Related papers: A generalized spatial sign covariance matrix
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
We derive in this paper expressions for the covariance matrix of the cosmic shear two-point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
Covariance functions are the core of spatial statistics, stochastic processes, machine learning as well as many other theoretical and applied disciplines. The properties of the covariance function at small and large distances determine the…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…
In many real-world applications data exhibits non-stationarity, i.e., its distribution changes over time. One approach to handling non-stationarity is to remove or minimize it before attempting to analyze the data. In the context of brain…
Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…
The stochastic mirror descent (SMD) algorithm is a general class of training algorithms, which includes the celebrated stochastic gradient descent (SGD), as a special case. It utilizes a mirror potential to influence the implicit bias of…
Tackling pattern recognition problems in areas such as computer vision, bioinformatics, speech or text recognition is often done best by taking into account task-specific statistical relations between output variables. In structured…
We present spatial-Slepian transform~(SST) for the representation of signals on the sphere to support localized signal analysis. We use well-optimally concentrated Slepian functions, obtained by solving the Slepian spatial-spectral…
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…
The physical properties of matter are typically described by coefficient matrices governed by crystal symmetry. Applying spatial operations, such as rotation, inversion, and mirror, to these matrices provides an effective approach for…
We derive explicit expressions for a family of radially symmetric, non-differentiable, Spartan covariance functions in $\mathbb{R}^2$ that involve the modified Bessel function of the second kind. In addition to the characteristic length and…
At lower energies, the resonances in scattering experiments are often isolated. The crucial parameter is the ratio of average resonance width and average mean level spacing. Towards larger energies, this parameter grows, because the…
Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in…
Motivated by recent data analyses in biomedical imaging studies, we consider a class of image-on-scalar regression models for imaging responses and scalar predictors. We propose using flexible multivariate splines over triangulations to…
This work continues the development of the raytracing method of [1] for computing the scattered fields from metasurfaces characterized by locally periodic reflection and transmission coefficients. In this work, instead of describing the…
There have been significant recent advances in our understanding of the potential use and limitations of early-warning signs for predicting drastic changes, so called critical transitions or tipping points, in dynamical systems. A focus of…
Spatial statistics is dominated by spatial autocorrelation (SAC) based Kriging and BHM, and spatial local heterogeneity based hotspots and geographical regression methods, appraised as the first and second laws of Geography (Tobler 1970;…