Related papers: Frequentist confidence intervals for orbits
An efficient Bayesian technique for estimation problems in fundamental stellar astronomy is tested on simulated data for a binary observed both astrometrically and spectroscopically. Posterior distributions are computed for the components'…
The problem of estimating the total mass of a visual binary when its orbit is incomplete is treated with Bayesian methods. The posterior mean of a mass estimator is approximated by a triple integral over orbital period, time of periastron…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
Knowledge of the orbits of visual binary stars has always been one of the fundamentals of astronomy. Based historically on the visual measures, nowadays the orbits rely more (or exclusively) on the accurate speckle data. This prompts…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
The most complete list of visual binary systems with known orbital elements is compiled. It is based on OARMAC and ORB6 data and contains 3139 orbits for 2278 pairs. A refined subset of high quality orbits with available distance was also…
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…
Methods used in the radial-velocity program of short-period binary systems at the David Dunlap Observatory are described with particular stress on the Broadening Function (BF) formalism. This formalism has permitted determination of radial…
The optimal instant of observation of astrophysical phenomena for objects that vary on human time-sales is an important problem, as it bears on the cost-effective use of usually scarce observational facilities. In this paper we address this…
We present a Bayesian inference methodology for the estimation of orbital parameters on single-line spectroscopic binaries with astrometric data, based on the No-U-Turn sampler Markov chain Monte Carlo algorithm. Our approach is designed to…
Estimating the difference between two binomial proportions will be investigated, where Bayesian, frequentist and fiducial (BFF) methods will be considered. Three vague priors will be used, the Jeffreys prior, a divergence prior and the…
We present orbital elements and mass sums for eighteen visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two double-line spectroscopic binaries with no previous…
The evaluation of the error to be attributed to cut efficiencies is a common question in the practice of experimental particle physics. Specifically, the need to evaluate the efficiency of the cuts for background removal, when they are…
The angle between the stellar spin-axis and the orbital plane of a stellar or planetary companion has important implications for the formation and evolution of such systems. A study by Hale (1994) found that binaries with separations $a <…
Under certain rather prevalent conditions (driven by dynamical orbital evolution), a hierarchical triple stellar system can be well approximated, from the standpoint of orbital parameter estimation, as two binary star systems combined. Even…
The orbital solutions for astrometric (unresolved) binary stars provided in the Gaia mission Data Release 3 reveal an obvious deficit of face-on orbits with line-of-sight inclinations close to 0 or $\pi$. This is shown to be an intrinsic…
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…
We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is…
We discuss a Bayesian approach to the analysis of radial velocities in planet searches. We use a combination of exact and approximate analytic and numerical techniques to efficiently evaluate chi-squared for multiple values of orbital…
In this paper we introduce an algorithm for determining the orbital elements and individual masses of visual binaries. The algorithm uses an optimal point, which minimizes a specific function describing the average length between the…