Related papers: Star discrepancy for new stratified random samplin…
Star-shaped bodies are an important nonconvex generalization of convex bodies (e.g., linear programming with violations). Here we present an efficient algorithm for sampling a given star-shaped body. The complexity of the algorithm grows…
The $L_{\infty}$ star discrepancy is a very well-studied measure used to quantify the uniformity of a point set distribution. Constructing optimal point sets for this measure is seen as a very hard problem in the discrepancy community.…
Geometric discrepancies are standard measures to quantify the irregularity of distributions. They are an important notion in numerical integration. One of the most important discrepancy notions is the so-called \emph{star discrepancy}.…
With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…
We propose a new method for the characterization of stellar stratification in stellar systems. The method uses the mean-square radius (also called the Spitzer radius) of the system as a diagnostic tool. An estimate of the observable…
We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the…
By a result of Heinrich, Novak, Wasilkowski and Wo\'zniakowski the inverse of the star discrepancy $n(d,\varepsilon)$ satisfies $n(d,\varepsilon)\leq c_{\abs}d\varepsilon^{-2}$. Equivalently for any $N$ and $d$ there exists a set of $N$…
We establish a novel criterion for comparing the performance of two densities, $g_1$ and $g_2$, within the context of corrupted data. Utilizing this criterion, we propose an algorithm to construct a density estimator within a star-shaped…
We analyse the joint distribution of dust attenuation and projected axis ratios, together with galaxy size and surface brightness profile information, to infer lessons on the dust content and star/dust geometry within star-forming galaxies…
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…
We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set consisting of $N$ points chosen uniformly at random in the $s$-dimensional unit cube $[0,1]^s$ with probability at least $1-\exp(-\Theta(s))$…
In 2001 Heinrich, Novak, Wasilkowski and Wo\'zniakowski proved that the inverse of the star discrepancy satisfies $n(d,\varepsilon)\leq c_{\abs}d \varepsilon^{-2}$ by showing that there exists a set of points in $[0,1)^d$ whose…
Low discrepancy point sets have been widely used as a tool to approximate continuous objects by discrete ones in numerical processes, for example in numerical integration. Following a century of research on the topic, it is still unclear…
The evolution of massive stars is the basis of several astrophysical investigations, from predicting gravitational-wave event rates to studying star-formation and stellar populations in clusters. However, uncertainties in massive star…
Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo…
We introduce a class of $\gamma$-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a…
A vast array of envy-free results have been found for the subdivision of one-dimensional resources, such as the interval $[0,1]$. The goal is to divide the space into $n$ pieces and distribute them among $n$ observers such that each…
Observations of the spatial distributions of young stars in star-forming regions can be linked to the theory of clustered star formation using spatial statistical methods. The MYStIX project provides rich samples of young stars from the…
We present a new method for detecting and correcting systematic errors in the distances to stars when both proper motions and line-of-sight velocities are available. The method, which is applicable for samples of 200 or more stars that have…
This paper investigates what can be inferred about an arbitrary continuous probability distribution from a finite sample of $N$ observations drawn from it. The central finding is that the $N$ sorted sample points partition the real line…