Full-Scale Approximations of Spatio-Temporal Covariance Models for Large Datasets

Zhang, Bohai; Sang, Huiyan; Huang, Jianhua Z.

doi:10.5705/ss.2013.260w

Cited by 18 publications

(23 citation statements)

References 32 publications

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“…A natural extension of the proposed method is the spatio-temporal setting (Katzfuss and Cressie (2011);Bevilacqua et al (2012); Zhang et al (2015)),…”

Section: Discussionmentioning

confidence: 99%

“…Alternatively, we can treat the knots as unknown parameters and model them stochastically (Guhaniyogi et al (2011);Katzfuss (2013);Zhang et al (2015)). For the block partition, Eidsvik et al…”

Section: Choices Of Tuning Parameters For Sfsamentioning

confidence: 99%

“…It turns out that FSA-Block outperforms FSA-Taper empirically (Sang et al (2011)), possibly due to its nature of being an unbiased approximation of covariance within each data block, and the convenience of using parallel computation. Zhang et al (2015) extends the FSA-Block approximation to GP models for large spatio-temporal datasets.…”

Section: Introductionmentioning

confidence: 99%

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Smoothed Full-Scale Approximation of Gaussian Process Models for Computation of Large Spatial Datasets

Zhang¹,

Sang²,

Huang³

2019

STAT SINICA

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Gaussian process (GP) models encounter computational difficulties with large spatial datasets since its computational complexity grows cubically with sample size n. Although the Full-Scale Approximation (FSA) using a block modulating function provides an effective way for approximating GP models, it has several shortcomings such as the less smooth prediction surface on block boundaries and sensitiveness to the knot set under small-scale data dependence. To address these issues, we propose a Smoothed Full-Scale Approximation (SFSA) method for the analysis of large spatial dataset. The SFSA leads to a class of scalable GP models, whose covariance functions consist of two parts: A reduced-rank covariance function capturing large-scale spatial dependence and a covariance adjusting local covariance approximation errors of the reduced-rank part both within blocks and between neighboring blocks. This method can alleviate the prediction errors on block boundaries; it also leads to more robust inference and prediction results under different dependence scales due to better approximation of the residual covariance. The proposed method provides a unified view of approximation methods for GP models, encompassing several existing computational methods for large spatial datasets into one common framework, including the predictive process, the FSA, and the nearest neighboring block Gaussian process methods, allowing efficient algorithms for more robust and accurate model inference and prediction for large spatial datasets in a unified framework. We illustrate the effectiveness of the SFSA approach through simulation studies and a total column ozone dataset.

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“…A natural extension of the proposed method is the spatio-temporal setting (Katzfuss and Cressie (2011);Bevilacqua et al (2012); Zhang et al (2015)),…”

Section: Discussionmentioning

confidence: 99%

Section: Choices Of Tuning Parameters For Sfsamentioning

confidence: 99%

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Smoothed Full-Scale Approximation of Gaussian Process Models for Computation of Large Spatial Datasets

Zhang¹,

Sang²,

Huang³

2019

STAT SINICA

Self Cite

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“…Zhang et al . () employed a procedure for joint estimation for knots and parameters in a composite approach. We shall follow the latter with a modification to allow for our assumed uniform distribution of knot locations.…”

Section: Estimation and Krigingmentioning

confidence: 99%

“…Gelfand et al (2012) proposed a predictive process approach to specify them separately from parameter estimation. Zhang et al (2015) employed a procedure for joint estimation for knots and parameters in a composite approach. We shall follow the latter with a modification to allow for our assumed uniform distribution of knot locations.…”

Section: Knot Specificationmentioning

confidence: 99%

Continuous Auto-Regressive Moving Average Random Fields on Rn

Brockwell

Matsuda

2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We define an isotropic Lévy‐driven continuous auto‐regressive moving average CARMA(p,q) random field on double-struckRn as the integral of a radial CARMA kernel with respect to a Lévy sheet. Such fields constitute a parametric family characterized by an auto‐regressive polynomial a and a moving average polynomial b having zeros in both the left and the right complex half‐planes. They extend the well‐balanced Ornstein–Uhlenbeck process of Schnurr and Woerner to a well‐balanced CARMA process in one dimension (with a much richer class of autocovariance functions) and to an isotropic CARMA random field on double-struckRn for n>1. We derive second‐order properties of these random fields and extend the results to a larger class of anisotropic CARMA random fields. If the driving Lévy sheet is compound Poisson it is trivial to simulate the corresponding random field on any bounded subset of double-struckRn. A method for joint estimation of the CARMA kernel parameters and knot locations is proposed for compound‐Poisson‐driven fields and is illustrated by applications to simulated data and Tokyo land price data.

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Separable spatio‐temporal kriging for fast virtual sensing

Miniato

Bellio

Grassetti

et al. 2022

Appl Stoch Models Bus & Ind

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Environmental monitoring is a task that requires to surrogate system-wide information with limited sensor readings. Under the proximity principle, an environmental monitoring system can be based on the virtual sensing logic and then rely on distance-based prediction methods, foremostly spatio-temporal kriging. The last one is cumbersome with large datasets, but we show that a suitable separability assumption reduces its computational cost to an extent broader than considered typically. Only spatial interpolation needs to be performed in a centralized way, while forecasting can be delegated to each sensor. This simplification is related to the fact that two separate models are involved, one in time and one in the space domain. Any of the two models can be replaced without re-estimating the other under a composite likelihood (CL) approach. Moreover, the use of convenient spatial and temporal models eases up computation, not only in the CL approach, but also in maximum likelihood estimation. We show that this perspective on kriging allows to perform virtual sensing even in the case of tall datasets.

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Full-Scale Approximations of Spatio-Temporal Covariance Models for Large Datasets

Cited by 18 publications

References 32 publications

Smoothed Full-Scale Approximation of Gaussian Process Models for Computation of Large Spatial Datasets

Smoothed Full-Scale Approximation of Gaussian Process Models for Computation of Large Spatial Datasets

Continuous Auto-Regressive Moving Average Random Fields on Rn

Separable spatio‐temporal kriging for fast virtual sensing

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