# Visual binary stars with partially missing data: Introducing multiple imputation in astrometric analysis

## TL;DR

This paper introduces a Bayesian framework using multiple imputation and Markov chain Monte Carlo methods to incorporate partial measurements of relative positions in the orbital analysis of visual binary stars, improving parameter estimation.

## Contribution

It presents a novel methodology for including partial observational data in orbital parameter estimation, reducing uncertainty in the results.

## Key findings

- Inclusion of partial measurements decreases the posterior uncertainty of orbital elements.
- The method is validated with synthetic and real data, showing improved inference.
- The impact of measurement informativeness on uncertainty reduction is analyzed.

## 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.