Comparison of Mathematical Methods of Potential Modeling

Schaeben, Helmut

doi:10.1007/s11004-011-9373-2

Cited by 16 publications

(9 citation statements)

References 43 publications

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“…By replacing probabilities with relative frequencies it must be assumed that all rockfalls are known and the applied methods are thus strongly dependent on the completeness of the inventory (Schaeben, 2012). This is however assumed to be not the case for this study and will thus lead to an underestimation of the prior probability resulting in a bias of the weights as well as the final susceptibility (Agterberg and Cheng, 2002).…”

Section: Discussionmentioning

confidence: 99%

“…Conditional dependence will lead to an overestimation of the final susceptibility. Based on our experience Weights-of-Evidence is a very powerful method for data exploration, but its application is limited for combining datasets to a susceptibility map due to the multiple assumption of conditional independence (Böhme, 2007;Schaeben, 2012). As logistic regression is closely related to Weights-of-Evidence, but not based on the assumption of conditional independence, this method yields a good alternative in generating susceptibility maps (Hosmer and Lemeshow, 2000).…”

Section: Discussionmentioning

confidence: 99%

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Quantitative spatial analysis of rockfalls from road inventories: a combined statistical and physical susceptibility model

Böhme

Derron

Jaboyedoff

2014

Preprint

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Abstract. Quantitative spatial analyses and statistical susceptibility assessments based on road inventories are often complicated due to the registration of impacts instead of source areas. A rockfall inventory from the Norwegian Directorate of Public Roads is analysed spatially in order to investigate potential controlling parameters in the Norwegian county Sogn and Fjordane. Quantitative spatial relationships are then used to model rockfall susceptibility with the help of the Weights-of-Evidence method. The controlling parameters tectono-stratigraphic position, quaternary geology, geological lineament density, relative relief and slope aspect resulted in the best performing model and thus yielded the basis for the statistical susceptibility map for the entire county of Sogn and Fjordane. Due to registered impacts instead of sources, the important parameter slope angle could not be included in the statistical models. Combining the statistical susceptibility model with a physically based model, restricts the susceptibility map to areas that are steep enough to represent a potential rockfall source. This combination makes it possible to use road inventories, with registered impacts instead of sources, for susceptibility modelling.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Quantitative spatial analysis of rockfalls from road inventories: a combined statistical and physical susceptibility model

Böhme

Derron

Jaboyedoff

2014

Preprint

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“…In mineral potential modeling, the analytical or empirical relationships between descriptive features and a mineral target express the possibility to predict a given mineral concentration in a location as function of descriptive features (e.g., Quadros et al 2006;Cheng 2008;Zuo and Carranza 2011;Schaeben 2012). Let evidences denote the set of observed features that are directly related to the mineralization process (e.g., mineral alterations in rocks during a hydrothermal event, or sorting of heavy-minerals grains during a depositional process).…”

Section: Curvature and Cu Assessments Potentials Assessments And Predmentioning

confidence: 99%

Curvature Attribute from Surface-Restoration as Predictor Variable in Kupferschiefer Copper Potentials

et al. 2014

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International audienceThis work explains a procedure to predict Cu potentials in the ore-Kupferschiefer using structural surface-restoration and logistic regression (LR) analysis. The predictor in the assessments are established from the restored horizon that contains the ore-series. Applying flexural-slip to unfold/unfault the 3D model of the Fore-Sudetic Monocline, we obtained curvature for each restored time. We found that curvature represents one of the main structural features related to the Cu mineralization. Maximum curvature corresponds to high internal deformation in the restored layers, evidencing faulting and damaged areas in the 3D model. Thus, curvature may highlight fault systems that drove fluid circulation from the basement and host the early mineralization stages. In the Cu potential modeling, curvature, distance to the Fore-Sudetic Block and depth of restored Zechstein at Cretaceous time are used as predictors and proven Cu-potential areas as targets. Then, we applied LR analysis establishing the separating function between mineralized and non-mineralized locations. The LR models show positive correspondence between predicted probabilities of Cu-potentials and curvature estimated on the surface depicting the mineralized layer. Nevertheless, predicted probabilities are particularly higher using curvatures obtained from Late Paleozoic and Late Triassic restorations

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“…Generally, i.e., without assuming conditional independence, the relationship of ordinary logistic regression parameters and the contrast of weights of evidence is clearly non-linear [21,22]; see Appendix 2 for an explicit derivation.…”

Section: Weights-of-evidence Vs Logistic Regressionmentioning

confidence: 99%

Targeting: Logistic Regression, Special Cases and Extensions

Schaeben

2014

IJGI

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Logistic regression is a classical linear model for logit-transformed conditional probabilities of a binary target variable. It recovers the true conditional probabilities if the joint distribution of predictors and the target is of log-linear form. Weights-of-evidence is an ordinary logistic regression with parameters equal to the differences of the weights of evidence if all predictor variables are discrete and conditionally independent given the target variable. The hypothesis of conditional independence can be tested in terms of log-linear models. If the assumption of conditional independence is violated, the application of weights-of-evidence does not only corrupt the predicted conditional probabilities, but also their rank transform. Logistic regression models, including the interaction terms, can account for the lack of conditional independence, appropriate interaction terms compensate exactly for violations of conditional independence. Multilayer artificial neural nets may be seen as nested regression-like models, with some sigmoidal activation function. Most often, the logistic function is used as the activation function. If the net topology, i.e., its control, is sufficiently versatile to mimic interaction terms, artificial neural nets are able to account for violations of conditional independence and yield very similar results. Weights-of-evidence cannot reasonably include interaction terms; subsequent modifications of the weights, as often suggested, cannot emulate the effect of interaction terms.

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Comparison of Mathematical Methods of Potential Modeling

Cited by 16 publications

References 43 publications

Quantitative spatial analysis of rockfalls from road inventories: a combined statistical and physical susceptibility model

Quantitative spatial analysis of rockfalls from road inventories: a combined statistical and physical susceptibility model

Curvature Attribute from Surface-Restoration as Predictor Variable in Kupferschiefer Copper Potentials

Targeting: Logistic Regression, Special Cases and Extensions

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