Data Configurations and the Cokriging System: Simplification by Screen Effects

Subramanyam, A.; Pandalai, H. S.

doi:10.1007/s11004-008-9153-9

Cited by 16 publications

(4 citation statements)

References 10 publications

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“…The stepwise selection algorithm can also be extended to the multivariate framework, when using cokriging under a coregionalization model. In this respect, Rivoirard [20] and Subramanyam and Pandalai [22] showed that the best data selection depends on the coregionalization model, which corroborates the findings made here in the univariate context.…”

Section: Stepwise Data Selectionsupporting

confidence: 87%

The kriging update equations and their application to the selection of neighboring data

Emery

2008

Comput Geosci

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A key problem in the application of kriging is the definition of a local neighborhood in which to search for the most relevant data. A usual practice consists in selecting data close to the location targeted for prediction and, at the same time, distributed as uniformly as possible around this location, in order to discard data conveying redundant information. This approach may however not be optimal, insofar as it does not account for the data spatial correlation. To improve the kriging neighborhood definition, we first examine the effect of including one or more data and present equations in order to quickly update the kriging weights and kriging variances. These equations are then applied to design a stepwise selection algorithm that progressively incorporates the most relevant data, i.e., the data that make the kriging variance decrease more. The proposed algorithm is illustrated on a soil contamination dataset.

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Section: Stepwise Data Selectionsupporting

confidence: 87%

The kriging update equations and their application to the selection of neighboring data

Emery

2008

Comput Geosci

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“…For instance, the data of a covariate may be screened out by the collocated data of the primary variable or, on the contrary, they may supplement the primary data and provide useful information to improve local estimation. As suggested by recent publications (Rivoirard, 2004;Subramanyam and Pandalai, 2008), the decision to include or not the covariate data should consider the correlation structure of the coregionalized variables and the sampling scheme (in particular, whether or not all the variables are measured at all the sampling locations). Some options include: a.…”

Section: Kriging and Cokriging Neighborhoodmentioning

confidence: 99%

Geostatistical Estimation of Biomass Stock in Chilean Native Forests and Plantations

Hernández¹,

Corvalán²,

Emery³

et al. 2012

Remote Sensing of Biomass - Principles and Applications

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“…With multiple variables, interpolation becomes a multivariate problem, and is traditionally accommodated via co-kriging, the multivariate extension of kriging. Co-kriging is often particularly useful when one variable is of primary importance, but is correlated with other types of processes that are more readily observed (Almeida and Journel (1994); Wackernagel (1994); Journel (1999); Shmaryan and Journel (1999); Subramanyam and Pandalai (2008)). Much expository work has been developed on co-kriging, see Myers (1982Myers ( , 1983Myers ( , 1991Myers ( , 1992, Long and Myers (1997), Furrer and Genton (2011) and Sang, Jun and Huang (2011) for discussion and technical details.…”

Section: Introduction 11 Motivationmentioning

confidence: 99%

Cross-Covariance Functions for Multivariate Geostatistics

Genton¹,

Kleiber²

2015

Statist. Sci.

259

211

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Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Mat\'{e}rn and nonstationary and space-time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems.Comment: Published at http://dx.doi.org/10.1214/14-STS487 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Data Configurations and the Cokriging System: Simplification by Screen Effects

Cited by 16 publications

References 10 publications

The kriging update equations and their application to the selection of neighboring data

The kriging update equations and their application to the selection of neighboring data

Geostatistical Estimation of Biomass Stock in Chilean Native Forests and Plantations

Cross-Covariance Functions for Multivariate Geostatistics

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