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Related papers: Half-Spectral Space-Time Covariance Models

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In this paper, we give a new covariation spectral representation of some non stationary symmetric $\alpha$-stable processes (S$\alpha$S). This representation is based on a weaker covariation pseudo additivity condition which is more general…

Probability · Mathematics 2008-02-22 Nourddine Azzaoui

.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…

Statistical Mechanics · Physics 2020-08-26 V. Sposini , D. S. Grebenkov , R. Metzler , G. Oshanin , F. Seno

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…

Instrumentation and Methods for Astrophysics · Physics 2017-11-15 Daniel Foreman-Mackey , Eric Agol , Sivaram Ambikasaran , Ruth Angus

We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…

Methodology · Statistics 2020-07-29 Evandro Konzen , Jian Qing Shi , Zhanfeng Wang

Using the white noise space framework, we define a class of stochastic processes which include as a particular case the fractional Brownian motion and its derivative. The covariance functions of these processes are of a special form,…

Probability · Mathematics 2009-09-24 Daniel Alpay , Haim Attia , David Levanony

The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…

Computation · Statistics 2024-05-01 Paul G. Beckman , Christopher J. Geoga

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

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…

Machine Learning · Statistics 2017-11-09 James Hensman , Nicolas Durrande , Arno Solin

The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…

Methodology · Statistics 2022-02-04 Javier Zapata , Sang-Yun Oh , Alexander Petersen

We provide a novel approach to model space-time random fields where the temporal argument is decomposed into two parts. The former captures the linear argument, which is related, for instance, to the annual evolution of the field. The…

Statistics Theory · Mathematics 2018-01-18 Alfredo Alegría , Emilio Porcu

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

Methodology · Statistics 2015-09-15 Mark D. Risser , Catherine A. Calder

A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued…

Methodology · Statistics 2018-07-18 Dominik Liebl , Fabian Walders

A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…

Machine Learning · Statistics 2015-07-10 Chintan A. Dalal , Vladimir Pavlovic , Robert E. Kopp

Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…

Methodology · Statistics 2023-03-17 Quan Vu , Andrew Zammit-Mangion , Stephen J. Chuter

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…

Machine Learning · Statistics 2017-03-31 Maziar Raissi , Paris Perdikaris , George Em Karniadakis

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…

Methodology · Statistics 2022-08-09 Emilio Porcu , Philip A. White , Marc G. Genton

We introduce a broad class of models called semiparametric spatial point process for making inference between spatial point patterns and spatial covariates. These models feature an intensity function with both parametric and nonparametric…

Methodology · Statistics 2025-09-24 Xindi Lin , Bumjun Park , Christopher Zahasky , Hyunseung Kang

Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…

Machine Learning · Statistics 2021-07-15 Wenqi Fang , Guanlin Wu , Jingjing Li , Zheng Wang , Jiang Cao , Yang Ping

We propose a statistical space-time model for predicting atmospheric wind speed based on deterministic numerical weather predictions and historical measurements. We consider a Gaussian multivariate space-time framework that combines…

Applications · Statistics 2016-10-21 Julie Bessac , Emil Mihai Constantinescu , Mihai Anitescu