Frequentist confidence intervals for orbits⋆
Astrophysics Group, Blackett Laboratory, Imperial College London, Prince Consort Road London SW7 2AZ UK
Received: 17 February 2014
Accepted: 25 March 2014
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-χ2 and the Bayesian approaches to parameter estimation. Numerical experiments with 104 independent realizations of an observed orbit confirm that the 1 − and 2σ confidence and credibility intervals have coverage fractions close to their frequentist values.
Key words: binaries: visual / stars: fundamental parameters / methods: statistical
Appendix is available in electronic form at http://www.aanda.org
© ESO, 2014