Related papers: Recent advances in directional statistics

Classical statistics deals with determined and precise data analysis. But in reality, there are many cases where the information is not accurate and a degree of impreciseness, uncertainty, incompleteness, and vagueness is observed. In these…

The aim of this guidance note is to provide recommendations on best statistical practices and to ensure consistent communication of statistical analysis and associated uncertainty across TOAR publications. The scope includes approaches for…

The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…

This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…

We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…

Understanding pedestrian dynamics is crucial for appropriately designing pedestrian spaces. The pedestrian fundamental diagram (FD), which describes the relationship between pedestrian flow and density within a given space, characterizes…

Patterns and nonlinear waves, such as spots, stripes, and rotating spirals, arise prominently in many natural processes and in reaction-diffusion models. Our goal is to compute boundaries between parameter regions with different prevailing…

In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…

Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…

This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…

Dimension reduction of multivariate data supervised by auxiliary information is considered. A series of basis for dimension reduction is obtained as minimizers of a novel criterion. The proposed method is akin to continuum regression, and…

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…

Consider measured positions of the paleomagnetic north pole over time. Each measured position may be viewed as a direction, expressed as a unit vector in three dimensions and incorporating some error. In this sequence, the true directions…

Superpositions of different statistics on different time or spatial scales (in short, superstatistics) can naturally lead to an effective description by nonextensive statistical mechanics. We first discuss the role of escort distributions…

The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are…

The present status of the (JR) dynamical parton distribution functions is reported. Different theoretical improvements, including the determination of the strange sea input distribution, the treatment of correlated errors and the inclusion…

This paper mainly contributes to a classification of statistical Einstein manifolds, namely statistical manifolds at the same time are Einstein manifolds. A statistical manifold is a Riemannian manifold, each of whose points is a…