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}