Related papers: Frequentist confidence intervals for orbits
Light curves of microlensing events involving stellar binaries and planetary systems can provide information about the orbital elements of the system due to orbital modulations of the caustic structure. Accurately measuring the orbit in…
We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…
Abstract abridged. Eclipsing binary systems provide the opportunity to measure the fundamental parameters of their component stars in a stellar-model-independent way. This makes them ideal candidates for testing and calibrating theories of…
For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…
A general method is presented for estimating the uncertainty in hybrid models of gravitational waveforms from binary black-hole systems with arbitrary physical parameters, and thence the highest allowable initial orbital frequency for a…
Consider a linear regression model with regression parameter beta and normally distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified vector. Define the parameter tau = c^T beta - t where c and…
Wide-field surveys for transiting planets, such as the NASA Kepler and TESS missions, are usually conducted without knowing which stars have binary companions. Unresolved and unrecognized binaries give rise to systematic errors in planet…
Consider a linear regression model with n-dimensional response vector, regression parameter \beta = (\beta_1, ..., \beta_p) and independent and identically N(0, \sigma^2) distributed errors. Suppose that the parameter of interest is \theta…
The observed orbits of emission-line stars may be affected by systematics owing to their broad emission lines being formed in complex and extended environments. This is problematic when orbital parameter probability distributions are…
Context. Establishing the multiplicity of O-type stars is the first step towards accurately determining their stellar parameters. Moreover, the distribution of the orbital parameters provides observational clues to the way that O-type stars…
It is shown that the fiducial distribution in a group model, or more generally a quasigroup model, determines the optimal equivariant frequentist inference procedures. The proof does not rely on existence of invariant measures, and…
We present an algorithmic solution to the problem of incremental belief updating in the context of Monte Carlo inference in Bayesian statistical models represented by probabilistic programs. Given a model and a sample-approximated…
One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the…
Background: Analyses of elastic scattering with the optical model (OMP) are widely used in nuclear reactions. Purpose: Previous work compared a traditional frequentist approach and a Bayesian approach to quantify uncertainties in the OMP.…
Several rapid parameter estimation methods have recently been advanced to deal with the computational challenges of the problem of Bayesian inference of the properties of compact binary sources detected in the upcoming science runs of the…
Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…
We have developed a new, fast method of estimating the orbital properties of a binary or triple system using as few as two epochs of astrometric data. FOBOS (Few Observation Binary Orbit Solver) uses a flat prior brute force Monte Carlo…
We present an optimization-based framework to construct confidence intervals for functionals in constrained inverse problems, ensuring valid one-at-a-time frequentist coverage guarantees. Our approach builds upon the now-called strict…
Planet formation is often considered in the context of one circumstellar disk around one star. Yet stellar binary systems are ubiquitous, and thus a substantial fraction of all potential planets must form and evolve in more complex,…
The eccentricity of a planet's orbit and the inclination of its orbital plane encode important information about its formation and history. However, exoplanets detected via direct-imaging are often only observed over a very small fraction…