Related papers: Minimization of the Probabilistic p-frame Potentia…
We propose a general and relatively simple method for the construction of goodness-of-fit tests on the sphere and the hypersphere. The method is based on the characterization of probability distributions via their characteristic function,…
Possibility and probability theories are alternative and complementary ways to deal with uncertainty, which has motivated over the last years an interest for the study of ways to transform probability distributions into possibility…
Particle swarm optimisation is a metaheuristic algorithm which finds reasonable solutions in a wide range of applied problems if suitable parameters are used. We study the properties of the algorithm in the framework of random dynamical…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also…
We consider the problem of rescaling the lengths of a finite frame thereby transforming it into a tight one. Such frames are called scalable and have received a lot of attention in recent years. In this note we investigate the question in…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares. We examine several statistics of these point sets, such as the electrostatic potential,…
This paper investigates the problem of optimal predictor design for distributed parameter systems using neural networks and shape optimization. Sensors with various shapes are placed on the domain of the distributed parameter system. Data…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
We relate scattering amplitudes in particle physics to maximum likelihood estimation for discrete models in algebraic statistics. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a…
We consider the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability. As expected, under the assumption of…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
The consideration of the N-body gravitational problem equations can give to us some class of boundary-value problems defined on the "beem's" construction. One can considere it as weak or so-called finite element method's approximation with…
In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the…
Given $d, N\geq 2$ and $p\in (0, \infty]$ we consider a family of functionals, the $p$-frame potentials FP$_{p, N, d}$, defined on the set of all collections of $N$ unit-norm vectors in $\mathbb R^d$. For the special case $p=2$ and…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…