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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…
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…
This article shortly introduces Gaussian processes (GP) as a new approach for modelling time series in the field of blazar physics. In the second part of the paper, recent results from an application of GP modelling to the multi-wavelength…
Non-Gaussian observations such as binary responses are common in some computer experiments. Motivated by the analysis of a class of cell adhesion experiments, we introduce a generalized Gaussian process model for binary responses, which…
We formulate the statistics of peaks of non-Gaussian random fields and implement it to study the sphericity of peaks. For non-Gaussianity of the local type, we present a general formalism valid regardless of how large the deviation from…
The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…
This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we…
A gentle introduction to Gaussian processes (GPs). The three parts of the document consider GPs for regression, classification, and dimensionality reduction.
In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
We consider the class of selfsimilar Gaussian generalized random fields introduced by Dobrushin in 1979. These fields are indexed by Schwartz functions on $\mathbb{R}^d$ and parametrized by a self-similarity index and the degree of…
Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional…
This paper presents a theory for how geometric image transformations can be handled by a first layer of linear receptive fields, in terms of true covariance properties, which, in turn, enable geometric invariance properties at higher levels…
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility…
Characterizing quantum processes is indispensable for the implementation of any task in quantum information processing. In this paper, we develop an efficient method to fully characterize arbitrary Gaussian processes in continuous-variable…
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 $\mathbb{R}^3$,…
Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…