Related papers: Towards a complete characterization of indicator v…

Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…

Anomaly detection in random fields is an important problem in many applications including the detection of cancerous cells in medicine, obstacles in autonomous driving and cracks in the construction material of buildings. Such anomalies are…

Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…

A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…

Roughly speaking, holonomic measures are parametric varifolds without boundary. They provide a setting appropriate for the analysis of many variational problems. In this paper, we characterize the space of variations for these objects, and…

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…

It has been known for years how random height variations of a repeated nano-scale structure can give rise to smooth angular color variations instead of the well-known diffraction pattern experienced if no randomization is present. However,…

So far, the pseudo cross-variogram is primarily used as a tool for the structural analysis of multivariate random fields. Mainly applying recent theoretical results on the pseudo cross-variogram, we use it as a cornerstone in the…

A necessary and sufficient condition for a random walk in a finite directed graph subject to a road coloring to be measurable with respect to the driving random road colors is proved to be that the road coloring is synchronizing. For this,…

We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…

Measurement system analysis aims to quantify the variability in data attributable to the measurement system and evaluate its contribution to overall data variability. This paper conducts a rigorous theoretical investigation of the…

Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…

This paper proposes robust estimators of the variogram, a statistical tool that is commonly used in geostatistics to capture the spatial dependence structure of data. The new estimators are based on the highly robust minimum covariance…

We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the…

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

This paper develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of Kolmogorov-Smirnov…

Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…

In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…

This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…