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1.
M. L.?SerreEmail author G.?Christakos H.?Li C. T.?Miller 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(6):354-369
In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined.
This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069. 相似文献
2.
Spatial statistics of clustered data 总被引:7,自引:7,他引:0
J. L.?KovitzEmail author G.?Christakos 《Stochastic Environmental Research and Risk Assessment (SERRA)》2004,18(3):147-166
Modern spatial statistics techniques are widely used to make predictions for natural processes that are continuously distributed over some convex domain. Implementation of these techniques often relies on the adequate estimation of certain spatial correlation functions such as the covariance and the variogram from the data sets available. This work studies the practical estimation of such spatial correlation functions in the case of clustered data. The coefficient of variation of the dimensionless spatial density of the point pattern of sample locations is suggested as a useful metric for degree of clusteredness of the clustered data set. We show that the common variogram estimator becomes increasingly unreliable with increasing coefficient of variation of the dimensionless spatial density of the point pattern of sample locations. Moreover, we present a modified form of the variogram estimator that incorporates declustering weights, and propose a scheme for estimating the declustering weights based on zones of proximity. Finally, insight is gained in terms of a numerical application of the common and modified methods on piezometric head data collected over an irregular network.Acknowledgments. This work has been supported by grants from the National Institute of Environmental Health Sciences (P42 ES05948-02), the Army Research Office (DAAG55-98-1-0289), and the National Aeronautics and Space Administration (60-00RFQ041). Some of the calculations conducted in support of this work were done on the SGI Origin 2400 at the North Carolina Supercomputing Center, RTP, NC. 相似文献
3.
T. G. Orton R. M. Lark 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(3):319-328
The Bayesian maximum entropy (BME) method can be used to predict the value of a spatial random field at an unsampled location
given precise (hard) and imprecise (soft) data. It has mainly been used when the data are non-skewed. When the data are skewed,
the method has been used by transforming the data (usually through the logarithmic transform) in order to remove the skew.
The BME method is applied for the transformed variable, and the resulting posterior distribution transformed back to give
a prediction of the primary variable. In this paper, we show how the implementation of the BME method that avoids the use
of a transform, by including the logarithmic statistical moments in the general knowledge base, gives more appropriate results,
as expected from the maximum entropy principle. We use a simple illustration to show this approach giving more intuitive results,
and use simulations to compare the approaches in terms of the prediction errors. The simulations show that the BME method
with the logarithmic moments in the general knowledge base reduces the errors, and we conclude that this approach is more
suitable to incorporate soft data in a spatial analysis for lognormal data. 相似文献
4.
Assimilation of fuzzy data by the BME method 总被引:1,自引:1,他引:0
J. L.?KovitzEmail author G.?Christakos 《Stochastic Environmental Research and Risk Assessment (SERRA)》2004,18(2):79-90
Modern spatiotemporal geostatistics provides a powerful framework for generation of predictive maps over a spatiotemporal domain by accounting for general knowledge to define a space of plausible events and then restricting this space of plausible events to be consistent with available site-specific knowledge. The Bayesian maximum entropy (BME) method is one of the most widely used modern geostatistics methods. BME results from assigning probabilities of plausible events based on general knowledge through information maximization and then applying operational Bayesian conditionalization that can explicitly assimilate stochastic representations of various uncertain (soft) data bases. The paper demonstrates that fuzzy data sets can be indirectly assimilated by BME through a two-step process: (a) reinterpretation of the fuzzy data as probabilistic through a generalized defuzzification procedure, and (b) efficient assimilation of the probabilistic results of generalized defuzzification by the BME method. A numerical demonstration involves site-specific probabilistic results obtained from the generalized defuzzification of a simulated fuzzy data set and general knowledge that includes the spatial mean trend and correlation structure models. The parameters of these models can be inferred from the hard data equivalent values of the probabilistic results. Accordingly, details of inference based on probabilistic soft data are also considered. 相似文献
5.
P. Bogaert 《Stochastic Environmental Research and Risk Assessment (SERRA)》2002,16(6):425-448
Being a non-linear method based on a rigorous formalism and an efficient processing of various information sources, the Bayesian
maximum entropy (BME) approach has proven to be a very powerful method in the context of continuous spatial random fields,
providing much more satisfactory estimates than those obtained from traditional linear geostatistics (i.e., the various kriging
techniques). This paper aims at presenting an extension of the BME formalism in the context of categorical spatial random
fields. In the first part of the paper, the indicator kriging and cokriging methods are briefly presented and discussed. A
special emphasis is put on their inherent limitations, both from the theoretical and practical point of view. The second part
aims at presenting the theoretical developments of the BME approach for the case of categorical variables. The three-stage
procedure is explained and the formulations for obtaining prior joint distributions and computing posterior conditional distributions
are given for various typical cases. The last part of the paper consists in a simulation study for assessing the performance
of BME over the traditional indicator (co)kriging techniques. The results of these simulations highlight the theoretical limitations
of the indicator approach (negative probability estimates, probability distributions that do not sum up to one, etc.) as well
as the much better performance of the BME approach. Estimates are very close to the theoretical conditional probabilities,
that can be computed according to the stated simulation hypotheses. 相似文献
6.
Accounting for the uncertainty in the local mean in spatial prediction by Bayesian Maximum Entropy 总被引:2,自引:2,他引:2
T. G. Orton R. M. Lark 《Stochastic Environmental Research and Risk Assessment (SERRA)》2007,21(6):773-784
Bayesian Maximum Entropy (BME) has been successfully used in geostatistics to calculate predictions of spatial variables given
some general knowledge base and sets of hard (precise) and soft (imprecise) data. This general knowledge base commonly consists
of the means at each of the locations considered in the analysis, and the covariances between these locations. When the means
are not known, the standard practice is to estimate them from the data; this is done by either generalized least squares or
maximum likelihood. The BME prediction then treats these estimates as the general knowledge means, and ignores their uncertainty.
In this paper we develop a prediction that is based on the BME method that can be used when the general knowledge consists
of the covariance model only. This prediction incorporates the uncertainty in the estimated local mean. We show that in some
special cases our prediction is equal to results from classical geostatistics. We investigate the differences between our
approach and the standard approach for predicting in this common practical situation. 相似文献
7.
Hwa-Lung Yu Alexander Kolovos George Christakos Jiu-Chiuan Chen Steve Warmerdam Boris Dev 《Stochastic Environmental Research and Risk Assessment (SERRA)》2007,21(5):647-572
This paper describes the spatiotemporal epistematics knowledge synthesis and graphical user interface (SEKS–GUI) framework
and its application in medical geography problems. Based on sound theoretical reasoning, the interactive software library
of SEKS–GUI explores heterogeneous (spatially non-homogeneous and temporally non-stationary) health attribute distributions
(disease incidence, mortality, human exposure, epidemic propagation etc.); expresses the health system’s dependence structure
using (ordinary and generalized) spatiotemporal covariance models; synthesizes core knowledge bases, empirical evidence and
multi-sourced system uncertainty; and generates a meaningful picture of the real-world system using space–time dependent probability
functions and associated maps of health attributes. The implementation stages of the SEKS–GUI library are described in considerable
detail using appropriate screens. The wide applicability of SEKS–GUI is demonstrated by reviewing a selection of real-world
case studies.
An erratum to this article can be found at 相似文献
8.
基于TRMM数据的福建省降水时空格局BME插值分析 总被引:1,自引:0,他引:1
传统空间插值方法可获得福建省区域内降水的总体分布,但该地区气象站点较稀疏且分布不均,导致该区域内降水的空间插值结果误差较大。为提高插值精度,本文利用TRMM卫星数据以弥补站点数据的不足,尝试将TRMM数据作为"软数据"、台站数据作为"硬数据",两者相结合后采用贝叶斯最大熵(Bayesian Maximum Entropy,BME)方法对福建省降水的时空格局进行分析。以2000-2012年近13年20个气象站点的年降水量和月降水量为基础数据,分别利用普通克里格法(Ordinary Kriging,OK)和TRMM为"软数据"的BME插值法,分析福建省多年降水的时空分布格局,并对2种方法的插值结果进行比较。结果表明:在时空分布上,以TRMM数据为辅助变量的贝叶斯最大熵插值结果能更好地体现降水的局部差异特征;在误差评价上,以TRMM数据为辅助变量的贝叶斯最大熵插值结果的MAE和RMSE较小,表明TRMM数据作为"软数据"参与插值的BME方法可以在一定程度上弥补站点数据的不足,有效降低预测结果的绝对误差。通过对福建省降水插值的时空分布格局分析和误差评价可看出,BME插值法通过对基础台站数据,以及TRMM卫星产品数据的利用,使降水的时空分析结果更加真实客观,同时,为TRMM卫星降水数据的应用提供了一个新思路。 相似文献
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