Hybrid Estimation of Semivariogram Parameters

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.     

The Use of Geographically Weighted Regression for Spatial Prediction: An Evaluation of Models Using Simulated Data Sets

Increasingly, the geographically weighted regression (GWR) model is being used for spatial prediction rather than for inference. Our study compares GWR as a predictor to (a) its global counterpart of multiple linear regression (MLR); (b) traditional geostatistical models such as ordinary kriging (OK) and universal kriging (UK), with MLR as a mean component; and (c) hybrids, where kriging models are specified with GWR as a mean component. For this purpose, we test the performance of each model on data simulated with differing levels of spatial heterogeneity (with respect to data relationships in the mean process) and spatial autocorrelation (in the residual process). Our results demonstrate that kriging (in a UK form) should be the preferred predictor, reflecting its optimal statistical properties. However the GWR-kriging hybrids perform with merit and, as such, a predictor of this form may provide a worthy alternative to UK for particular (non-stationary relationship) situations when UK models cannot be reliably calibrated. GWR predictors tend to perform more poorly than their more complex GWR-kriging counterparts, but both GWR-based models are useful in that they provide extra information on the spatial processes generating the data that are being predicted.     

模糊加权优化适线法的改进及统计特征分析

水文序列长度有限,频率曲线参数估计存在抽样误差,采用加权适线法能够很好地减小误差。模糊加权优化适线法的诺模图长度有限,而且隶属度函数不是以样本无穷大为前提,对模糊加权优化适线法改进,提出半降正态分布的隶属度函数,运用大样本统计试验方法延长诺模图。以理想数据、蒙特卡洛随机数和实测序列对改进的方法检验,以无偏性和有效性为评价指标,运用评分法和百分率法对统计结果分析评价。结果表明改进的模糊加权优化适线法的统计特性好,适线精度高,能够促进模糊加权优化适线法在实际工程中的推广应用。     

压制截断效应的Radon变换在波场分离中的应用

由于离散运算,Radon变换方法中存在截断效应,传统的最小二乘约束反演并不能有效抑制这种效应。介绍了一种频域空间稀疏约束算法,在反演迭代过程中,根据前一次迭代的结果,通过贝叶斯原理将加权矩阵与前一次迭代的结果联系起来,得到新的加权矩阵;然后求解这个加权矩阵方程,得到频率域的稀疏解。比较了用最小二乘反演和压制截断效应的Radon域变换的效果,后者效果明显优于前者。模拟了一个5层的水平地层的地质模型,用这种压制截断效应的Radon变换进行了VSP资料的上下行波场的分离,得到了较好的效果。     

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

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.      

考虑历史洪水资料的期望概率权重矩法参数估计统计试验研究

为有效利用历史洪水资料,提高洪水资料系列参数的估计精度,研究期望概率权重矩法在广义极值分布参数估计中的应用。采用蒙特卡洛试验研究期望概率权重矩法的统计特性,并与部分概率权重矩法做比较。结果表明:期望概率权重矩法具有良好的稳定统计特性,并且是具有历史洪水资料系列进行参数估计的一种简单、稳定和有效的参数估计方法,具有推广意义。     

Estimation of semivariogram parameters and evaluation of the effects of data sparsity

Semivariogram parameters are estimated by a weighted least-squares method and a jackknife kriging method. The weighted least-squares method is investigated by differing the lag increment and maximum lag used in the fit. The jackknife kriging method minimizes the variance of the jackknifing error as a function of semivariogram parameters. The effects of data sparsity and the presence of a trend are investigated by using 400-, 200-, and 100-point synthetic data sets. When the two methods yield significantly different results, more data may be needed to determine reliably the semivariogram parameters, or a trend may be present in the data.     

考虑冻融影响的岩土类材料导热系数计算新方法

从多孔随机混合介质理念出发,提出了考虑相变及未冻水影响的冻融条件下岩土类材料的导热系数计算的新方法,并根据已有的试验数据,利用多孔随机混合介质模型求出了同等条件下的导热系数,研究结果表明：模型的计算结果和试验结果基本一致,其平均偏差为2.3%,最大偏差为5.4%。另外,通过与现有的3种导热系数的取值方法的比较发现：目前广泛使用的指数加权平均法在0℃以上时计算结果较准确,但并不适合计算低温（0℃以下）岩土类材料的导热系数。加权调和平均法和加权算术平均法计算结果误差都很大,且不能反映相变对导热系数的影响。研究成果为低温相变条件下岩土介质温度场的正确求解提供了理论前提。     

用SHRIMP测定锆石U-Pb年龄的工作方法

用SHRIMP测定锆石U-Pb年龄涉及锆石单矿物分选、样品靶制备、U-Pb同位素组成测定、原始数据处理、数据解释等多方面。锆石分选中要避免不同样品的交叉污染,要尽量将岩石中所有的锆石分选出来;淘洗岩石粉末时要避免丢失细小的锆石,因细小的锆石更重要。制作样品靶时,粘贴到样品靶的锆石应反映岩石中锆石的全貌。数据处理中,要修正或剔除异常数据、评估拟参加加权平均计算的每个数据权重的合理性。通常用测得的众数年龄的加权平均值作为侵位年龄或喷发年龄会老于实际年龄,应使用样品中最年轻的锆石年龄来限定岩浆侵位或喷发年龄。     

A Mathematical View of Weights-of-Evidence,Conditional Independence,and Logistic Regression in Terms of Markov Random Fields

New light is shed on mathematical methods of potential modeling from the point of view of Markov random fields. In particular, weights-of-evidence and logistic regression models are discussed in terms of graphical models possessing Markov properties, where the notion of conditional independence is essential, and will be related to log-linear models. While weights-of-evidence with respect to indicator predictor variables and logistic regression with unrestricted predictor variables model conditional probabilities of an indicator random target variable, the subject of log-linear models is the joint probability of random variables. The relationship to log-linear models leads to a likelihood ratio test of conditional independence, rendering an omnibus test of conditional independence restricted by a normality assumption obsolete. Moreover, it reveals a hierarchy of methods comprising weights-of-evidence, logistic regression without interaction terms, and logistic regression including interaction terms, where each former method is a special case of the consecutive latter method. The assumptions of conditional independence of all predictor variables given the target variable lead to logistic regression without interaction terms. Violations of conditional independence are compensated exactly by corresponding interaction terms, no cumbersome approximate corrections are needed. Thus, including interaction terms into logistic regression models is an appropriate means to account for lacking conditional independence. Logistic regression exempts from the burden to worry about lack of conditional independence. Eventually, the relationship to log-linear models renders logistic regression with indicator predictor variables optimum for discrete predictor variables. Weights-of-evidence applies for indicator predictor variables only, logistic regression applies without restrictions of the type of predictor variables and approximates the proper distribution in the general case.     

基于水流阻力与图论的河网连通性评价

河网连通是区域防洪、供水和生态安全的重要基础。基于图论将河网概化为图模型,考虑不同类型河道输水能力差异,以河道水流阻力倒数表征水流通畅度,并以河道水流通畅度为权值,借助ArcGIS平台建立河网图模型加权邻接矩阵,再利用MATLAB工具进行顶点水流通畅度计算和河网连通度分析,从而实现对河网连通性的定量化分析。以太湖流域嘉兴平原河网为例,进行河道疏浚前后的河网连通程度定量评价,结果表明河道疏浚后河网连通度明显增加。     

Kriging Prediction Intervals Based on Semiparametric Bootstrap

Kriging is a widely used method for prediction, which, given observations of a (spatial) process, yields the best linear unbiased predictor of the process at a new location. The construction of corresponding prediction intervals typically relies on Gaussian assumptions. Here we show that the distribution of kriging predictors for non-Gaussian processes may be far from Gaussian, even asymptotically. This emphasizes the need for other ways to construct prediction intervals. We propose a semiparametric bootstrap method with focus on the ordinary kriging predictor. No distributional assumptions about the data generating process are needed. A simulation study for Gaussian as well as lognormal processes shows that the semiparametric bootstrap method works well. For the lognormal process we see significant improvement in coverage probability compared to traditional methods relying on Gaussian assumptions.     

Mercury in Western Canadian subbituminous coal—a weighted average study to evaluate potential mercury reduction by selective mining

Western Canadian subbituminous coal is mined using strip-mining methods. The coal is used to feed coal-fired power plants for electricity generation. Parameters that influence the mercury content of these coals include the occurrence and frequency of partings in the seam, weathering, and epigenetic mineralization. Most partings have higher mercury content than the coal layers in the same seam, with the single bentonite bed having the highest Hg content. However, some high ash components, such as sandy siltstone, do not follow this trend. The incorporation of the high mercury partings into the as-mined coal may increase the Hg content in the feed coal. Epigenetic mineralization may also increase the mercury content of coal, depending on the nature of the mineralization.Calculation of the weighted mean of mercury content for various combination of lithological components of a seam illustrates how these components influence the total mercury content of the seam. This approach also suggests how selective mining might be used to reduce mercury in “as-mined” coal.Results of weighted average calculations of mercury indicate that the thin lithological units with moderate mercury may not necessarily influence that overall weighted average of Hg for a seam. However, there can be exception, such as presence of thin (3.5 cm) bentonite parting with high mercury in a 94.5 cm seam that increased the mercury content of seam by 83.4%.     

Block Kriging for Lognormal Spatial Processes

Lognormal spatial data are common in mining and soil-science applications. Modeling the underlying spatial process as normal on the log scale is sensible; point kriging allows the whole region of interest to be mapped. However, mining and precision agriculture is carried out selectively and is based on block averages of the process on the original scale. Finding spatial predictions of the blocks assuming a lognormal spatial process has a long history in geostatistics. In this article, we make the case that a particular method for block prediction, overlooked in past times of low computing power, deserves to be reconsidered. In fact, for known mean, it is optimal. We also consider the predictor based on the “law” of permanence of lognormality. Mean squared prediction errors of both are derived and compared both theoretically and via simulation; the predictor based on the permanence-of-lognormality assumption is seen to be less efficient. Our methodology is applied to block kriging of phosphorus to guide precision-agriculture treatment of soil on Broom's Barn Farm, UK.     

加权支持向量回归机及其在水质预测中的应用

支持向量机是一种基于结构风险最小化原理的学习技术，也是一种新的具有很好泛化性能的回归方法。本文对用于回归估计的标准支持向量机加以改进，提出了一种新的用于回归估计的支持向量机学习算法，针对各样本重要性的差异，给各个样本的惩罚系数和误差要求赋予不同权重，并利用加权支持向量回归机的理论及其算法构建水质预测模型。实验结果表明，该方法对水质具有较好的预测效果。     

偏重钻铤在丁集矿冻结造孔施工中的应用

钻井技术的关键是预防及控制孔斜,通过对目前常用4种防斜钻具组合的适岩性、井深、井斜及钻效等指标对比,在冻结造孔施工中选用了适用地层广、防斜性能好并具有纠斜作用的偏重钻铤。为发挥偏重钻铤的防斜作用,宜增大转速,并使钻铤减去部分的重量应位于离轴线尽可能远的部位。在淮南丁集冻结孔施工的三十多口钻孔中,井斜一般均在0．5°以内,钻效超过2400m/台·月。     

油气地表化探中基于R型因子分析的综合指标及工区N级划分

作者对油气化探单指标基础上的综合指标以及工区异常划分问题进行了研究和探讨,认为综合指标不仅本身具有综合反师异常的能力,同时也是单指标解释的参照系,而多级划分则能提高给探信息的利用程度。基于Ｒ型因子分析,作者在文中提出了定量确定单指标权系数的加权平均意义下的综合指标和因子得分意义下的综合指标,并且指出了在特定条件下的这二种指标的归一性。在所形成的综合指标基础上,作者又归纳了一咱对研究地区进行多级划分     

改进加权马尔科夫链模型在喀什地区承压含水层参数动态识别中的应用研究

承压含水层的估算对于地下水开发利用的合理规划十分重要。而承压含水层参数识别对于含水层水量参数估算至关重要。结合改进加权马尔科夫链模型,以喀什为研究实例,对该地区承压含水层参数进行动态识别,从置信区间分析结果可看出,喀什地区承压含水层参数的变幅为7.93 m^2/min,而承压含水层参数μ的变幅为0.048,从不同置信度下的变幅结果可看出,相比于传统模型,改进加权马尔科夫链模型提高了参数识别收敛效率和计算精度。计算结果的可靠性程度较高。研究成果对于喀什地区含水层水量估算具有重要的参考价值。     

加权信息量模型在滑坡易发性评价中的应用以湖北省恩施市为例

信息量模型物理意义明确、操作简单,在滑坡易发性评价中得到广泛应用,但该模型未考虑各评价因子的权重。本文提出了基于层次分析法的加权信息量模型,并以湖北省恩施市为例,采用基于GIS的空间分析方法,分析了地形、断裂、水系、工程地质岩组等因子对研究区滑坡的影响,利用加权信息量将研究区划分为高易发区、中易发区、低易发区和极低易发区。     

Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators

Hesitant fuzzy set is an extension of the traditional fuzzy set, and it has the membership function which was expressed by several possible numbers. Since it was introduced, it has been received wide attention from scholars due to its powerful ability in describing the uncertainty. In this paper, we first introduce some new operations on hesitant fuzzy elements (HFEs) based on Dombi t-conorm and t-norm and then proposed some new aggregation operators for HFEs, such as hesitant fuzzy Dombi weighted averaging, hesitant fuzzy Dombi ordered weighted averaging, hesitant fuzzy Dombi weighted geometric, hesitant fuzzy Dombi ordered weighted geometric, hesitant fuzzy Dombi hybrid averaging and hesitant fuzzy Dombi hybrid geometric operator. Finally, a multiple attribute group decision-making approach under hesitant fuzzy environment is presented based on these proposed operators. A real example about typhoon disaster assessment is presented to show the advantages of the proposed method.