Spatial sampling design for prediction with estimated parameters

Zhu, Zhengyuan; Stein, Michael L.

doi:10.1198/108571106x99751

Cited by 175 publications

(96 citation statements)

References 40 publications

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“…This allows us to optimize sampling schemes for spatial prediction, accounting for both the uncertainty in the final predictions due to spatial variability of the variable in question (which can be reduced by reducing the interval of the final sampling grid) and effects of uncertainty in the covariance parameters. A similar approach was proposed by Zhu and Stein [18].…”

Section: Linear Mixed Models: Soil Knowledge In the Fixed Effectsmentioning

confidence: 98%

Towards soil geostatistics

Lark

2012

Spatial Statistics

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In a brief survey of some issues in the application of geostatistics in soil science it is shown how the recasting of classical geostatistical methods in the linear mixed model (LMM) framework has allowed the more effective integration of soil knowledge (classifications, covariates) with statistical spatial prediction of soil properties. The LMM framework has also allowed the development of models in which the spatial covariance need not be assumed to be stationary. Such models are generally more plausible than stationary ones from a pedological perspective, and when applied to soil data they have been found to give prediction error variances that better describe the uncertainty of predictions at validation sites. Finally consideration is given to how scientific understanding of variable processes in the soil might be used to infer the likely statistical form of the observed soil variation.

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Section: Linear Mixed Models: Soil Knowledge In the Fixed Effectsmentioning

confidence: 98%

Towards soil geostatistics

Lark

2012

Spatial Statistics

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“…A relevant theme from geostatistics [35] is sampling design, i.e., finding the best locations to sample, out of a finite set of possible locations. In sensor networks it has been examined as optimum sensor placement [16].…”

Section: Relation To Previous Workmentioning

confidence: 99%

Efficient Sensing Topology Management for Spatial Monitoring with Sensor Networks

Liaskovitis

Schurgers

2010

J Sign Process Syst

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We focus on exploiting redundancy for sensor networks in the context of spatial interpolation. The network acts as a distributed sampling system, where sensors periodically sample a physical phenomenon of interest, e.g. temperature. Samples are then used to construct a continuous spatial estimate of the phenomenon over time through interpolation. In this regime, the notion of sensing range typically utilized to characterize redundancy in event detection applications is meaningless and sensor selection schemes based on it become unsuitable. Instead, this paper presents pragmatic approaches for exploiting redundancy in such applications. Their underlying characteristic is that no a-priori assumptions need to be made on the statistical properties of the physical phenomenon. These are instead learned by the network after deployment. Our approaches are evaluated through real as well as synthetic sensor network data showing that significant reductions in the number of active sensors are indeed possible.

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“…For example, Van Groenigen optimized the sampling scheme by minimizing the mean kriging variance (AKV) or maximum kriging variance (MaxKV) using spatial-simulated annealing (SSA) (Van Groenigen and Stein, 1998;Van Groenigen et al, 1999;Van Groenigen, 2000). Zhu and Stein (2006) designed a sampling method for spatial prediction when the covariance parameters have to be estimated from the same data. They incorporated the parameter uncertainty of the semivariogram into a design criterion to represent the uncertainty in prediction and used a simulated annealing algorithm to search for the optimal design.…”

Section: Introductionmentioning

confidence: 99%

“…Uncertainty-directed sampling in the spatial domain is largely based on geostatistical methods that draw samples by specifying a covariancebased criterion (McBratney and Webster, 1981;Haining, 2003;Simbahan and Dobermann, 2006;Zhu and Stein, 2006;Delmelle and Goovaerts, 2009). The uncertainty of a prediction is determined by the kriging model.…”

Section: Introductionmentioning

confidence: 99%

Supplemental sampling for digital soil mapping based on prediction uncertainty from both the feature domain and the spatial domain

Zhu

Shi

et al. 2016

Geoderma

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This paper presents an uncertainty-directed sampling method that can be used to design additional samples for soil mapping. The method is based on uncertainty from both the feature domain (the domain of relationships with environmental covariates) and the spatial domain (the domain of spatial autocorrelation). Existing soil samples are also taken into account. The method comprises three steps: 1) the selection of a ranked list of additional sample locations based on uncertainty from the feature domain using individual predictive soil mapping (iPSM); 2) the selection of a ranked list of additional sample locations based on uncertainty from the spatial domain using ordinary kriging; 3) the determination of a final ranked list created by merging the ranked lists from steps 1) and 2) based on both uncertainties. To evaluate the method, the three lists were used to map soil organic matter (SOM) in a 299.14 km 2 study area near Fuyang city in the northwest region of Zhejiang Province, China.The mapping accuracy of each list was then calculated and used to assess the effectiveness of the method. Compared with the sampling scheme based on the uncertainty from either the feature domain or the spatial domain alone, the root-mean-squared error (RMSE), with the addition of the final list based on both uncertainties, was found to be the smallest, ranging from 0.829 to 1.126, and the agreement coefficient (AC) was the largest, ranging from 0.634 to 0.737. This confirms that sampling based on two uncertainties is better than sampling based on uncertainty from either the feature domain or the spatial domain alone. The results suggest that the proposed combined additional sampling method is more effective for sampling additional points in soil mapping.

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Spatial sampling design for prediction with estimated parameters

Cited by 175 publications

References 40 publications

Towards soil geostatistics

Towards soil geostatistics

Efficient Sensing Topology Management for Spatial Monitoring with Sensor Networks

Supplemental sampling for digital soil mapping based on prediction uncertainty from both the feature domain and the spatial domain

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