-square distributions. In order to study the feasibility of our approach, we examine the convergence rate of some iterative schemes on suitably chosen ensembles of Wishart matrices. We finally discuss the practical difficulties arising in sample space and outline a regularization of the problem based on perturbation theory.