Visual binary stars with partially missing data: Introducing multiple imputation in astrometric analysis. (arXiv:1905.05832v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Claveria_R/0/1/0/all/0/1">Ruben M. Claveria</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Mendez_R/0/1/0/all/0/1">Rene A. Mendez</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Silva_J/0/1/0/all/0/1">Jorge F. Silva</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Orchard_M/0/1/0/all/0/1">Marcos E. Orchard</a>
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.
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.
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