共查询到20条相似文献，搜索用时 93 毫秒
1.
Marc G. Genton 《Mathematical Geology》2000,32(1):127-137
The classical variogram estimator proposed by Matheron can be written as a quadratic form of the observations. When data have an elliptically contoured distribution with constant mean, the correlation between the classical variogram estimator at two different lags is a function of the spatial design matrix, the covariance matrix, and the kurtosis. Several specific cases are studied closely. A subclass of elliptically contoured distributions with a particular family of covariance matrices is shown to possess exactly the same correlation structure for the classical variogram estimator as the multivariate independent Gaussian distribution. The consequences on variogram fitting by generalized least squares are discussed. 相似文献
2.
The classical variogram estimator proposed by Matheron can be written as a quadratic form of the observations. When data have an elliptically contoured distribution with constant mean, the correlation between the classical variogram estimator at two different lags is a function of the spatial design matrix, the covariance matrix, and the kurtosis. Several specific cases are studied closely. A subclass of elliptically contoured distributions with a particular family of covariance matrices is shown to possess exactly the same correlation structure for the classical variogram estimator as the multivariate independent Gaussian distribution. The consequences on variogram fitting by generalized least squares are discussed. 相似文献
3.
Variogram Fitting by Generalized Least Squares Using an Explicit Formula for the Covariance Structure 总被引：4，自引：0，他引：4
Marc G. Genton 《Mathematical Geology》1998,30(4):323-345
In the context of spatial statistics, the classical variogram estimator proposed by Matheron can be written as a quadratic form of the observations. If data are Gaussian with constant mean, then the correlation between the classical variogram estimator at two different lags is a function of the spatial design matrix and the variance matrix. When data are independent with unidimensional and regular support, an explicit formula for this correlation is available. The same is true for a multidimensional and regular support as can be shown by using Kronecker products of matrices. As variogram fitting is a crucial stage for correct spatial prediction, it is proposed to use a generalized least squares method with an explicit formula for the covariance structure (GLSE). A good approximation of the covariance structure is achieved by taking account of the explicit formula for the correlation in the independent situation. Simulations are carried out with several types of underlying variograms, as well as with outliers in the data. Results show that this technique (GLSE), combined with a robust estimator of the variogram, improves the fit significantly. 相似文献
4.
Fred J. Molz Tomasz J. Kozubowski Krzysztof Podgórski James W. Castle 《Hydrogeology Journal》2007,15(4):809-816
In order to generalize the fractal/facies concept, a new stochastic fractal model for ln(K) increment probability density functions (PDFs) is presented that produces non-Gaussian behavior at smaller lags and converges to Gaussian at larger lags. The model is based on the classical Laplace PDF. The new stochastic fractal family is called fractional Laplace motion (fLam) having stationary increments called fractional Laplace noise (fLan). This fractal is different from other fractals because the character of the underlying increment PDFs changes dramatically with lag size, which leads to lack of self-similarity. Data also appear to display this characteristic. In the larger lag size ranges, approximate self-affinity does hold. The basic field procedure for further testing of the fractional Laplace theory is to measure ln(K) increment distributions along transects, calculate frequency distributions from the data, and compare results to appropriate fLan family members. The variances of the frequency distributions should also change with lag size (scale) in a prescribed manner. There are mathematical reasons such as the geometric central limit theorem, for surmising that fLam/fLan may be more fundamental than other approaches that have been proposed for modeling ln(K) frequency distributions. 相似文献
5.
本文从最大后验概率密度观点出发，在数据噪音向量和待求模型向量为具有零均值的独立高斯随机过程的假设前提下，建立起了随机反演的非线性系统方程；给出了模型方差估计的函数表达式，并在文章最后，证明了反演解的稀疏性，即解释了随机反演的输出解的高分辨率特征。文章在最小二乘反演方法的基础上，发展并完善了随机反演方法的理论基础；揭示了随机反演方法与最小二乘反演方法之间的本质区别；阐述了随机反演方法的优越性，并指出了其广阔的应用前景。 相似文献
6.
The multiquadric method (MQ) with high interpolation accuracy has been widely used for interpolating spatial data. However, MQ is an exact interpolation method, which is improper to interpolate noisy sampling data. Although the least squares MQ (LSMQ) has the ability to smooth out sampling errors, it is inherently not robust to outliers due to the least squares criterion in estimating the weights of sampling knots. In order to reduce the impact of outliers on the accuracy of digital elevation models (DEMs), a robust method of MQ (MQ-R) has been developed. MQ-R includes two independent procedures: knot selection and the solution of the system of linear equations. The two independent procedures were respectively achieved by the space-filling design and the least absolute deviation, both of which are very robust to outliers. Gaussian synthetic surface, which is subject to a series of errors with different distributions, was employed to compare the performance of MQ-R with that of LSMQ. Results indicate that LSMQ is seriously affected by outliers, whereas MQ-R performs well in resisting outliers, and can construct satisfactory surfaces even though the data are contaminated by severe outliers. A real-world example of DEM construction was employed to evaluate the robustness of MQ-R, LSMQ, and the classical interpolation methods including inverse distance weighting method, thin plate spline, and ANUDEM. Results showed that compared with the classical methods, MQ-R has the highest accuracy in terms of root mean square error. In conclusion, when sampling data is subject to outliers, MQ-R can be considered as an alternative method for DEM construction. 相似文献
7.
I. C. Lemmer 《Mathematical Geosciences》1986,18(7):605-623
The theory of mononodal variography developed in the preceeding paper is checked against a simulated deposit consisting of 60,500 grade values, called Stanford II. In the case of this deposit at least, assumptions underlying the concept of mononodal variography are borne out accurately. In particular, a linear relationship does exist indeed between indicator and grade variogram values of Stanford II at corresponding lags. Furthermore, such grade-indicator plots, and the information deduced from them, are robust under reduction of data at the mononodal cutoff. The method thus has predictive potential for grade variograms of highly variant deposits. Forecasting a grade variogram from the associated mononodal indicator variogram and grade-indicator plot is illustrated. Agreement with the experimental variogram is shown to be excellent. 相似文献
8.
Assessment of the sampling variance of the experimental variogram is an important topic in geostatistics as it gives the uncertainty of the variogram estimates. This assessment, however, is repeatedly overlooked in most applications mainly, perhaps, because a general approach has not been implemented in the most commonly used software packages for variogram analysis. In this paper the authors propose a solution that can be implemented easily in a computer program, and which, subject to certain assumptions, is exact. These assumptions are not very restrictive: second-order stationarity (the process has a finite variance and the variogram has a sill) and, solely for the purpose of evaluating fourth-order moments, a Gaussian distribution for the random function. The approach described here gives the variance–covariance matrix of the experimental variogram, which takes into account not only the correlation among the experiemental values but also the multiple use of data in the variogram computation. Among other applications, standard errors may be attached to the variogram estimates and the variance–covariance matrix may be used for fitting a theoretical model by weighted, or by generalized, least squares. Confidence regions that hold a given confidence level for all the variogram lag estimates simultaneously have been calculated using the Bonferroni method for rectangular intervals, and using the multivariate Gaussian assumption for K-dimensional elliptical intervals (where K is the number of experimental variogram estimates). A general approach for incorporating the uncertainty of the experimental variogram into the uncertainty of the variogram model parameters is also shown. A case study with rainfall data is used to illustrate the proposed approach. 相似文献
9.
We present the applicability of differential system (DS) method for identification of hydraulic conductivity and effective porosity in a phreatic aquifer. In the original setting, the first step of the DS system is to solve an overdetermined algebraic system in the least squares sense. A natural extension of the method is to pose a least squares problem in an appropriate functional space. We show an improvement of the identification by considering the least square problem in the space of square integrable functions in the time variable for a finite interval. 相似文献
10.
B. Paláncz A. Somogyi N. Rehány T. Lovas B. Molnár 《Australian Journal of Earth Sciences》2016,63(5):665-673
Environmental, engineering and industrial modelling of natural features (e.g. trees) and man-made features (e.g. pipelines) requires some form of fitting of geometrical objects such as cylinders, which is commonly undertaken using a least-squares method that—in order to get optimal estimation—assumes normal Gaussian distribution. In the presence of outliers, however, this assumption is violated leading to a Gaussian mixture distribution. This study proposes a robust parameter estimation method, which is an improved and extended form of vector algebraic modelling. The proposed method employs expectation maximisation and maximum likelihood estimation (MLE) to find cylindrical parameters in case of Gaussian mixture distribution. MLE computes the model parameters assuming that the distribution of model errors is a Gaussian mixture corresponding to inlier and outlier points. The parameters of the Gaussian mixture distribution and the membership functions of the inliers and outliers are computed using an expectation maximisation algorithm from the histogram of the model error distribution, and the initial guess values for the model parameters are obtained using total least squares. The method, illustrated by a practical example from a terrestrial laser scanning point cloud, is novel in that it is algebraic (i.e. provides a non-iterative solution to the global maximisation problem of the likelihood function), is practically useful for any type of error distribution model and is capable of separating points of interest and outliers. 相似文献
11.
I. C. Lemmer 《Mathematical Geology》1986,18(7):605-623
The theory of mononodal variography developed in the preceeding paper is checked against a simulated deposit consisting of 60,500 grade values, called Stanford II. In the case of this deposit at least, assumptions underlying the concept of mononodal variography are borne out accurately. In particular, a linear relationship does exist indeed between indicator and grade variogram values of Stanford II at corresponding lags. Furthermore, such grade-indicator plots, and the information deduced from them, are robust under reduction of data at the mononodal cutoff. The method thus has predictive potential for grade variograms of highly variant deposits. Forecasting a grade variogram from the associated mononodal indicator variogram and grade-indicator plot is illustrated. Agreement with the experimental variogram is shown to be excellent.This paper is based in part on a PhD thesis submitted to the Department of Applied Earth Sciences, Stanford University, Stanford, California 94305, in 1984 (unpublished). 相似文献
12.
Yong Ge Tianjun Wu Jianghao Wang Jianghong Ma Yunyan Du 《Earth Science Informatics》2012,5(3-4):137-152
In optical image registration, the reference control points (RCPs) used as explanatory variables in the polynomial regression model are generally assumed to be error free. However, this most frequently used assumption is often invalid in practice because RCPs always contain errors. In this situation, the extensively applied estimator, the ordinary least squares (LS) estimator, is biased and incapable of handling the errors in RCPs. Therefore, it is necessary to develop new feasible methods to address such a problem. This paper discusses the scaled total least squares (STLS) estimator, which is a generalization of the LS estimator in optical remote sensing image registration. The basic principle and the computational method of the STLS estimator and the relationship among the LS, total least squares (TLS) and STLS estimators are presented. Simulation experiments and real remotely sensed image experiments are carried out to compare LS and STLS approaches and systematically analyze the effect of the number and accuracy of RCPs on the performances in registration. The results show that the STLS estimator is more effective in estimating the model parameters than the LS estimator. Using this estimator based on the error-in-variables model, more accurate registration results can be obtained. Furthermore, the STLS estimator has superior overall performance in the estimation and correction of measurement errors in RCPs, which is beneficial to the study of error propagation in remote sensing data. The larger the RCP number and error, the more obvious are these advantages of the presented estimator. 相似文献
13.
介绍了一种线性模型参数回归分析方法-正交最小二乘法，并以电子探针微区分析技术分析环境样品的数据为例，对正交最小二乘法和经典最小二乘法的结果进行了详细比较。数据处理结果表明，当变自量和因变量都同时存在测量误差时（或自变量的测量误差与因变量的测量误差相比不能忽略时），正交最小二乘法获得的回归系数优于经典最小二乘法。对正交最小二乘法中的线性模型能解释的方差与经典最小二乘法中的相关系数的关系也进行了讨论。 相似文献
14.
Determining whether a reaction can be written between a set of minerals within error is an example of the more general problem of determining whether a set of compositions are coplanar within error. Generally if the compositions are of minerals, ‘within error’ should allow the minerals to maintain stoichiometry. The problem is addressed via the addition of a ‘bogus’ composition to the set, and calculating the reaction coefficients for a reaction between the compositions in this augmented set. A reaction can be written if a confidence interval on the reaction coefficient of ‘bogus’ includes zero. The reaction coefficients can be solved for directly when the problem is posed in terms of least squares with equality constraints. The confidence interval is determined with a bootstrap method, allowing the result to depend on the scatter of the data around the solution of the least squares problem, not on the data uncertainties 相似文献
15.
16.
Ákos Gyulai Mátyás Krisztián Baracza Norbert Péter Szabó 《Environmental Earth Sciences》2014,71(1):383-392
Geophysical surveying methods are of great importance in environmental exploration. Inversion-based data processing methods are applied for the determination of geometrical and physical parameters of the target model. The use of this geoelectric inversion method is advantageous in environmental research where highly reliable information with large spatial resolution is required. The 2D combined geoelectric inversion (CGI) method performs more accurate parameter estimation than conventional 1D single inversion methods by efficiently decreasing the number of unknowns of the inverse problem (single means that data sets of individual vertical electric sounding stations are inverted separately). The quality improvement in parameter space is demonstrated by comparing the traditional 1D inversion procedure with a 2D series expansion-based inversion technique. The CGI method was further developed by weighting individual direct current geoelectric data sets automatically in order to improve inversion results. The new algorithm was named combined geoelectric weighted inversion, which extracts the solution by a special weighted least squares technique. It is shown that the new inversion methodology is applicable to resolve near-surface structures such as rapidly varying layer boundaries, laterally inhomogeneous formations and pinch-outs. 相似文献
17.
Before optimal linear prediction can be performed on spatial data sets, the variogram is usually estimated at various lags and a parametric model is fitted to those estimates. Apart from possible a priori knowledge about the process and the user's subjectivity, there is no standard methodology for choosing among valid variogram models like the spherical or the exponential ones. This paper discusses the nonparametric estimation of the variogram and its derivative, based on the spectral representation of positive definite functions. The use of the estimated derivative to help choose among valid parametric variogram models is presented. Once a model is selected, its parameters can be estimated—for example, by generalized least squares. A small simulation study is performed that demonstrates the usefulness of estimating the derivative to help model selection and illustrates the issue of aliasing. MATLAB software for nonparametric variogram derivative estimation is available at http://www-math.mit.edu/~gorsich/derivative.html. An application to the Walker Lake data set is also presented. 相似文献
18.
The least squares Monte Carlo method is a decision evaluation method that can capture the effect of uncertainty and the value of flexibility of a process. The method is a stochastic approximate dynamic programming approach to decision making. It is based on a forward simulation coupled with a recursive algorithm which produces the near-optimal policy. It relies on the Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir engineering problems because this requires running many reservoir simulations. The objective of this study was to enhance the performance of the least squares Monte Carlo method by improving the sampling method used to generate the technical uncertainties used in obtaining the production profiles. The probabilistic collocation method has been proven to be a robust and efficient uncertainty quantification method. By using the sampling methods of the probabilistic collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision evaluation method. Thus, we introduce the least squares probabilistic collocation method. The decision evaluation considered a number of technical and economic uncertainties. Three reservoir case studies were used: a simple homogeneous model, the PUNQ-S3 model, and a modified portion of the SPE10 model. The results show that using the sampling techniques of the probabilistic collocation method produced relatively accurate responses compared with the original method. Different possible enhancements were discussed in order to practically adapt the least squares probabilistic collocation method to more realistic and complex reservoir models. Furthermore, it is desired to perform the method to evaluate high-dimensional decision scenarios for different chemical enhanced oil recovery processes using real reservoir data. 相似文献
19.
Hybrid Estimation of Semivariogram Parameters 总被引：1，自引：0，他引：1
Two widely used methods of semivariogram estimation are weighted least squares estimation and maximum likelihood estimation.
The former have certain computational advantages, whereas the latter are more statistically efficient. We introduce and study
a “hybrid” semivariogram estimation procedure that combines weighted least squares estimation of the range parameter with
maximum likelihood estimation of the sill (and nugget) assuming known range, in such a way that the sill-to-range ratio in
an exponential semivariogram is estimated consistently under an infill asymptotic regime. We show empirically that such a
procedure is nearly as efficient computationally, and more efficient statistically for some parameters, than weighted least
squares estimation of all of the semivariogram’s parameters. Furthermore, we demonstrate that standard plug-in (or empirical)
spatial predictors and prediction error variances, obtained by replacing the unknown semivariogram parameters with estimates
in expressions for the ordinary kriging predictor and kriging variance, respectively, perform better when hybrid estimates
are plugged in than when weighted least squares estimates are plugged in. In view of these results and the simplicity of computing
the hybrid estimates from weighted least squares estimates, we suggest that software that currently estimates the semivariogram
by weighted least squares methods be amended to include hybrid estimation as an option. 相似文献