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1.
Helmut Schaeben 《Mathematical Geosciences》2014,46(7):887-893
Despite a missing definition of equivalence of mathematical models or methods by Zhang et al. (Math Geosci, 2013), an “equivalence” (Zhang et al., Math Geosci, 2013, p. 6,7,8,14) of modified weights-of-evidence (Agterberg, Nat Resour Res 20:95–101, 2011) and logistic regression does not generally exist. Its alleged proof is based on a previously conjectured linear relationship between weights of evidence and logistic regression parameters (Deng, Nat Resour Res 18:249–258, 2009), which does not generally exist either (Schaeben and van den Boogaart, Nat Resour Res 20:401–406, 2011). In fact, an extremely simple linear relationship exists only if the predictor variables are conditionally independent given the target variable, in which case the contrasts, i.e., the differences of the weights, are equal to the logistic regression parameters. Thus, weights-of-evidence is the special case of logistic regression if the predictor variables are binary and conditionally independent given the target variable. 相似文献
2.
Weidong Li 《Mathematical Geology》2007,39(3):321-335
Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating
categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces
a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation
(or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional
probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general
solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’
theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional
simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models
are nonlinear. 相似文献
3.
Weidong Li 《Mathematical Geosciences》2007,39(3):321-335
Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation (or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’ theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models are nonlinear. 相似文献
4.
A. Porwal I. González-Álvarez V. Markwitz T.C. McCuaig A. Mamuse 《Ore Geology Reviews》2010,38(3):184-196
Bayesian weight-of-evidence and logistic regression models are implemented in a GIS environment for regional-scale prospectivity modeling of greenstone belts in the Yilgarn Craton, Western Australia, for magmatic nickel sulfide deposits. The input variables for the models consisted of derivative GIS layers that were used as proxies for mappable exploration criteria for magmatic nickel sulfide deposits in the Yilgarn. About 70% of the 165 known deposits of the craton were used to train the models; the remaining 30% was used to validate the models and, therefore, had to be treated as if they had not been discovered. The weights-of-evidence and logistic regression models, respectively, classify 71.4% and 81.6% validation deposits in prospective zones that occupy about 9% of the total area occupied by the greenstone belts in the craton. The superior performance of the logistic regression model is attributed to its capability to accommodate conditional dependencies amongst the input predictor maps, and provide less biased estimates of prospectivity. 相似文献
5.
The Random Forests (RF) algorithm has recently become a fledgling method for data-driven predictive mapping of mineral prospectivity, and so it is instructive to further study its efficacy in this particular field. This study, carried out using Baguio gold district (Philippines), examines (a) the sensitivity of the RF algorithm to different sets of deposit and non-deposit locations as training data and (b) the performance of RF modeling compared to established methods for data-driven predictive mapping of mineral prospectivity. We found that RF modeling with different training sets of deposit/non-deposit locations is stable and reproducible, and it accurately captures the spatial relationships between the predictor variables and the training deposit/non-deposit locations. For data-driven predictive mapping of epithermal Au prospectivity in the Baguio district, we found that (a) the success-rates of RF modeling are superior to those of weights-of-evidence, evidential belief and logistic regression modeling and (b) the prediction-rate of RF modeling is superior to that of weights-of-evidence modeling but approximately equal to those of evidential belief and logistic regression modeling. Therefore, the RF algorithm is potentially much more useful than existing methods that are currently used for data-driven predictive mapping of mineral prospectivity. However, further testing of the method in other areas is needed to fully explore its usefulness in data-driven predictive mapping of mineral prospectivity. 相似文献
6.
Approximate local confidence intervals are constructed from uncertainty models in the form of the conditional distribution of the random variable Z given values of variables [Zi, i=1,...,n]. When the support of the variable Z is any support other than that of the data, the conditional distributions require a change of support correction. This paper investigates the effect of change of support on the approximate local confidence intervals constructed by cumulative indicator kriging, class indicator kriging, and probability kriging under a variety of conditions. The conditions are generated by three simulated deposits with grade distributions of successively higher degree of skewness; a point support and two different block supports are considered. The paper also compares the confidence intervals obtained from these methods using the most used measures of confidence interval effectiveness. 相似文献
7.
Daojun Zhang Frits Agterberg Qiuming Cheng Renguang Zuo 《Mathematical Geosciences》2014,46(7):869-885
Weights of evidence and logistic regression are two of the most popular methods for mapping mineral prospectivity. The logistic regression model always produces unbiased estimates, whether or not the evidence variables are conditionally independent with respect to the target variable, while the weights of evidence model features an easy to explain and implement modeling process. It has been shown that there exists a model combining weights of evidence and logistic regression that has both of these advantages. In this study, three models consisting of modified fuzzy weights of evidence, fuzzy weights of evidence, and logistic regression are compared with each other for mapping mineral prospectivity. The modified fuzzy weights of the evidence model retains the advantages of both the fuzzy weights of the evidence model and the logistic regression model; the advantages being (1) the predicted number of deposits estimated by the modified fuzzy weights of evidence model is nearly equal to that of the logistic regression model, and (2) it can deal with missing data. This method is shown to be an effective tool for mapping iron prospectivity in Fujian Province, China. 相似文献
8.
Four statistical techniques for modelling landslide susceptibility were compared: multiple logistic regression (MLR), multivariate adaptive regression splines (MARS), classification and regression trees (CART), and maximum entropy (MAXENT). According to the literature, MARS and MAXENT have never been used in landslide susceptibility modelling, and CART has been used only twice. Twenty independent variables were used as predictors, including lithology as a categorical variable. Two sets of random samples were used, for a total of 90 model replicates (with and without lithology, and with different proportions of positive and negative data). The model performance was evaluated using the area under the receiver operating characteristic curve (AUC) statistic. The main results are (a) the inclusion of lithology improves the model performance; (b) the best AUC values for single models are MLR (0.76), MARS (0.76), CART (0.77), and MAXENT (0.78); (c) a smaller amount of negative data provides better results; (d) the models with the highest prediction capability are obtained with MAXENT and CART; and (e) the combination of different models is a way to evaluate the model reliability. We further discuss some key issues in landslide modelling, including the influence of the various methods that we used, the sample size, and the random replicate procedures. 相似文献
9.
Xavier Emery 《Mathematical Geology》2002,34(1):79-100
This paper presents a conditional simulation procedure that overcomes the limits of gaussian models and enables one to simulate regionalized variables with highly asymmetrical histograms or with partial or total connectivity of extreme values. The philosophy of the method is similar to that of sequential indicator technique, but it is more accurate because it is based on a complete bivariate model by means of an isofactorial law. The resulting simulations, which can be continuous or categorical, not only honor measured values at data points, but also reproduce the mono and bivariate laws of the random function associated to the regionalized variable, that is, every one or two-point statistic: histogram, variogram, indicator variograms. The sequential isofactorial method can also be adapted to conditional simulation of block values, without resorting to point–support simulations. 相似文献
10.
证据权方法是目前最常用的信息综合方法之一,广泛应用于矿产资源定量预测与评价.然而,它要求变量间相互独立,地质上很难满足这一条件.如何削弱条件不独立对证据权预测结果的影响,已成为当前数学地球科学研究的热点.解决该问题的途径之一是对传统证据权模型进行校正,比如采取加权的方法对原证据权模型计算的证据权重进行修正,以便消除非条件独立性的影响.对近期提出的多种加权证据权模型进行了系统的对比研究,基于同样的应用实例和实验方案,对不同方法的应用效果进行了比较,结果表明,各种加权证据权模型均可不同程度地削弱证据图层条件不独立性的影响,其中,基于逻辑回归的加权证据权模型优于其他加权方法. 相似文献
11.
Which Models for Collocated Cokriging? 总被引：1，自引：0，他引：1
Jacques Rivoirard 《Mathematical Geology》2001,33(2):117-131
When a target variable is sparsely sampled, compared to a densely sampled auxiliary variable, cokriging requires simplifications. In its strict sense, collocated cokriging makes use of the auxiliary variable only at the current point where the target variable is to be estimated; in the multicollocated form, it also makes use of the auxiliary variable at all points where the target variable is available. This paper looks for the models that support these collocated cokrigings, i.e., the models in which the simplification resulting from the collocated forms does not result in any loss of information. In these models, the cross-structure between the two variables is shown to be proportional to the structure of the auxiliary variable, not to the structure of the target variable as is often assumed (except, of course, when all structures are proportional). The target variable depends on the auxiliary variable and on a spatially uncorrelated residual. Collocated cokriging simplifies to the simple method, which consists in kriging this residual. The strictly collocated cokriging corresponds to the particular case where the residual has a pure nugget structure, but it is then reduced to the single regression at the target point. Except for this trivial case, there are no models in which strictly collocated cokriging is exactly a cokriging. 相似文献
12.
“证据权”法在西南“三江”南段矿产资源评价中的应用 总被引：3，自引：5，他引：3
证据权法本身是一种离散的多元统计方法。阐述了矿物资源潜力区的概念,简述证据权法的基本原理。以西南“三江”南段为例,首先在地质、地球物理、地球化学以及遥感地质等致矿信息提取的基础上,运用证据权法定量分析各类致矿信息(控矿因素)与矿产资源空间分布的关系;进而选择最佳控矿因素作为资源评价变量,据其变量计算每个单元的后验成矿概率;最终根据后验成矿概率定量圈定和评价找矿靶区。实践证明:在GIS环境下“,证据权”与找矿信息结合能够有效区分矿化有利地段和不利地段,从而达到定量快速圈定和评价找矿靶区之目的。整个过程是借助于MOPAS3.0评价系统实现的。 相似文献
13.
Construction of Binary Multi-grid Markov Random Field Prior Models from Training Images 总被引：1，自引：1，他引：0
Bayesian modeling requires the specification of prior and likelihood models. In reservoir characterization, it is common practice to estimate the prior from a training image. This paper considers a multi-grid approach for the construction of prior models for binary variables. On each grid level we adopt a Markov random field (MRF) conditioned on values in previous levels. Parameter estimation in MRFs is complicated by a computationally intractable normalizing constant. To cope with this problem, we generate a partially ordered Markov model (POMM) approximation to the MRF and use this in the model fitting procedure. Approximate unconditional simulation from the fitted model can easily be done by again adopting the POMM approximation to the fitted MRF. Approximate conditional simulation, for a given and easy to compute likelihood function, can also be performed either by the Metropolis–Hastings algorithm based on an approximation to the fitted MRF or by constructing a new POMM approximation to this approximate conditional distribution. The proposed methods are illustrated using three frequently used binary training images. 相似文献
14.
A logistic regression model is developed within the framework of a Geographic Information System (GIS) to map landslide hazards
in a mountainous environment. A case study is conducted in the mountainous southern Mackenzie Valley, Northwest Territories,
Canada. To determine the factors influencing landslides, data layers of geology, surface materials, land cover, and topography
were analyzed by logistic regression analysis, and the results are used for landslide hazard mapping. In this study, bedrock,
surface materials, slope, and difference between surface aspect and dip direction of the sedimentary rock were found to be
the most important factors affecting landslide occurrence. The influence on landslides by interactions among geologic and
geomorphic conditions is also analyzed, and used to develop a logistic regression model for landslide hazard mapping. The
comparison of the results from the model including the interaction terms and the model not including the interaction terms
indicate that interactions among the variables were found to be significant for predicting future landslide probability and
locating high hazard areas. The results from this study demonstrate that the use of a logistic regression model within a GIS
framework is useful and suitable for landslide hazard mapping in large mountainous geographic areas such as the southern Mackenzie
Valley. 相似文献
15.
A Fixed-Path Markov Chain Algorithm for Conditional Simulation of Discrete Spatial Variables 总被引：4，自引：0，他引：4
Weidong Li 《Mathematical Geology》2007,39(2):159-176
The Markov chain random field (MCRF) theory provided the theoretical foundation for a nonlinear Markov chain geostatistics.
In a MCRF, the single Markov chain is also called a “spatial Markov chain” (SMC). This paper introduces an efficient fixed-path SMC algorithm for conditional simulation of discrete spatial variables
(i.e., multinomial classes) on point samples with incorporation of interclass dependencies. The algorithm considers four nearest
known neighbors in orthogonal directions. Transiograms are estimated from samples and are model-fitted to provide parameter
input to the simulation algorithm. Results from a simulation example show that this efficient method can effectively capture
the spatial patterns of the target variable and fairly generate all classes. Because of the incorporation of interclass dependencies
in the simulation algorithm, simulated realizations are relatively imitative of each other in patterns. Large-scale patterns
are well produced in realizations. Spatial uncertainty is visualized as occurrence probability maps, and transition zones
between classes are demonstrated by maximum occurrence probability maps. Transiogram analysis shows that the algorithm can
reproduce the spatial structure of multinomial classes described by transiograms with some ergodic fluctuations. A special
characteristic of the method is that when simulation is conditioned on a number of sample points, simulated transiograms have
the tendency to follow the experimental ones, which implies that conditioning sample data play a crucial role in determining
spatial patterns of multinomial classes. The efficient algorithm may provide a powerful tool for large-scale structure simulation
and spatial uncertainty analysis of discrete spatial variables. 相似文献
16.
Using multiple logistic regression and GIS technology to predict landslide hazard in northeast Kansas, USA 总被引：60，自引：0，他引：60
Landslides in the hilly terrain along the Kansas and Missouri rivers in northeastern Kansas have caused millions of dollars in property damage during the last decade. To address this problem, a statistical method called multiple logistic regression has been used to create a landslide-hazard map for Atchison, Kansas, and surrounding areas. Data included digitized geology, slopes, and landslides, manipulated using ArcView GIS. Logistic regression relates predictor variables to the occurrence or nonoccurrence of landslides within geographic cells and uses the relationship to produce a map showing the probability of future landslides, given local slopes and geologic units. Results indicated that slope is the most important variable for estimating landslide hazard in the study area. Geologic units consisting mostly of shale, siltstone, and sandstone were most susceptible to landslides. Soil type and aspect ratio were considered but excluded from the final analysis because these variables did not significantly add to the predictive power of the logistic regression. Soil types were highly correlated with the geologic units, and no significant relationships existed between landslides and slope aspect. 相似文献
17.
A landslide susceptibility zonation (LSZ) map helps to understand the spatial distribution of slope failure probability in
an area and hence it is useful for effective landslide hazard mitigation measures. Such maps can be generated using qualitative
or quantitative approaches. The present study is an attempt to utilise a multivariate statistical method called binary logistic
regression (BLR) analysis for LSZ mapping in part of the Garhwal Lesser Himalaya, India, lying close to the Main Boundary
Thrust (MBT). This method gives the freedom to use categorical and continuous predictor variables together in a regression
analysis. Geographic Information System has been used for preparing the database on causal factors of slope instability and
landslide locations as well as for carrying out the spatial modelling of landslide susceptibility. A forward stepwise logistic
regression analysis using maximum likelihood estimation method has been used in the regression. The constant and the coefficients
of the predictor variables retained by the regression model have been used to calculate the probability of slope failure for
the entire study area. The predictive logistic regression model has been validated by receiver operating characteristic curve
analysis, which has given 91.7% accuracy for the developed BLR model. 相似文献
18.
Olivier Dubrule 《Mathematical Geosciences》2017,49(4):441-465
Many variogram (or covariance) models that are valid—or realizable—models of Gaussian random functions are not realizable indicator variogram (or covariance) models. Unfortunately there is no known necessary and sufficient condition for a function to be the indicator variogram of a random set. Necessary conditions can be easily obtained for the behavior at the origin or at large distance. The power, Gaussian, cubic or cardinal-sine models do not fulfill these conditions and are therefore not realizable. These considerations are illustrated by a Monte Carlo simulation demonstrating nonrealizability over some very simple three-point configurations in two or three dimensions. No definitive result has been obtained about the spherical model. Among the commonly used models for Gaussian variables, only the exponential appears to be a realizable indicator variogram model in all dimensions. It can be associated with a mosaic, a Boolean or a truncated Gaussian random set. In one dimension, the exponential indicator model is closely associated with continuous-time Markov chains, which can also lead to more variogram models such as the damped oscillation model. One-dimensional random sets can also be derived from renewal processes, or mosaic models associated with such processes. This provides an interesting link between the geostatistical formalism, focused mostly on two-point statistics, and the approach of quantitative sedimentologists who compute the probability distribution function of the thickness of different geological facies. The last part of the paper presents three approaches for obtaining new realizable indicator variogram models in three dimensions. One approach consists of combining existing realizable models. Other approaches are based on the formalism of Boolean random sets and truncated Gaussian functions. 相似文献
19.
A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach. 相似文献
20.
加权证据权模型和逐步证据权模型及其在个旧锡铜矿产资源预测中的应用 总被引：7，自引：2，他引：5
为了消除和减弱当证据层不满足条件独立性假设时对预测结果产生的影响, 提出了逐步证据权模型和加权证据权模型.加权证据权模型通过对logit模型进行修改, 对各个证据层给予一定的权重, 以调整由于证据层与其他证据层的条件相关性对模型的影响; 逐步证据权模型是将证据层按照一定的顺序逐步加入到模型中, 在加入到模型的过程中依次用已经获得的后验概率作为模糊训练层的方法.以个旧锡铜多金属矿产资源预测为例, 应用4种证据权模型的后验概率进行异常圈定, 结果表明两种新的模型对减弱证据层不满足条件独立性假设所产生的影响是有效的. 相似文献