共查询到20条相似文献，搜索用时 484 毫秒
1.
A new approach has been arrived at for determining the linear unbiased minimum variance estimate of ore reserves, or the Kriging. The approach rests heavily on geometric intuition, which reduces the estimation to the simple task of determining an orthogonal projection. First, the problem is presented and solved in ordinary three-dimensional space. The result is stated in matrix formulation, lending itself to a simple generalization in higher dimensions. Then, the general problem is stated in random-variable notation and solved via the results derived. Finally, an illustrative example is given to demonstrate the new approach. 相似文献
2.
Peter K. Kitanidis 《Mathematical Geology》1985,17(2):195-208
The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging. 相似文献
3.
Ana F. Militino 《Mathematical Geology》1997,29(2):221-229
Kriging as an interpolation method, uses as predictor a linear function of the observations, minimizing the mean squared prediction
error or estimation variance. Under multivariate normality assumptions, the given predictor is the best unbiased predictor,
and will be vulnerable to outliers. To overcome this problem, a robust weighted estimator of the drift model coefficients
is proposed, where unequally spaced data may be weighted through the tile areas of the Dirichlet tessellation. 相似文献
4.
In an open pit mine, the selection of blocks for mill feed necessitates the use of a conditionally unbiased estimator not only to maximize profits, but also to predict precisely the grades at the mill. Estimation of blocks usually is done using a series of blasthole assays on a regular grid. In many instances, the blasthole grades show a lognormal-like distribution. This study examines an estimator based on the hypothesis of bilognormality between the true block grade and the estimate obtained using the blastholes. The properties of the estimator are established and the estimator is proven to be conditionally unbiased. It is almost as precise as the lognormal kriging estimator when the points are multilognormal. However, it is more precise than lognormal krigings when only univariate lognormality is present or when the distribution is not exactly lognormal. The estimator also is shown to be robust to errors in the specifications of the variogram model or of the expectation of Z. Contrary to lognormal krigings, the estimator does only a slight correction to the original estimate obtained using the blastholes assays. 相似文献
5.
BLU Estimators and Compositional Data 总被引：5，自引：0，他引：5
One of the principal objections to the logratio approach for the statistical analysis of compositional data has been the absence of unbiasedness and minimum variance properties of some estimators: they seem not to be BLU estimator. Using a geometric approach, we introduce the concept of metric variance and of a compositional unbiased estimator, and we show that the closed geometric mean is a c-BLU estimator (compositional best linear unbiased estimator with respect to the geometry of the simplex) of the center of the distribution of a random composition. Thus, it satisfies analogous properties to the arithmetic mean as a BLU estimator of the expected value in real space. The geometric approach used gives real meaning to the concepts of measure of central tendency and measure of dispersion and opens up a new way of understanding the statistical analysis of compositional data. 相似文献
6.
Robert F. Shurtz 《Mathematical Geosciences》1991,23(3):443-479
Stochastic process theory involves integrals of measurable functions over probability measure spaces. One of these is the ensemble space, Ω, whose members are sample functions on Euclidean spaceR k and the other isR k itself. What geostatisticians call the “theory of regionalized variables” is said to based on stochastic theory. A recent paper inMathematical Geology proclaims a distinction between “probabilistic” and “deterministic” geostatistics. The former is said to rely on “ensemble integrals” over Ω and the latter on “spatial integrals” overR k. This study shows that the proposed distinction rests on an arbitrary choice between two estimators for the covariance of a stochastic process; neither is an ensemble integral, both are spatial integrals, and both are Kolmogorov inconsistent. The “deterministic” estimator is identical with that of classical bivariate least-squares regression in which “spatial structure” is of no consequence. This study shows that both stochastic models are suboptimal approximations to the unique nonstationary classical statistical multivariate regression model generated by each sample pattern. The stochastic process model and its “spatial continuity measures,” thus, appear as questionable mathematical embellishments on suboptimal estimates, correspondence with geomorphic reality is tenuous, and estimates are biased and distorted. Various related misconceptions in the paper are also discussed. 相似文献
7.
Generalized covariance functions in estimation 总被引：3，自引：0，他引：3
Peter K. Kitanidis 《Mathematical Geology》1993,25(5):525-540
I discuss the role of generalized covariance functions in best linear unbiased estimation and methods for their selection. It is shown that the experimental variogram (or covariance function) of the detrended data can be used to obtain a preliminary estimate of the generalized covariance function without iterations and I discuss the advantages of other parameter estimation methods. 相似文献
8.
This paper presents a modified ordinary kriging technique referred to as the “Area Influence Kriging” (AIK). The method is a simple and practical tool to use for more accurate prediction of global recoverable ore resources in any type of deposit. AIK performs well even in deposits with skewed grade distributions when the ordinary kriging (OK) results are unreasonably smooth. It is robust and globally unbiased like OK. The AIK method is not intended to replace OK, which is a better estimator of the average grade of the blocks. Rather it aims to complement OK with its excellent performance in predicting recoverable resources that have been the major pitfalls of OK in many resource estimation cases. The paper details the methodology of AIK with a couple of examples. It also reports the results from its application to a gold deposit. 相似文献
9.
线性回归抗剪强度指标方法的改进 总被引：3，自引：1，他引：2
准确计算土体抗剪强度指标的大小对于评估岩土工程的安全性和经济性有十分重要的意义。目前常用线性回归方法来统计抗剪强度指标。通过研究发现,目前使用的线性回归方法在样本容量增加时,得到的标准差和变异系数会随之变小,当样本容量趋于无穷时,计算值会趋于0。因此,现有方法无法反映抗剪强度指标真实的变异性,统计得到的抗剪强度指标可能不准确。对一简单算例以及小浪底心墙防渗料的64组320个三轴试验成果统计验证了这一问题。本文以概率论为基础,提出了考虑因变量变异性的改进加权线性回归方法,其计算结果是稳定的,不随样本容量而变化。使用改进后的方法对算例和小浪底心墙防渗料的抗剪强度指标重新进行了统计,其结果与矩法十分接近,证实了改进方法的正确性和实用性。 相似文献
10.
The origins of kriging 总被引：30，自引：0，他引：30
Noel Cressie 《Mathematical Geology》1990,22(3):239-252
In this article, kriging is equated with spatial optimal linear prediction, where the unknown random-process mean is estimated with the best linear unbiased estimator. This allows early appearances of (spatial) prediction techniques to be assessed in terms of how close they came to kriging. 相似文献
11.
Noel Cressie 《Mathematical Geosciences》1990,22(3):239-252
In this article, kriging is equated with spatial optimal linear prediction, where the unknown random-process mean is estimated with the best linear unbiased estimator. This allows early appearances of (spatial) prediction techniques to be assessed in terms of how close they came to kriging. 相似文献
12.
This paper presents the analyses of twelve prestressed concrete (PSC) instrumented test piles that were driven in different bridge construction projects of Louisiana in order to develop analytical models to estimate the increase in pile capacity with time or pile setup. The twelve test piles were driven mainly in cohesive soils. Detailed soil characterizations including laboratory and in situ tests were conducted to determine the different soil properties. The test piles were instrumented with vibrating wire strain gauges, piezometers, pressure cells that were monitored during the whole testing period. Several static load tests (SLTs) and dynamic load tests were conducted on each test pile at different times after end of driving (EOD) to quantify the magnitude and rate of setup. Measurements of load tests confirmed that pile capacity increases almost linearly with the logarithm of time elapsed after EOD. Case pile wave analysis program was performed on the restrikes data and was used along with the load distribution plots from the SLTs to evaluate the increase in skin friction capacity of individual soil layers along the length of the piles. The logarithmic linear setup parameter “A” for unit skin friction was calculated of the 70 individual clayey soil layers and was correlated with different soil properties such as undrained shear strength (Su), plasticity index, vertical coefficient of consolidation (cv), over consolidation ratio and sensitivity (St). Nonlinear multivariable regression analyses were performed, and three different empirical models are proposed to predict the pile setup parameter “A” as a function of soil properties. For verification, the subsurface soil conditions and setup information for additional 18 PSC piles collected from local database were used to compare the measured versus predicted “A” parameters from the proposed models, which showed good agreement.
相似文献13.
《International Geology Review》2012,54(4):289-311
An unbiased estimate of the 3He/4He ratio (R) along the Earth's spreading ridge system is 9.14 ± 3.59 Ra (n = 503) where Ra is the atmospheric ratio (1.38 × 10～6). By arbitrarily excluding all values with R > 11 Ra and from ocean depths less than 2500 meters, I obtain 7.91 ± 1.50 Ra (n = 212), which is close to previous “filtered” estimates based on the hypothesis that the excluded values have been influenced by plumes. These are biased estimates. Based on unbiased statistics, many of the socalled high-3He hotspot regions have isotopic ratios well within the MORB range, and all have absolute 3He concentrations much less than MORB. The high variance of some oceanic-island data compared to MORB reflects, in part, the difference between a small sample and a large sample, and magma-chamber processes. Values of 11 to 15 Ra are commonly attributed to deep mantle plumes and “indicative of lower mantle involvement,” but these values are within 2σ of the mean and are not exceptional. Much higher values combined with low absolute helium concentrations are commonly associated with the onset of rifting, or volcanism, and may reflect a shallow, or lithospheric, low-238U/3He (LONU) source. The temporal progression to average MORB-like values suggests that the bulk of the magmas at spreading ridges and large oceanic constructs comes from below the LONU level. The termination of spreading is associated with low ratios, 6 to 7 Ra, similar to values associated with the high-238U/204Pb (HIMU) mantle component and some oceanic islands. 相似文献
14.
Kriging without negative weights 总被引：1，自引：0，他引：1
Under a constant drift, the linear kriging estimator is considered as a weighted average ofn available sample values. Kriging weights are determined such that the estimator is unbiased and optimal. To meet these requirements, negative kriging weights are sometimes found. Use of negative weights can produce negative block grades, which makes no practical sense. In some applications, all kriging weights may be required to be nonnegative. In this paper, a derivation of a set of nonlinear equations with the nonnegative constraint is presented. A numerical algorithm also is developed for the solution of the new set of kriging equations. 相似文献
15.
A simple model for the dynamics of stars located in a sphere with a radius of one-tenth of the central parsec, designed to enable estimation of the probability of capture in the close vicinity (r < 10?3 pc) of a supermassive black hole (SMBH) is presented. In the case of binary stars, such a capture with a high probability results in the formation of a hyper-velocity star. The population of stars in a sphere of radius <0.1 pc is calculated based on data for the Galactic rotation curve. To simulate the distortion of initially circular orbits of stars, these are subjected to a series of random shock encounters (“kicks”), whose net effect is to “push” these binary systems into the region of potential formation of hyper-velocity stars. The mean crossing time of the border of the close vicinity of the SMBH (r < 10?3 pc) by the stellar orbit can be used to estimate the probability that a binary system is captured, followed by the possible ejection of a hyper-velocity star. 相似文献
16.
近年来,随着“治沟造地”和“固沟保塬”等工程在黄土高原的陆续开展,出现了许多直线型黄土填方边坡。降雨是诱发边坡失稳的重要因素,但对降雨诱发直线型黄土填方边坡变形演化特征和破坏模式的研究较少。以直线型黄土填方边坡为研究对象,通过传感器监测、三维激光扫描和人工降雨,开展室内降雨模型试验,记录了降雨入渗下边坡内部水文响应特征和边坡失稳破坏过程,并对湿润锋、土颗粒运移、坡体内部变形响应、裂缝演化特征及破坏模式进行了分析。试验结果表明:随着降雨入渗,湿润锋达到后,体积含水率增加,并在峰值后保持稳定,而基质吸力则减小,到达最低点后保持稳定。冲沟对填方边坡的影响较大,它的发育改变了坡体内含水率特征,同时也是控制边坡整体滑动的边界;边坡变形响应区域主要是以填方边坡前缘堆积区和后缘滑塌区为主;裂缝演化方向由边坡前缘向后缘发展,它的发育为雨水入渗提供优势通道,同时也加剧边坡的变形破坏;降雨形成的水动力驱使坡体中细颗粒从填方边坡后缘向前缘流失,减弱了土体颗粒之间的胶结能力,使其抗剪强度降低,进而使边坡失稳破坏。因此,在降雨入渗下,直线型黄土填方边坡的变形破坏模式为:坡顶冲沟破坏、坡脚软化→局部牵引坍塌、整体失稳→块体分割、流滑破坏。研究结果可为直线型黄土填方边坡的工程建设和滑坡灾害防治提供理论参考。 相似文献
17.
The landslide blockage length along a man-made linear structure, the Alishan railway, is analyzed herein. The Alishan railway runs from Chiayi City to the Alishan scenic area. Numerous landslide and debris flow disasters have blocked the railway since it began operations in 1911. In this study, features of landslides are interpreted from Spot 5 images along the Alishan railway. The results show that larger landslides along the railway exhibit a power-law distribution in frequency-area analysis. The railway blockage length by landslide and its frequency can be linearized by plotting it in a log scale for a blockage length over 0.02?km. The characteristics may be attributed to the fact that the landslide magnitude for its area and volume versus frequency exhibits a power-law distribution. It may thus be possible to estimate the blockage length of linear structures (e.g., railway and expressway) by landslides using the power-law distribution. 相似文献
18.
三轴试验抗剪强度指标线性回归方法的讨论 总被引：6，自引：1，他引：5
利用线性回归统计抗剪强度指标是岩土工程中的常用手段。对于常规三轴试验,可以通过线性拟合p-q曲线或者拟合大小主应力的方法来求解抗剪强度参数,并给出了这两种方法的完整计算公式,同时应用矩法和线性回归方法统计了小浪底64组320个固结排水三轴试验和多个水利工程大坝填筑料的试验资料,发现对于常规三轴试验,拟合p-q曲线求解抗剪强度参数存在高估摩擦系数、低估粘聚力的问题;利用概率理论对两种方法进行了对比分析也发现了同样的趋势。因此,根据常规三轴试验统计抗剪强度参数时采用直接拟合大小主应力更为合理。 相似文献
19.
A common problem in experimental geochemistry is the derivation of equilibrium constants from solubility experiments. A simple method of deriving these equilibrium constants, multiple linear regression, often results in the appearance of negative values. This has been a significant obstacle to continuing research in this field. The problem occurs for the most part because of significant correlations among the “independent” concentration variables. These correlations are an inescapable result of the nature of the experiments and the physical model being fitted. Ridge regression is an appropriate modification to simple linear regression which overcomes this difficulty. Ridge regression results in a simple procedure to obtain physically plausible, yet statistically rigorous stability constants. Of course, other problems may further degrade the quality of derived equilibrium constants, e.g. uncertainty in activity coefficients and no purely statistical method can overcome these types of problems. However, ridge regression is an effective procedure to overcome the multicolinearity which is the main cause of negative equilibrium constants. We demonstrate the use of ridge regression with a general mathematical model and then illustrate its use in the determination of iron-chloro complex equilibrium constants from solubility studies of pyrite-pyrrhotite-magnetite in NaCl solutions at 250°C. Ridge regression may also be of use in other geochemical problems where one must estimate parameters with a physical interpretation and where the independent variables are significantly intercorrelated. 相似文献
20.
S. G. Viladkar 《Journal of the Geological Society of India》2018,92(2):141-144
In the Amba Dongar diatreme, “ferrocarbonatite” is not a single unit of late differentiate of calciocarbonatite magma but it is a family with variation on field occurrence, mineralogy and chemistry of each unit. The family includes dikes of ankeritic carbonatites (phase I and II), plugs of ankeritic carbonatite within sövite ring dike, dikes of sideritic carbonatite in ankeritic carbonatite plug and rödberg veins. Their intrusive relations are very clear in the field and each phase has characteristic mineralogy and trace and REE geochemistry. According to the nomenclature suggested by Harmer and Gittins (1997) majority of “ferrocarbonatites” of Amba Dongar plot in field of “ferruginous calciocarbonatite” and only siderite and rödberg plot in the field of “ferrocarbonatite”. Within these family members, their trace and REE show clear increase from early phase to last phase of sideritic carbonatite. The present short communication discusses various aspects of “ferrocarbonatites”. 相似文献