Visual Binary Stars with Partially Missing Data: Introducing Multiple Imputation in Astrometric Analysis
Abstract
Partial measurements of relative position are a relatively common event during the observation of visual binary stars. However, these observations are typically discarded when estimating the orbit of a visual pair. In this article we present a novel framework to characterize the orbits from a Bayesian standpoint, including partial observations of relative position as an input for the estimation of orbital parameters. Our aim is to formally incorporate the information contained in those partial measurements in a systematic way into the final inference. In the statistical literature, an imputation is defined as the replacement of a missing quantity with a plausible value. To compute posterior distributions of orbital parameters with partial observations, we propose a technique based on Markov chain Monte Carlo with multiple imputation. We present the methodology and test the algorithm with both synthetic and real observations, studying the effect of incorporating partial measurements in the parameter estimation. Our results suggest that the inclusion of partial measurements into the characterization of visual binaries may lead to a reduction in the uncertainty associated to each orbital element, in terms of a decrease in dispersion measures (such as the interquartile range) of the posterior distribution of relevant orbital parameters. The extent to which the uncertainty decreases after the incorporation of new data (either complete or partial) depends on how informative those newly incorporated measurements are. Quantifying the information contained in each measurement remains an open issue.
 Publication:

Publications of the Astronomical Society of the Pacific
 Pub Date:
 August 2019
 DOI:
 10.1088/15383873/ab22e2
 arXiv:
 arXiv:1905.05832
 Bibcode:
 2019PASP..131h4502C
 Keywords:

 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 Nine figures, six tables, 23 pages including three appendices. Accepted for publication in PASP. First mention and explicit application of imputation technique in astrometry as applied to binary stars