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Self-consistent relativistic random-phase approximation (RPA) in the radial coordinate representation is established by using the finite amplitude method (FAM). Taking the isoscalar giant monopole resonance in spherical nuclei as example,…
We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…
It is common and convenient to treat distributed physical parameters as Gaussian random fields and model them in an "inverse procedure" using measurements of various properties of the fields. This article presents a general method for this…
Gaussian processes (GP) are a popular and powerful tool for spatial modelling of data, especially data that quantify environmental processes. However, in stationary form, whether covariance is isotropic or anisotropic, GPs may lack the…
Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analysing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
Gaussian fields (GFs) are frequently used in spatial statistics for their versatility. The associated computational cost can be a bottleneck, especially in realistic applications. It has been shown that computational efficiency can be…
In this work, we study a family of wireless channel simulation models called geometry-based stochastic channel models (GBSCMs). Compared to more complex ray-tracing simulation models, GBSCMs do not require an extensive characterization of…
In this paper, we propose a novel and efficient two-stage variable selection approach for sparse GLARMA models, which are pervasive for modeling discrete-valued time series. Our approach consists in iteratively combining the estimation of…
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…
These days we live in a world with a permanent electromagnetic field. This raises many questions about our health and the deployment of new equipment. The problem is that these fields remain difficult to visualize easily, which only some…
Engineering simulations using boundary-value partial differential equations often implicitly assume that the uncertainty in the location of the boundary has a negligible impact on the output of the simulation. In this work, we develop a…
The efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning. Today's prevalent random field representations are either intended for unbounded domains…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
We introduce a new approximate multiresolution analysis (MRA) using a single Gaussian as the scaling function, which we call Gaussian MRA (GMRA). As an initial application, we employ this new tool to accurately and efficiently compute the…
This paper presents a solution for persistent monitoring of real-world stochastic phenomena, where the underlying covariance structure changes sharply across time, using a small number of mobile robot sensors. We propose an adaptive…