共查询到20条相似文献，搜索用时 747 毫秒
1.
Nonparametric estimation of spatial distributions 总被引：4，自引：0，他引：4
A. G. Journel 《Mathematical Geosciences》1983,15(3):445-468
The indicator approach, whereby the data are used through their rank order, allows a nonparametric approach to the data bivariate distribution. Such rich structural information allows a nonparametric risk-qualified, estimation of local and global spatial distributions. 相似文献
2.
Gordon Woo 《地学学报》1989,1(1):79-83
The estimation of risk confidence bounds is an important element of a comprehensive probabilistic risk assessment for a radioactive waste repository. Normal distribution bounds may be used in the asymptotic limit of a very large number of Monte Carlo simulations, but sharp skewness of the risk distribution may severely retard the convergence process. The Tchebycheff bounds are parameter-free and may be applied regardless of distribution, save for the finiteness of variance. These bounds may be generally applicable, but they are invariably very broad. Better parameter-free bounds for mean risk are presented here, based on an inequality originally derived by Guttman. 相似文献
3.
Eulogio Pardo-Igúzquiza 《Mathematical Geology》1998,30(1):95-108
In this paper, the maximum likelihood method for inferring the parameters of spatial covariances is examined. The advantages of the maximum likelihood estimation are discussed and it is shown that this method, derived assuming a multivariate Gaussian distribution for the data, gives a sound criterion of fitting covariance models irrespective of the multivariate distribution of the data. However, this distribution is impossible to verify in practice when only one realization of the random function is available. Then, the maximum entropy method is the only sound criterion of assigning probabilities in absence of information. Because the multivariate Gaussian distribution has the maximum entropy property for a fixed vector of means and covariance matrix, the multinormal distribution is the most logical choice as a default distribution for the experimental data. Nevertheless, it should be clear that the assumption of a multivariate Gaussian distribution is maintained only for the inference of spatial covariance parameters and not necessarily for other operations such as spatial interpolation, simulation or estimation of spatial distributions. Various results from simulations are presented to support the claim that the simultaneous use of maximum likelihood method and the classical nonparametric method of moments can considerably improve results in the estimation of geostatistical parameters. 相似文献
4.
Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities. 相似文献
5.
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
6.
Projection Pursuit Multivariate Transform 总被引：5，自引：2，他引：3
Transforming complex multivariate geological data to a Gaussian distribution is an important and challenging problem in geostatistics. A variety of transforms are available for this goal, but struggle with high dimensional data sets. Projection pursuit density estimation (PPDE) is a well-established nonparametric method for estimating the joint density of multivariate data. A central component of the PPDE algorithm transforms the original data toward a multivariate Gaussian distribution. The PPDE approach is modified to map complex data to a multivariate Gaussian distribution within a geostatistical modeling context. Traditional modeling may then take place on the transformed Gaussian data, with a back-transform used to return simulated variables to their original units. This approach is referred to as the projection pursuit multivariate transform (PPMT). The PPMT shows the potential to be an effective means for modeling high dimensional and complex geologic data. The PPMT algorithm is developed before discussing considerations and limitations. A case study compares modeling results against more common techniques to demonstrate the value and place of the PPMT within geostatistics. 相似文献
7.
The cumulative distribution function (CDF) of magnitude of seismic events is one of the most important probabilistic characteristics in Probabilistic Seismic Hazard Analysis (PSHA). The magnitude distribution of mining induced seismicity is complex. Therefore, it is estimated using kernel nonparametric estimators. Because of its model-free character the nonparametric approach cannot, however, provide confidence interval estimates for CDF using the classical methods of mathematical statistics.To assess errors in the seismic events magnitude estimation, and thereby in the seismic hazard parameters evaluation in the nonparametric approach, we propose the use of the resampling methods. Resampling techniques applied to a one dataset provide many replicas of this sample, which preserve its probabilistic properties. In order to estimate the confidence intervals for the CDF of magnitude, we have developed an algorithm based on the bias corrected and accelerated method (BCa method). This procedure uses the smoothed bootstrap and second-order bootstrap samples. We refer to this algorithm as the iterated BCa method. The algorithm performance is illustrated through the analysis of Monte Carlo simulated seismic event catalogues and actual data from an underground copper mine in the Legnica–Głogów Copper District in Poland.The studies show that the iterated BCa technique provides satisfactory results regardless of the sample size and actual shape of the magnitude distribution. 相似文献
8.
Seismic hazard assessment under complex source size distribution of mining-induced seismicity 总被引：1，自引：0，他引：1
It is well-documented that a variety of factors controlling the rockmass fracturing process in mines often results in a complexity of mining event size distribution. In such cases, the estimation of the probability functions of source size parameterizations, with the use of presently known distribution models, brings about an unacceptable and systematic over- or underestimation of the seismic hazard parameters. It is, therefore, recommended that the non-parametric, kernel estimators of the event size distribution functions, be applied to stationary hazard studies in mining seismicity.These data-driven estimators, adapted to seismic source size characterization, accurately fit all kinds of data underlying distributions, regardless of their complexity. Recently, the non-parametric approach to size characterization was supported by a special method of uncertainty analysis based on resampling techniques. At present, it is a fully developed method, which provides point and interval estimates of size distribution functions and related hazard parameters. Two examples of its use in studying mining seismic data are presented and discussed in this paper. The analyzed data sets were recorded in two different copper mines in Poland. The smoothed bootstrap test for multimodality, which is a specialized tool for investigating the shapes of probability densities, provided highly significant proof that in both cases the probability densities of source size parameterization were complex thus implied the superiority of the non-parametric estimation to the classic, model-based approach in the studied cases. The data were then used to construct non-parametric, kernel estimates of the source size cumulative distribution function (CDF), the exceedance probability and the mean return period. Furthermore, confidence intervals for these quantities were also estimated. The intervals for CDF were narrow, showing that the procedures of non-parametric estimation and resampling based uncertainty analysis were precise. Due to the fact that the mean return period is very sensitive to values of the CDF, in particular for larger events sizes, the uncertainty of the return period estimates was not insignificant but remained manageable. The point and interval estimates of source size CDF and hazard parameters so obtained were compared with the respective point estimates achieved from the inappropriate in the case of complex magnitude distributions, model-based approach. 相似文献
9.
Pilar García-Soidán Raquel Menezes Óscar Rubiños-López 《Environmental Earth Sciences》2012,66(2):615-624
The use of kriging for construction of prediction or risk maps requires estimating the dependence structure of the random
process, which can be addressed through the approximation of the covariance function. The nonparametric estimators used for
the latter aim are not necessarily valid to solve the kriging system, since the positive-definiteness condition of the covariance
estimator typically fails. The usage of a parametric covariance instead may be attractive at first because of its simplicity,
although it may be affected by misspecification. An alternative is suggested in this paper to obtain a valid covariance from
a nonparametric estimator through the Fourier series tool, which involves two issues: estimation of the Fourier coefficients
and selection of the truncation point to determine the number of terms in the Fourier expansion. Numerical studies for simulated
data have been conducted to illustrate the performance of this approach. In addition, an application to a real environmental
data set is included, related to the presence of nitrate in groundwater in Beja District (Portugal), so that pollution maps
of the region are generated by solving the kriging equations with the use of the Fourier series estimates of the covariance. 相似文献
10.
Multivariate Intrinsic Random Functions for Cokriging 总被引：2，自引：0，他引：2
In multivariate geostatistics, suppose that we relax the usual second-order-stationarity assumptions and assume that the component
processes are intrinsic random functions of general orders. In this article, we introduce a generalized cross-covariance function
to describe the spatial cross-dependencies in multivariate intrinsic random functions. A nonparametric method is then proposed
for its estimation. Based on this class of generalized cross-covariance functions, we give cokriging equations for multivariate
intrinsic random functions in the presence of measurement error. A simulation is presented that demonstrates the accuracy
of the proposed nonparametric estimation method. Finally, an application is given to a dataset of plutonium and americium
concentrations collected from a region of the Nevada Test Site used for atomic-bomb testing. 相似文献
11.
A new approach to estimate shaft capacity of bored piles in sandy soils, based on numerical analysis, is presented. The topic is relevant as current design methods often largely underestimate the shaft capacity of piles in sands, thus resulting in an over-conservative design. The proposed approach is based on explicitly modelling the thin cylinder of soil surrounding the pile, where strain localization concentrates (shear band), and on the fundamental mechanic behaviour of sandy soils (e.g. dilatancy, softening). This approach is both simple and easy to apply. Results of a broad parametric study involving axially loaded single piles embedded in different sandy soils are presented, highlighting that relative density and grain size distribution mainly affect the shaft capacity. The capability of the procedure to predict shaft friction is checked against data from a well-documented full-scale axial load test on instrumented pile. Some suggestions for calibration and application of the method are also reported. 相似文献
12.
Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation 总被引：5，自引：0，他引：5
The statistical analysis of compositional data based on logratios of parts is not suitable when zeros are present in a data set. Nevertheless, if there is interest in using this modeling approach, several strategies have been published in the specialized literature which can be used. In particular, substitution or imputation strategies are available for rounded zeros. In this paper, existing nonparametric imputation methods—both for the additive and the multiplicative approach—are revised and essential properties of the last method are given. For missing values a generalization of the multiplicative approach is proposed. 相似文献
13.
《地学前缘(英文版)》2016,7(1)
Learning incorporates a broad range of complex procedures. Machine learning(ML) is a subdivision of artificial intelligence based on the biological learning process. The ML approach deals with the design of algorithms to learn from machine readable data. ML covers main domains such as data mining, difficultto-program applications, and software applications. It is a collection of a variety of algorithms(e.g. neural networks, support vector machines, self-organizing map, decision trees, random forests, case-based reasoning, genetic programming, etc.) that can provide multivariate, nonlinear, nonparametric regression or classification. The modeling capabilities of the ML-based methods have resulted in their extensive applications in science and engineering. Herein, the role of ML as an effective approach for solving problems in geosciences and remote sensing will be highlighted. The unique features of some of the ML techniques will be outlined with a specific attention to genetic programming paradigm. Furthermore,nonparametric regression and classification illustrative examples are presented to demonstrate the efficiency of ML for tackling the geosciences and remote sensing problems. 相似文献
14.
The current state of art for limit equilibrium analysis of slope stability problems lacks a satisfactory procedure for stability evaluation under general, rapid (undrained) loading conditions. Some procedures are available for the analysis of rapid drawdown, but these suffer from several shortcomings and, furthermore, are not applicable to other types of rapid loading. An approach is presented which overcomes these limitations. The approach integrates four components-establishment of soil behaviour on the basis of laboratory testing, estimation of steady-state conditions in the slope using a boundary value analysis, estimation of distribution of undrained strength in the slope using undrained stress paths, and identification of the critical slip surface followed by calculation of its factor of safety. The approach is illustrated through its application to the stability analysis of an earth dam under rapid drawdown and earthquake conditions. 相似文献
15.
A Methodology for Reliability-Based Design of Rock Slopes 总被引：10，自引：0，他引：10
Summary A reliability-based methodology for the design of rock slopes, that can easily be implemented by the practicing engineers
is proposed. The advanced first-order second-moment (AFOSM) method is adopted as the reliability assessment model and its
application is illustrated for the case of plane failure. A model is developed within the framework of first-order second-moment
approach to analyze the uncertainties underlying the in situ shear strength properties of rock discontinuities. Here, particular
emphasis is given on the assessment of uncertainties related to the shear characteristics of clean, unfilled rock discontinuities
under low normal stress levels. An extensive literature survey on the shear characteristics of discontinuities is carried
out in order to collect data for the quantification of uncertainties. The data extracted from this literature survey are classified
and reprocessed so that they can be utilized in the uncertainty analysis model. A user friendly software called ROCKREL is
developed to carry out the numerical computations and to make the proposed design format more practical.
Received April 16, 2001; accepted June 10, 2002; Published online November 19, 2002
Authors' address: Prof. Celal Karpuz, Middle East Technical University, Faculty of Engineering, Department of Mining Engineering, 06531 Ankara,
Turkey; e-mail: karpuz @metu.edu.tr 相似文献
16.
Modelling shallow landslide susceptibility: a new approach in logistic regression by using favourability assessment 总被引：2，自引：0，他引：2
María José Domínguez-Cuesta Montserrat Jiménez-Sánchez Ana Colubi Gil González-Rodríguez 《International Journal of Earth Sciences》2010,99(3):661-674
A new method for estimating shallow landslide susceptibility by combining Geographical Information System (GIS), nonparametric
kernel density estimation and logistic regression is described. Specifically, a logistic regression is applied to predict
the spatial distribution by estimating the probability of occurrence of a landslide in a 16 km2 area. For this purpose, a GIS is employed to gather the relevant sample information connected with the landslides. The advantages
of pre-processing the explanatory variables by nonparametric density estimation (for continuous variables) and a reclassification
(for categorical/discrete ones) are discussed. The pre-processing leads to new explanatory variables, namely, some functions
which measure the favourability of occurrence of a landslide. The resulting model correctly classifies 98.55% of the inventaried
landslides and 89.80% of the landscape surface without instabilities. New data about recent shallow landslides were collected
in order to validate the model, and 92.20% of them are also correctly classified. The results support the methodology and
the extrapolation of the model to the whole study area (278 km2) in order to obtain susceptibility maps. 相似文献
17.
Andrew P. Bunger 《Rock Mechanics and Rock Engineering》2010,43(3):275-286
Extraction of diamond-drilled core from high stress environments can result in the core breaking into discs. Through four
decades of research, a variety of computational tools and experimental approaches have been used to analyze the details of
the failure processes leading to core-discing-type breakage of diamond-drilled cores. One motivation for this research is
to use these calculations for stress estimation based on, for example, the disc length (i.e., thickness) measured in a particular
core. This application requires that the core discs lengths do not deviate much from an average or typical value. This paper
presents a stochastic approach, based on analyzis of the entire distribution of disc lengths, that provides a basis for application
of existing core discing models even when it is unclear how to define a typical disc length, for example when the disc length
distribution is highly non-Gaussian. The viability of the stochastic approach is demonstrated by comparison with data collected
from 900 m of core extracted from a South Australian granite formation. 相似文献
18.
Some Bayesian methods of dealing with inaccurate or vague data are introduced in the framework of seismic hazard assessment. Inaccurate data affected by heterogeneous errors are modeled by a probability distribution instead of the usual value plus a random error representation; these data are generically called imprecise. The earthquake size and the number of events in a certain time are modeled as imprecise data. Imprecise data allow us to introduce into the estimation procedures the uncertainty inherent in the inaccuracy and heterogeneity of the measuring systems from which the data were obtained. The problem of estimating the parameter of a Poisson process is shown to be feasible by the use of Bayesian techniques and imprecise data. This background technique can be applied to a general problem of seismic hazard estimation. Initially, data in a regional earthquake catalog are assumed imprecise both in size and location (i.e errors in the epicenter or spreading over a given source). By means of scattered attenuation laws, the regional catalog can be translated into a so-called site catalog of imprecise events. The site catalog is then used to estimate return periods or occurrence probabilities, taking into account all sources of uncertainty. Special attention is paid to priors in the Bayesian estimation. They can be used to introduce additional information as well as scattered frequency-size laws for local events. A simple example is presented to illustrate the capabilities of this methodology. 相似文献
19.
20.
Structural analysis of data displaying trends may be performed with the help of generalized increments, the variance of these
increments being a function of a generalized covariance. Generalized covariances are estimated primarily by parametric methods
(i. e., methods searching for the best coefficients of a predetermined function), but also may be computed by one known nonparametric
alternative. In this paper, a new nonparametric method is proposed. It is founded on the following principles: (1) least-squares
residues are generalized increments; and (2) the generalized covariance is not a unique function, but a family of functions
(the system is indeterminate). The method is presented in a general context of a k order trend in Rd, although the full solution is given only fork = I in Ri. In Ri, higher order trends may be developed easily with the equations included in this paper. For higher dimensions in space, the
problem is more complex, but a research approach is proposed. The method is tested on soil pH data and compared to a parametric
and nonparametric method. 相似文献