Efficient models for correlated data via convolutions of intrinsic processes

Lee, Herbert K. H.; Higdon, Dave; Calder, Catherine A.; Holloman, Christopher

doi:10.1191/1471082x05st085oa

Cited by 37 publications

(29 citation statements)

References 30 publications

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“…In order to circumvent that limitation, several non-stationary approaches have been proposed in the recent literature, including convolution kernels (see [32] or [27]), kernels incorporating non-linear transformations of the input space ( [20,4,47]), or treed gaussian processes ( [19]), to cite an excerpt of some of the most popular approaches.…”

Section: Introductionmentioning

confidence: 99%

Argumentwise invariant kernels for the approximation of invariant functions

Ginsbourger¹,

Bay²,

Roustant³

et al. 2012

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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Abstract. We consider the problem of designing adapted kernels for approximating functions invariant under a known finite group action. We introduce the class of argumentwise invariant kernels, and show that they characterize centered square-integrable random fields with invariant paths, as well as Reproducing Kernel Hilbert Spaces of invariant functions. Two subclasses of argumentwise kernels are considered, involving a fundamental domain or a double sum over orbits. We then derive invariance properties for Kriging and conditional simulation based on argumentwise invariant kernels. The applicability and advantages of argumentwise invariant kernels are demonstrated on several examples, including a symmetric function from the reliability literature.Résumé. Nous considérons le problème d'approximation par méthodes a noyaux de fonctions invariantes sous l'action d'un groupe fini. Nous introduisons les noyaux doublement invariants, et montrons qu'ils caractérisent les champs aléatoires centrés de carré intégrableà trajectoires invariantes, ainsi que les espaces de Hilbertà noyau reproduisant de fonctions invariantes. Deux classes particulières de noyaux doublement invariants sont considérées, basées respectivement sur un domaine fondamental ou sur une double somme sur les orbites. Nousétablissons ensuite des propriétés d'invariance pour les modèles de Krigeage et les simulations consitionnelles associés. L'applicabilité et les avantages de tels noyaux sont illustrés sur plusieurs exemples, incluant une fonction symétrique issue d'un problème de fiabilité des structures.

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Section: Introductionmentioning

confidence: 99%

Argumentwise invariant kernels for the approximation of invariant functions

Ginsbourger¹,

Bay²,

Roustant³

et al. 2012

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

View full text Add to dashboard Cite

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“…Higdon (1998) and Higdon (2002) develop such a method for spatio-temporal data by allowing the parameters of a separable kernel k to vary over space and/or time. A simpler example for a purely spatial process is provided by Lee et al (2005), who allow the convolved process W to be more general than white noise. They treat W as an "intrinsically stationary" process, such as a random walk or Markov random field on a discrete set of locations, while fixing k as a Gaussian kernel.…”

Section: Other Approachesmentioning

confidence: 99%

Bivariate geostatistical modelling: a review and an application to spatial variation in radon concentrations

Fanshawe

Diggle

2011

Environ Ecol Stat

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We present a comprehensive review of multivariate geostatistical models, focusing on the bivariate case. We compare in detail three approaches, the linear model of coregionalisation, the common component model and the kernel convolution approach, and discuss similarities between them. We demonstrate the merits of the common component class of models as a flexible means for modelling bivariate geostatistical data of the type that frequently arises in environmental applications. In particular, we show how kernel convolution can be used to approximate the common component model, and demonstrate the method using a data-set of calcium and magnesium concentrations in soil samples. We then apply the model to a study of domestic radon concentrations in the city of Winnipeg, Canada, in which exposure was measured at two sites (bedroom and basement) in each residential location. Our analysis demonstrates that in this study the correlation between the two sites within each house dominates the short-range spatial correlation typical of the distribution of radon.

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“…The FMM in (7) has the same form described in spatial statistics as a "process convolution" (or kernel convolution; e.g., Barry and Ver Hoef 1996;Higdon 1998;Lee et al 2005;Calder 2007). The process convolution has been instrumental in many fields, but especially in spatial statistics for allowing both complicated and efficient representations of covariance structure.…”

Section: Smoothness In Trajectory Modelsmentioning

confidence: 99%

Basis Function Models for Animal Movement

Hooten

Johnson

2017

Journal of the American Statistical Association

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Advances in satellite-based data collection techniques have served as a catalyst for new statistical methodology to analyze these data. In wildlife ecological studies, satellite-based data and methodology have provided a wealth of information about animal space use and the investigation of individual-based animal-environment relationships. With the technology for data collection improving dramatically over time, we are left with massive archives of historical animal telemetry data of varying quality. While many contemporary statistical approaches for inferring movement behavior * The authors thank Mat Alldredge, are specified in discrete time, we develop a flexible continuous-time stochastic integral equation framework that is amenable to reduced-rank second-order covariance parameterizations. We demonstrate how the associated first-order basis functions can be constructed to mimic behavioral characteristics in realistic trajectory processes using telemetry data from mule deer and mountain lion individuals in western North America. Our approach is parallelizable and provides inference for heterogeneous trajectories using nonstationary spatial modeling techniques that are feasible for large telemetry data sets.

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Efficient models for correlated data via convolutions of intrinsic processes

Cited by 37 publications

References 30 publications

Argumentwise invariant kernels for the approximation of invariant functions

Argumentwise invariant kernels for the approximation of invariant functions

Bivariate geostatistical modelling: a review and an application to spatial variation in radon concentrations

Basis Function Models for Animal Movement

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