Kriging in a global neighborhood

Davis, Michael W.; Grivet, Cyril

doi:10.1007/bf01032690

Cited by 28 publications

(5 citation statements)

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“…(7) refers to ordinary kriging, and when M contains the trend model, it is universal kriging or kriging with external drift. The formulation of (5) as an alternative to the standard kriging form (7) was also proposed by Davis and Grivet (1984). This form takes advantage of the explicit use of the symmetric positive definite form of K. The inverse of K can be achieved in a more efficient and stable computation using Cholesky factorisation.…”

Section: Blupmentioning

confidence: 98%

Spatial prediction of soil properties using EBLUP with the Matérn covariance function

2007

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Section: Blupmentioning

confidence: 98%

Spatial prediction of soil properties using EBLUP with the Matérn covariance function

2007

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“…Kriging generated a near continuous grid of georeferenced points (26,208 geospatial points on 0.05 Â 0.05 km grid) within the West African region. All 26,208 geospatial points are considered in estimating residuals and the predicted CFR for each geospatial point covering districts with both recorded and unrecorded estimates (Davis and Grivet, 1984). The kriged residuals were then added to the kriged predicted CFR adjusted for imputation from the BRT model to produce a best linear unbiased predicted isopleth (i.e.…”

Section: Spatiotemporal Analysismentioning

confidence: 99%

Spatiotemporal variability in case fatality ratios for the 2013–2016 Ebola epidemic in West Africa

Forna

Dorigatti

Nouvellet

et al. 2020

International Journal of Infectious Diseases

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Background: For the 2013-2016 Ebola epidemic in West Africa, the largest Ebola virus disease (EVD) epidemic to date, we aim to analyse the patient mix in detail to characterise key sources of spatiotemporal heterogeneity in the case fatality ratios (CFR). Methods: We applied a non-parametric Boosted Regression Trees (BRT) imputation approach for patients with missing survival outcomes and adjusted for model imperfection. Semivariogram analysis and kriging were used to investigate spatiotemporal heterogeneities. Results: CFR estimates varied significantly between districts and over time over the course of the epidemic. BRT modelling accounted for most of the spatiotemporal variation and interactions in CFR, but moderate spatial autocorrelation remained for distances up to approximately 90 km. Combining districtlevel CFR estimates and kriged district-level residuals provided the best linear unbiased predicted map of CFR accounting for the both explained and unexplained spatial variation. Temporal autocorrelation was not observed in the district-level residuals from the BRT estimates. Conclusions: This study provides new insight into the epidemiology of the 2013-2016 West African Ebola epidemic with a view of informing future public health contingency planning, resource allocation and impact assessment. The analytical framework developed in this analysis, coupled with key domain knowledge, could be deployed in real time to support the response to ongoing and future outbreaks.

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“…In [9], an alternative solution was introduced which is called moving window or local neighbourhood kriging where a circular or elliptic moving window centred on the prediction location is used to select the observations within its boundaries that are to used for prediction. It is pointed out in [10] that local neighbourhoods can produce spurious behaviour, this happens particularly when we cross boundaries as new observations are introduced and removed from the moving window.…”

Section: Introductionmentioning

confidence: 99%

“…Since the computation necessary to invert a matrix grows as O n 3 , it can be seen that a naïve implementation of kriging is not feasible for large datasets. An additional problem that can arise with large datasets is due to instabilities associated with solving large systems of equations [10,11] particularly when the ratio of the highest eigenvalue to the lowest eigenvalue of the covariance matrix becomes large (ill-conditioning). Concerns about the large linear systems involved in kriging and the instabilities in their solutions has motivated a search for better methods.…”

Section: Introductionmentioning

confidence: 99%

Fast algorithms for automatic mapping with space-limited covariance functions

Ingram

Cornford

Evans

2007

Stoch Environ Res Risk Assess

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In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O nm 2 , where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation.

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Kriging in a global neighborhood

Cited by 28 publications

References 1 publication

Spatial prediction of soil properties using EBLUP with the Matérn covariance function

Spatial prediction of soil properties using EBLUP with the Matérn covariance function

Spatiotemporal variability in case fatality ratios for the 2013–2016 Ebola epidemic in West Africa

Fast algorithms for automatic mapping with space-limited covariance functions

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