Related papers: Robust Comparison of Kernel Densities on Spherical…

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…

Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…

Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point…

Spatial patterning is common in ecological systems and has been extensively studied via different modeling approaches. Individual-based models (IBMs) accurately describe nonlinear interactions at the organism level and the stochastic…

One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…

The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…

We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…

A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length,…

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…

The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…

Spatially-explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density Surface Models (DSMs) are a two-stage approach for estimating spatially-varying…

Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical…

This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly…

Recent work on background subtraction has shown developments on two major fronts. In one, there has been increasing sophistication of probabilistic models, from mixtures of Gaussians at each pixel [7], to kernel density estimates at each…

Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…

Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…

The approaches taken to describe and develop spatial discretisations of the domains required for geophysical simulation models are commonly ad hoc, model or application specific and under-documented. This is particularly acute for…