Frequentist confidence intervals for orbits

Abstract

The problem of efficiently computing the orbital elements of a visual binary while still deriving confidence intervals with frequentist properties is treated. When formulated in terms of the Thiele-Innes elements, the known distribution of probability in Thiele-Innes space allows efficient grid-search plus Monte-Carlo-sampling schemes to be constructed for both the minimum-${\chi }^2$ and Bayesian approaches to parameter estimation. Numerical experiments with $10^4$ independent realizations of an observed orbit confirm that the $1-$ and $2\sigma$ confidence and credibility intervals have coverage fractions close to their frequentist values. \keywords{binaries: visual - stars: fundamental parameters - methods:statistical}

7 pages, 2 figures. Minor changes. Accepted by Astronomy and Astrophysics

References in corpus (2)

• EXOFAST: A fast exoplanetary fitting suite in IDL
• Dynamical Mass Estimates for Incomplete Orbits: Young Multiple Stars in Taurus and Ophiuchus

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