Related papers: Frequentist confidence intervals for orbits
We present in this article the use of probabilistic background constraints in astronomical image deconvolution to approach to a solution as an interval estimate. We elaborate our objective -- the interval estimate of the unknown object from…
Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
The frequency of planets in binaries is an important issue in the field of extrasolar planet studies because of its relevance in the estimation of the global planet population of our galaxy and the clues it can give to our understanding of…
I present a critical review of techniques for estimating confidence intervals on binomial population proportions inferred from success counts in small-to-intermediate samples. Population proportions arise frequently as quantities of…
We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…
In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds…
We investigate the relation between frequentist and Bayesian approaches. Namely, we find the "frequentist" Bayes prior \pi_{f}(\lambda,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,\lambda)}{\partial…
Wide binary stars are important for testing alternative models of gravitation in the weak-field regime and understanding the statistical outcomes of dynamical interactions in the general Galactic field. The Gaia mission's collection of…
We describe regularized methods for image reconstruction and focus on the question of hyperparameter and instrument parameter estimation, i.e. unsupervised and myopic problems. We developed a Bayesian framework that is based on the \post…
In many common situations, a Bayesian credible interval will be, given the same data, very similar to a frequentist confidence interval, and researchers will interpret these intervals in a similar fashion. However, no predictable similarity…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
Eclipsing binaries are crucial for understanding stellar physics, allowing detailed studies of stellar masses, radii, and orbital dynamics. Recent space missions like the Transiting Exoplanet Survey Satellite (TESS) have significantly…
We study asymptotic frequentist coverage and approximately Gaussian properties of Bayes posterior credible sets in nonlinear inverse problems when a Gaussian prior is placed on the parameter of the PDE. The aim is to ensure valid…
A large number of direct imaging surveys for exoplanets have been performed in recent years, yielding the first directly imaged planets and providing constraints on the prevalence and distribution of wide planetary systems. However, like…
In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of…
The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized. Computationnally effective fast and accurate)tools for constructing gravitational wave templates from binary…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
Statistics of orbital parameters of binary stars as well as statistics of their physical characteristics bear traces of star formation history. However, statistical investigations of binaries are complicated by lacking or incomplete…
We investigate potential biases in the measurements of exoplanet orbital parameters obtained from radial velocity observations for single-planet systems. We create a mock catalog of radial velocity data, choosing input planet masses,…