Related papers: Bayesian inference for orbital eccentricities
We outline the eccentricity evolution of sub-parsec massive black hole binaries (MBHBs) forming in galaxy mergers. In both stellar and gaseous environments, MBHBs are expected to grow large orbital eccentricities before they enter the…
We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over…
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
We explore the eccentricity measurement threshold of LISA for gravitational waves radiated by massive black hole binaries (MBHBs) with redshifted BH masses $M_z$ in the range $10^{4.5}$-$10^{7.5}~{\rm M}_\odot$ at redshift $z=1$. The…
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…
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…
In this paper, we will consider an $hp$-finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational formulation by Cessenat and Depr\'{e}s. We will introduce an…
Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…
We present a first study based on the analysis of the DEep Spectra of Ionized REgions Database (DESIRED). This is a compilation of 190 high signal-to-noise ratio optical spectra of HII regions and other photoionized nebulae, mostly observed…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
Although the gravitational waves observed by advanced LIGO and Virgo are consistent with compact binaries in a quasi-circular inspiral prior to coalescence, eccentric inspirals are also expected to occur in Nature. Due to their complexity,…
In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…
Tidal heating in a binary black hole system is driven by the absorption of energy and angular momentum by the black hole's horizon. Previous works have shown that this phenomenon becomes particularly significant during the late stages of an…
In the canonical model for tidal disruption events (TDEs), the stellar debris circularizes quickly to form an accretion disk of size about twice the orbital pericenter of the star. Most TDEs and candidates discovered in the optical/UV have…
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…
We establish the existence of liftings into discrete subspaces of $\mathbf{H}(\mathrm{div})$ of piecewise polynomial data on locally refined simplicial partitions of polygonal/polyhedral domains. Our liftings are robust with respect to the…
The detection of orbital eccentricity for a binary black hole system via gravitational waves is a key signature to distinguish between the possible binary origins. The identification of eccentricity has been difficult so far due to the…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
We derive analytical expressions for the change in the orbital eccentricity of a binary following a distant encounter with a third star on a hyperbolic or parabolic orbit. To establish the accuracy of these expressions, we present detailed…