Related papers: Simulating space-time random fields with nonsepara…
This work introduces a novel approach for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are jointly…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
Explosive growth in spatio-temporal data and its wide range of applications have attracted increasing interests of researchers in the statistical and machine learning fields. The spatio-temporal regression problem is of paramount importance…
We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
This paper discusses the technical aspects - mathematical and numerical - associated with the numerical simulations of a mesoscopic system in the time domain (i.e. beyond the single frequency AC limit). After a short review of the state of…
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…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…
Fractional Gaussian fields are scalar-valued random functions or generalized functions on an $n$-dimensional manifold $M$, indexed by a parameter $s$. They include white noise ($s = 0$), Brownian motion ($s=1, n=1$), the 2D Gaussian free…
The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
In this paper, we attempt to shed light on a new class of nonstationary random fields which exhibit, what we call, local invariant nonstationarity. We argue that the local invariant property has a special interaction with a new generalized…
An explicit optimal linear spatial predictor is derived. The spatial correlations are imposed by means of Gibbs energy functionals with explicit coupling coefficients instead of covariance matrices. The model inference process is based on…
We construct a Gaussian random field (GRF) that combines fractional smoothness with spatially varying anisotropy. The GRF is defined through a stochastic partial differential equation (SPDE), where the range, marginal variance, and…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
In sound field control applications, it is commonly assumed that one has access to an accurate representation of the sound field in the region of interest. This is a problematic assumption since the reconstruction of a sound field from…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical…