A Comparison Between Bayesian and Ordinary Kriging Based on Validation Criteria: Application to Radiological Characterisation

Wieskotten, Martin; Crozet, Marielle; Iooss, Bertrand; Lacaux, Céline; Marrel, Amandine

doi:10.1007/s11004-023-10072-y

Cited by 4 publications

(5 citation statements)

References 34 publications

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“…IAEα lies in [0, 1] and the closer to zero the IAEα, better the PI in average. Note that this criterion is very close to the so-called "mean squared error α" of Wieskotten et al [55], defined with L 2 norm instead of L 1 norm. As in Wieskotten et al [55], IAEα will be computed in practice with a regular discretization of α over ]0, 1[.…”

Section: Criteria To Assess the Accuracy Of The Whole Gaussian Proces...supporting

confidence: 59%

“…Note that this criterion is very close to the so-called "mean squared error α" of Wieskotten et al [55], defined with L 2 norm instead of L 1 norm. As in Wieskotten et al [55], IAEα will be computed in practice with a regular discretization of α over ]0, 1[. The L 1 norm is preferred here to give a homogeneous weight whatever α, avoiding to give too much weight to the strongest deviations and having a direct interpretation w.r.t.…”

Section: Criteria To Assess the Accuracy Of The Whole Gaussian Proces...supporting

confidence: 59%

“…Full Bayesian approach thus allows to take into account the uncertainty on the estimation of the GP hyperparameters and to propagate it in the GP predictive law. It has been illustrated in dimension two by Wieskotten et al [55] showing that it is relevant and can outperform the ordinary GP in terms of both predictivity and accuracy of predictive intervals. This is especially true when the sample size is small, the benefit decreasing as the size increases, as one might expect.…”

Section: Bayesian Approachmentioning

confidence: 99%

See 2 more Smart Citations

Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation

Marrel,

Iooss

2024

Reliability Engineering & System Safety

Self Cite

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Section: Criteria To Assess the Accuracy Of The Whole Gaussian Proces...supporting

confidence: 59%

Section: Criteria To Assess the Accuracy Of The Whole Gaussian Proces...supporting

confidence: 59%

Section: Bayesian Approachmentioning

confidence: 99%

See 1 more Smart Citation

Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation

Marrel,

Iooss

2024

Reliability Engineering & System Safety

Self Cite

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“…The main advantage of this approach is that it requires minimal interactive modeling. In comparison with other kriging methods, EBK provides more accurate predictions with smaller standard errors, in particular in analyses of small datasets [92,93]. The main disadvantage of the applied approach is that processing time rapidly increases with an increase in the number of input points, subset size, or the overlap factor [94].…”

Section: Resultsmentioning

confidence: 99%

Land-Use Change Dynamics in Areas Subjected to Direct Urbanization Pressure: A Case Study of the City of Olsztyn

Biłozor,

Cieślak,

Czyża

et al. 2024

Sustainability

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Urbanization is one of the most visible symptoms of global changes. This process has been driven by the evolution of life on Earth, and it gradually modifies the structure of land use. Urban development is the most apparent indicator and measure of urbanization. The demand for vacant land and sustainable spatial development plans require new methods that support decision-making in the process of changing land use in suburban areas. The aim of this study was to describe a methodology for identifying and localizing urban development boundaries with the use of fuzzy set theory, to evaluate the degree of urbanization, and to analyze the dynamics of land-use changes in areas subjected to direct urbanization pressure with the use of photogrammetric data for 2005, 2010, 2017, and 2022. A case study was conducted in the Polish city of Olsztyn. The study’s results determined the degree of urbanization of the areas in the [0, 1] range, as well as the dynamics of change in each of the twenty-four adopted forms of land use. The results indicate that the proposed methods are useful for identifying the rate and direction of urbanization, and can be applied to optimize and counterbalance the development of settlements and infrastructure.

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“…Thus, the advantage of this method is the statistical formulation of the best linear unbiased estimate. However, the disadvantage of that method could be that the weights must be computed for each node of the grid, that is why this method is usually used for small samples where Ordinary Kriging approaches could produce undesirable "pits" and "circular" contours (Wieskotten, et al, 2023).…”

Section: Where: γ(H) = the Semivariogram For The Elevation Variable H...mentioning

confidence: 99%

Comparative Analysis of the Digital Terrain Models Created from Ground Surveying Measurements with the Use of Different Ordinary Kriging Models

Fahim Fahmy Asal

2023

Engineering Research Journal

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Digital Terrain Model (DTM) is a continuous surface containing ground elevation values as well as other elements describing the topographic surface such as slope, aspect, curvature, etc. DTM is created from discrete elevation data through an interpolation operation. Ordinary Kriging methods are geostatistical approaches that incorporate spatial autocorrelation and generate estimated surfaces from scattered sets of points through minimizing the errors between the predicted values and the statistical model of the surface (Maune and Nayegandhi, 2018). This research aimed at comparative analysis of the DTMs created from ground surveying digital elevation data through exploitation of the different models of the ordinary kriging. DTMs have been created from ground surveying sample data using t ordinary kriging models. Statistical analysis of the DTMs indicated that Gaussian model DTM depicts the smallest standard deviation of elevations. Additionally, the spherical, linear, circular, and exponential model DTMs achieve standard deviations of elevations of 101.99%, 102.21%, 102.40% and 102.43% of the standard deviation of elevations given by the Gaussian model DTM, respectively. Moreover, statistical analysis of the elevation residuals extracted from the different DTMs using external checkout points shows that the DTM from the Gaussian model achieve the highest standard deviation of elevation residuals which refers to the lowest accuracy DTM. Thus, the DTMs from the linear, spherical, circular, and exponential models achieve smaller and remarkably close Fahmy Fahim Fahmy Asal / Engineering Research Journal 180 (Decamber2023) cv28-cv46 cv29 standard deviation of elevation residuals that are about 80.83%, 80.88%, 81.11% and 81.3% respectively of the standard deviation of elevation residuals achieved by the Gaussian DTM model.

show abstract

A Comparison Between Bayesian and Ordinary Kriging Based on Validation Criteria: Application to Radiological Characterisation

Cited by 4 publications

References 34 publications

Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation

Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation

Land-Use Change Dynamics in Areas Subjected to Direct Urbanization Pressure: A Case Study of the City of Olsztyn

Comparative Analysis of the Digital Terrain Models Created from Ground Surveying Measurements with the Use of Different Ordinary Kriging Models

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