Related papers: Gaussian Processes with Sample Paths in Reproducin…
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…
With the proliferation of screening tools for chemical testing, it is now possible to create vast databases of chemicals easily. However, rigorous statistical methodologies employed to analyse these databases are in their infancy, and…
Quantitative modeling of post-transcriptional regulation process is a challenging problem in systems biology. A mechanical model of the regulatory process needs to be able to describe the available spatio-temporal protein concentration and…
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…
The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…
If $\mu_1,\mu_2,\dots$ are positive measures on a measurable space $(X,\Sigma)$ and $v_1,v_2, \dots$ are elements of a Banach space ${\mathbb E}$ such that $\sum_{n=1}^\infty \|v_n\| \mu_n(X) < \infty$, then $\omega (S)= \sum_{n=1}^\infty…
In this article, we solve a deterministically generalized interpolation problem by a stochastic approach. We introduce a kernel-based probability measure on a Banach space by a covariance kernel which is defined on the dual space of the…
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…
Continuing the analysis initiated in Lachi\'eze-Rey and Peccati (2011), we use contraction operators to study the normal approximation of random variables having the form of a U-statistic written on the points in the support of a random…
Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of…
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum…
We develop a Radon transform on Banach spaces using Gaussian measure and prove that if a bounded continuous function on a separable Banach space has zero Gaussian integral over all hyperplanes outside a closed bounded convex set in the…
In this work we introduce a reduced-rank algorithm for Gaussian process regression. Our numerical scheme converts a Gaussian process on a user-specified interval to its Karhunen-Lo\`eve expansion, the $L^2$-optimal reduced-rank…
Let $P$ be a linear differential operator over $\mathcal{D} \subset \mathbb{R}^d$ and $U = (U_x)_{x \in \mathcal{D}}$ a second order stochastic process. In the first part of this article, we prove a new necessary and sufficient condition…
Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
The focus of this work is the convergence of non-stationary and deep Gaussian process regression. More precisely, we follow a Bayesian approach to regression or interpolation, where the prior placed on the unknown function $f$ is a…
The Wegner orbital model is a class of random operators introduced by Wegner to model the motion of a quantum particle with many internal degrees of freedom (orbitals) in a disordered medium. We consider the case when the matrix potential…
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…
We derive unique Banach-valued solutions to stochastic Volterra equations with random coefficients that may depend on pure chance and involve singular kernels. In particular, for controlled and distribution-dependent coefficients these…