Related papers: Inferring the eccentricity distribution
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…
We characterize the eccentricity distribution of a sample of ~50 short-period planet candidates using transit and occultation measurements from NASA's Kepler Mission. First, we evaluate the sensitivity of our hierarchical Bayesian modeling…
This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameter-dependent normalising constant of the Bingham distribution,…
Bayesian hierarchical models are frequently used in practical data analysis contexts. One interpretation of these models is that they provide an indirect way of assigning a prior for unknown parameters, through the introduction of…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
Astronomers generally assume planet-forming disks are aligned with the rotation of their host star. However, recent observations have shown evidence of warping in protoplanetary disks. One can measure the statistical alignment between the…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…
We examine the eccentricity distribution(s) of radial velocity detected exoplanets. Previously, the eccentricity distribution was found to be described well by a Beta distribution with shape parameters $a=0.867, b=3.03$. Increasing the…
Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
Highest posterior density intervals (HPDI's) are derived for the true eccentricities of spectroscopic binaries with measured values e ~ 0. These yield upper limits when e is below the detection threshold e_th and seamlessly transform to…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
When searching for exoplanets, one wants to count how many planets orbit a given star, and to determine what their characteristics are. If the estimated planet characteristics are too far from those of a planet truly present, this should be…
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
Binarity is often invoked to explain peculiarities that can not be explained by the standard theory of stellar evolution. Detecting orbital motion via the Doppler effect is the best method to test binarity when direct imaging is not…
Inspiraling supermassive black hole binary systems with high orbital eccentricity are important sources for space-based gravitational wave (GW) observatories like the Laser Interferometer Space Antenna (LISA). Eccentricity adds orbital…
We focus on the automated classification of eclipsing binary stars using deep learning methods to handle the vast data generated by large-scale photometric sky surveys. These surveys produce extensive datasets that are impractical for…