Related papers: Constructing Optimal $L_{\infty}$ Star Discrepancy…
In this paper we propose an acceptance-rejection sampler using stratified inputs as diver sequence. We estimate the discrepancy of the points generated by this algorithm. First we show an upper bound on the star discrepancy of order…
We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed,…
Triangulation refers to the problem of finding a 3D point from its 2D projections on multiple camera images. For solving this problem, it is the common practice to use so-called optimal triangulation method, which we call the L2 method in…
The achievable level of precision on photospheric abundances of stars is a major limiting factor on investigations of exoplanet host star characteristics, the chemical histories of star clusters, and the evolution of the Milky Way and other…
This paper is concerned with Lagrange interpolation by total degree polynomials in moderate dimensions. In particular, we are interested in characterising the optimal choice of points for the interpolation problem, where we define the…
The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive,…
In this paper, we consider the upper bound of the probabilistic star discrepancy based on Hilbert space filling curve sampling. This problem originates from the multivariate integral approximation, but the main result removes the strict…
We study points in cut-and-project sets which are visible from the origin, continuing a direction of inquiry initiated in [6,14] where the asymptotic density of visible points was investigated. We establish an error bound for the density of…
Context: Massive amounts of spectroscopic data obtained by stellar surveys are feeding an ongoing revolution in our knowledge of stellar and Galactic astrophysics. Analysing these data sets to extract the best possible astrophysical…
It is known that there is a constant $c > 0$ such that for every sequence $x_1, x_2, \ldots$ in $[0,1)$ we have for the star discrepancy $D_N^*$ of the first $N$ elements of the sequence that $N D_N^* \ge c \cdot \log N$ holds for…
We present novel retrospective change point detection approach based on optimal transport and geometric discrepancy. The method does not require any parametric assumptions about distributions separated by change points. It can be used both…
Geometrical objects with integral side lengths have fascinated mathematicians through the ages. We call a set $P=\{p_1,...,p_n\}\subset\mathbb{Z}^2$ a maximal integral point set over $\mathbb{Z}^2$ if all pairwise distances are integral and…
One of the most common problems in statistical experimentation is computing D-optimal designs on large finite candidate sets. While optimal approximate (i.e., infinite-sample) designs can be efficiently computed using convex methods,…
Experimental designs intended to match arbitrary target distributions are typically constructed via a variable transformation of a uniform experimental design. The inverse distribution function is one such transformation. The discrepancy is…
Low-discrepancy points are designed to efficiently fill the space in a uniform manner. This uniformity is highly advantageous in many problems in science and engineering, including in numerical integration, computer vision, machine…
The problem of finding the largest number of points in the unit cross-polytope such that the $l_{1}$-distance between any two distinct points is at least $2r$ is investigated for $r\in\left(1-\frac{1}{n},1\right]$ in dimensions $\geq2$ and…
We give an explicit construction of two-dimensional point sets whose $L_p$ discrepancy is of best possible order for all $1\le p\le \infty$. It is provided by folding Hammersley point sets in base $b$ by means of the $b$-adic baker's…
A change point problem occurs in many statistical applications. If there exist change points in a model, it is harmful to make a statistical analysis without any consideration of the existence of the change points and the results derived…
This study introduces a new "Non-Dimensional" star identification algorithm to reliably identify the stars observed by a wide field-of-view star tracker when the focal length and optical axis offset values are known with poor accuracy. This…
Let $\Omega \subset \mathbb{R}^2$ be a convex set. We study the problem of distributing a one-dimensional set $S$ with total length $L$ so that for any line $\ell$ in $\mathbb{R}^2$ the number of intersections $\#(\ell \cap S)$ is…