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The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…
The hypothesis that high dimensional data tend to lie in the vicinity of a low dimensional manifold is the basis of manifold learning. The goal of this paper is to develop an algorithm (with accompanying complexity guarantees) for fitting a…
The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert-Schmidt and Bures-Hall ensembles. In this…
Three-dimensional (3D) maps of the Galactic interstellar matter (ISM) are a potential tool of wide use, however accurate and detailed maps are still lacking. One of the ways to construct the maps is to invert individual distance-limited ISM…
We study isometry-invariant probability measures on the space $\Omega$ of tilings of the hyperbolic plane with right-angled hexagons of varying shapes. We prove that, for each measure $\mu$ in a certain natural family of measures on…
Whilst X-rays and Sunyaev-Zel'dovich observations allow to study the properties of the intra-cluster medium (ICM) of galaxy clusters, their gravitational potential may be constrained using strong gravitational lensing. Although being…
We measure three-dimensional bispectra of halo intrinsic alignments (IA) and dark matter overdensities in real space from N-body simulations for halos of mass $10^{12}-10^{12.5} M_\odot /h$. We show that their multipoles with respect to the…
We present a simple proof of some interpolation inequalities between H\"{o}lder and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate…
Dust polarisation observations at optical wavelengths help understand the dust grain properties and trace the plane-of-the-sky component of the magnetic field. In this study, we make use of published optical polarisation data acquired with…
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space,…
In this paper, we consider interaction-free measurement (IFM) with imperfect interaction. In the IFM proposed by Kwiat et al., we assume that interaction between an absorbing object and a probe photon is imperfect, so that the photon is…
We conduct a small-scale pathfinding survey designed to identify the average polarization properties of the diffuse ISM locally at the lowest dust content regions. We perform deep optopolarimetric surveys within three $\sim 15' \times 15'$…
The properties of black-hole and neutron-star binaries are extracted from gravitational-wave signals using Bayesian inference. This involves evaluating a multi-dimensional posterior probability function with stochastic sampling. The…
Random integral mappings $I^{h,r}_{(a,b]}$ give isomorphisms between the sub-semigroups of the classical $(ID, \ast)$ and the free-infinite divisible $(ID,\boxplus)$ probability measures. This allows us to introduce new examples of such…
Standard CMB analysis assumes a direct deterministic mapping between the multipole probed by the CMB $\ell$ and the primordial wavenumber $k$. Since the recombination era has a finite duration, this mapping is probabilistic by construction.…
The Galactic interstellar turbulence affects the density distribution and star formation. We introduce a new method of measuring interstellar turbulent density spectra by using the dispersion measures (DMs) of a large sample of pulsars.…
We present two measurements of the temperature-density relationship (TDR) of the intergalactic medium (IGM) in the redshift range $2.55 < z < 2.95$ using a sample of 13 high-quality quasar spectra and high resolution numerical simulations…
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
We present measurements of the neutral atomic hydrogen (HI) mass function (HIMF) and cosmic HI density ($\Omega_{\rm HI}$) at $0 \leq z \leq 0.088$ from the Looking at the Distant Universe with MeerKAT Array (LADUMA) survey. Using LADUMA…
We determine an absolute calibration of the initial mass function (IMF) of early-type galaxies, by studying a sample of 56 gravitational lenses identified by the SLACS Survey. Under the assumption of standard Navarro, Frenk & White dark…