多参数统计定值模式及其在标样定值中的应用

本文用多参数统计定值的新模式进行标样定值。对离群值的处理提出了新方案。采用11种统计参数对原始数据进行处理,并将这11种参数的算术平均值、中位值、几何平均值、选择平均值、Hampel M估计值和主族众数的平均值作为最佳定值。在NCR TOWER-1632多用户高档微机UNIX操作系统下开发了多参数模式定值软件MPDPS,对6个新研制的标样进行了定值。     

A Laterite Standard Reference Material: Venezuelan Laterite VL-1*

Details on the preparation of a Laterite Standard Reference Material (SRM) from Venezuela, on the homogeneity-testing and the round-robin testing scheme from 11 international laboratories are given. The proposed values (%) for the concentrations of the main constituents are: Al₂O₃: 37.38, SiO₂: 1.16, TiO₂: 3.15, Fe₂O₃: 35.77 and LOI, 22.44. The following statistical parameters are also reported: the arithmetic mean, the variance, the standard deviation, the coefficient of variation, the median, the skewness factor, the preferred mean, the geometric mean, the Gastwirth Median and the dominant cluster mode.     

Estimation of the Mode by the Dominant Cluster Method

A method is presented fop estimation of the mode of analytical data reported by cooperating analysts in the preparation of reference materials. The method is referred to as the dominant cluster method, and the nodal value obtained is the value that shows most agreement between analysts.
Several examples demonstrate that this mode (for which approximate confidence intervals have been estimated), is not inconsistent with the recommended values that have been assigned to well-known geochemical reference samples. Features in its favour are that the calculation is simple, it is independent of the type of distribution, and outliers are automatically excluded.     

常量金标准物质定值中离群值的统计识别

离群值的剔除常用数理统计的方法,如格拉布斯检验法和迪克逊检验法等,但是这些统计方法用于常量金标准物质分析结果的统计检验,都存在着对离群值剔除明显不够的问题.本文建立了以常量金重复分析相对偏差允许限为依据的离群值统计识别方法,包括统计计算待定值样品中金的算术平均值x和相对偏差允许限YG,确定合格的测定结果的数据区间,从而识别出离群值并予以剔除;一次剔除后,按照新的统计量确定下一轮的离群值剔除范围,直到无离群值后,给出金的平均值及其波动范围.以15个人工组合的常量金标准物质为例,模拟金标准物质定值分析,以密码形式分派给不同单位和分析者,共收集10套独立分析结果,采用本法剔除离群值后,所得金算术平均值与金标准参考值更加接近,其相对偏差的质量分数为0.35,达到优秀;而格拉布斯法(或迪克逊法)和中位值法的质量分数分别为0.42和0.40,只能达到良好.应用本文建立的离群值统计识别方法,质量分数等级有了明显提高,增强了数据统计分析的有效性.     

Summary statistics in geochemistry: A study of the performance of robust estimates

Numerical data summaries in many geochemical papers rely on arithmetic means, with or without standard deviations. Yet the mean is the worst average (estimate of location) for those extremely common geochemical data sets which are non-normally distributed or include outliers. The widely used geometric mean, although allowing for skewed distributions, is equally susceptible to outliers. The superior performance of 19 robust estimates of location (simple median, plus various combined, adaptive, trimmed, and skipped,L, M, andW estimates) is illustrated using real geochemical data sets varying in sources of error (pure analytical error to multicomponent geological variability), modality (unimodal to polymodal), size (20 to >2000 data values), and continuity (continuous to truncated in either or both tails). The arithmetic mean tends to overestimate location of many geochemical data sets because of positive skew and large outliers; robust estimates yield consistent smaller averages, although some (e.g., Hampel's and Andrew's) do perform better than others (e.g., Shorth mean, dominant cluster mode). Recommended values for international standard rocks, and for such important geochemical concepts as average chondrite, can be reproduced far more simply via robust estimation on complete interlaboratory data sets than via the rather complicated and subjective methods (e.g., laboratory ratings) so far used in the literature. Robust estimates also seem generally less affected by truncation than the mean; for example, if values below machine detection limits are alternatively treated as missing values or as real values of zero, similar averages are obtained. The standard (and mean) deviations yield consistently larger values of scale for many geochemical data sets than the hinge width (interquartile range) or median absolute deviation from the median. Therefore, summaries of geochemical data should always include at least the simple median and hinge width, to complement the often misleading mean and standard deviation.     

A Study of Robust Estimators

Using the compiled analytical data for the constituents of four Canadian iron-formation reference samples, a comparison is made among nine different "robust" estimators of "true" value, including the median, median, Gastwirth median, trimean, quarter-trimmed and sixthtrimmed means and the three Hampel estimators. Individual estimators and combinations of them are compared by means of the summation and "iron-oxide compatibility" tests. Comparisons are also made with values derived by the "select laboratories" method.     

Quality control in geochemistry from a comparison of four central tendency and five dispersion estimators and example of a geochemical reference material

Data quality control in geochemistry constitutes a fundamental problem that is still to be solved from the application of statistics and computation. We used refined Monte Carlo simulations of 10,000 replications and 190 independent experiments for sample sizes of 5 to 100. Statistical contaminations of 1 to 4 observations were used to compare 9 statistical parameters (4 central tendency—mean, median, trimean, and Gastwirth mean, and 5 dispersion estimates—standard deviation, median absolute deviation, S _n , Q _n , and \( {\widehat{\sigma}}_n \)). The presence of discordant observations in the data arrays rendered the outlier-based and robust parameters to disagree with each other. However, when the mean and standard deviation (outlier-based parameters) were estimated from censored data arrays obtained after the identification and separation of outlying observations, they generally provided a better estimate of the population than the robust estimates obtained from the original data arrays. This inference is contrary to the general belief, and therefore, reasons for the better performance of the outlier-based methods as compared to the robust methods are suggested. However, when all parameters were estimated from censored arrays and appropriate precise and accurate correction factors put forth in this work were applied, all of them became fully consistent, i.e., the mean agreed with the median, trimean and Gastwirth mean, and the standard deviation with the median absolute deviation, S _n , Q _n , and \( {\widehat{\sigma}}_n \). An example of inter-laboratory chemical data for a Hawaiian reference material BHVO-1 included sample sizes from 5 to 100, which showed that small samples of up to 20 provide inconsistent estimates, whereas larger samples of 20–100, especially >40, were more appropriate for estimating statistical parameters through robust or outlier-based methods. Although all statistical estimators provided consistent results, our simulation study shows that it is better to use the censored sample mean and population standard deviation as the best estimates.     

Confidence Limits for the Gastwirth Median*

Although the Gastwirth median is fairly robust (resistant to effects of contamination), it does not, as far as is known, have appropriate confidence limits. It was suspected that it would have confidence limits similar to those of the median. This was borne out in this investigation, which was confined to symmetrical distributions. It is concluded that, for practical purposes, in approximately symmetrical distributions the confidence limits for the median can be assumed to approximate those for the Gastwirth median.     

Relative Efficiency of Single-Outlier Discordancy Tests for Processing Geochemical Data on Reference Materials and Application to Instrumental Calibrations by a Weighted Least-Squares Linear Regression Model

Numerous studies report geochemical data on reference materials (RMs) processed by outlier-based methods that use univariate discordancy tests. However, the relative efficiency of the discordancy tests is not precisely known. We used an extensive geochemical database for thirty-five RMs from four countries (Canada, Japan, South Africa and USA) to empirically evaluate the performance of nine single-outlier tests with thirteen test variants. It appears that the kurtosis test (N15) is the most powerful test for detecting discordant outliers in such geochemical RM databases and is closely followed by the Grubbs type tests (N1 and N4) and the skewness test (N14). The Dixon-type tests (N7, N8, N9 and N10) as well as the Grubbs type test (N2) depicted smaller global relative efficiency criterion values for the detection of outlying observations in this extensive database. Upper discordant outliers were more common than the lower discordant outliers, implying that positively skewed inter-laboratory geochemical datasets are more frequent than negatively skewed ones and that the median, a robust central tendency indicator, is likely to be biased especially for small-sized samples. Our outlier-based procedure should be useful for objectively identifying discordant outliers in many fields of science and engineering and for interpreting them accordingly. After processing these databases by single-outlier discordancy tests and obtaining reliable estimates of central tendency and dispersion parameters of the geochemical data for the RMs in our database, we used these statistical data to apply a weighted least-squares linear regression (WLR) model for the major element determinations by X-ray fluorescence spectrometry and compared the WLR results with an ordinary least-squares linear regression model. An advantage in using our outlier procedure and the new concentration values and uncertainty estimates for these RMs was clearly established.     

北极黄河站秋季气团传输影响下大气气溶胶数谱分布特征

2013 年9月在北极黄河站开展了气溶胶数谱（10~400nm）的短期观测实验。数浓度小时平均值主要出现在300~400cm^-3,平均值为350cm^-3,高于新奥尔松Zeppelin 全球大气本底站及环北极海洋大气7-9月航测报道的浓度。大气气溶胶的三个模态（核模态、爱根核模态和积聚模态）数浓度平均分别为35、122和193cm^-3。观测期间没有发生新粒子生成事件,平均数谱分布呈现双模态的分布特征,模态峰值分别出现在30nm和115nm,由积聚模态主导。平均数谱分布的几何中值粒径出现在约100~110nm。从单颗粒分析结果来看,观测期间黄河站地区大气气溶胶主要以海盐气溶胶为主,但是在来自挪威海域和北欧大陆的气团影响下,也观测到煤烟颗粒、富硫颗粒物和含碳颗粒物等人为气溶胶。     

Statistical analysis of vitrinite reflectance data—a new approach

The reflectance of vitrinite (collotelinite) particles is a widely used parameter as a geothermometer for the estimation of the thermal maturity of organic matter enclosed in rocks. However, several problems have occurred during the last decades, which can be traced back to basically three causes: human mistakes, technical problems, and problems associated with the structural and compositional inhomogeneity of organic matter. Whilst in most cases the first two types of uncertainties can be handled by standardization, the third can cause significant problems during interpretation due to its generally inestimable character. The suppression of vitrinite reflectance and statistical problems originated from small sample size, and outliers belong to this latter type.International standards, such as the ASTM and the ISO, define the vitrinite reflectance parameter as a statistical average of measured data, disregarding the fact that the average is an unresisting and unrobust statistical parameter. In other words, the average is very sensitive to outliers and distribution.The aim of this research was to find and test a better, more resistant, and robust statistical parameter used by traditional parametric and nonparametric statistics, which can be applied in practice instead of the average. Three categories of statistical problems were studied on coal and disperse organic matter (DOM) samples: the distribution of measured values, the effect of data number, and the effect of outliers on statistical parameters. The statistical experiments carried out on numerous original and generated sample sets show that the median (med) and the most frequent value (Mn), a special weighted average, are better parameters to estimate the thermal maturity of organic matter especially above 1% reflectance value.     

利用MODIS fAPAR傅立叶时间序列分析研究植被光合作用活动对净辐射和降雨的响应：青藏高原个例研究

气候变化对植被动力学有非常大的影响。为了定量描述气候变化对植被的影响，文章利用MODIS fAPAR 数据和NCEP 的净辐射和降雨再分析数据对青藏高原地区气候变化对植被的影响进行了时间序列分析。研究所用的数据时间跨度为2000年至2005年。首先利用NCEP 再分析数据建立了干旱度因子的时间序列，为了与MODIS fAPAR 具有相同的时间采样间隔，由NCEP的日净辐射和日降雨量得到每8天的平均净辐射和8日降雨的和。根据一定时间间隔的净辐射与降雨量的比可以用来衡量相对于可利用水分的剩余能量，因此该比值也是干旱灾害的度量。其次，对MODIS fAPAR 的傅立叶时间序列分析提供了两个植被光合作用对干旱相应的因子，即fAPAR的年平均值及其年振幅值。在时间和空间尺度上对植被光合作用活动与干旱指数之间的关系进行了定量分析。对湿年和干年之间的响应差异进行了比较。研究表明较干地区对气候变化的响应最为显著。分析应该扩展到更长的时间跨度以便更加有效地在时间和空间尺度上评估气候变化对植被动力学的影响。     

Condensing multi-element reconnaissance geochemical data from south Greenland using empirical discriminant analysis

Empirical discriminant analysis classified multivariate data from 2174 geochemical reconnaissance samples from South Greenland, so that they were related to known geological units or characterized as outliers. Training sets, comprising 514 samples from 14 geologic units were selected in order to reflect only the background conditions of each geological unit. A smoothing parameter of 0.5 maximized correct classification of the training sets and extracted a reasonable number of outliers (289, 13% of the samples) representing geographically grouped anomalies. Plots of the geochemical samples classified into the geological units corresponded well to the geological map.Q-mode cluster analysis classified the 289 outliers into 30 groups with different element associations. All types of mineral occurrence known in South Greenland could be recognized amongst the clusters. For example, there were seven clusters which were characterized by samples with high U values and different associated elements each one related to a different type of U mineralization. Another cluster containing samples with high Zr, Nb, and Y values reflects recently discovered pyrochlore mineralization. Other clusters were explained on the basis of geological units which were too small to be mapped or included amongst the training sets.Empirical discriminant analysis successfully reduced the multivariate data to one map, which made it easier to evaluate the varying element levels over the different geological units. Incorrectly classified samples require follow-up in order to appraise the accuracy of the geological mapping. Classification of the outliers by cluster analysis assists both in identifying samples influenced by mineral occurrences and in predicting the type of mineralization to be expected, thereby substantially aiding in the selection of areas for mineral exploration.     

基于变动范围法(RVA)的信江水文改变及生态流量研究

选择信江下游梅港站1950~2010年日径流量,根据流域大型水库界牌枢纽运行时间将梅港站径流序列分为建库前(1953~2001)和建库后(2002~2010)两个时段。采用变动范围法(Range of Variability Approach,简称:RVA)分析水库运行对下游梅港站流域生态水文指标改变度,并分析了信江下游生态流量。研究表明:33个水文指标有22个发生中高度改变,11个指标发生低度改变,其水文综合改变度为0.51,属于中度改变;梅港站生态流量值均在RVA阈值内,基本能够保持河流稳定流量,但2月、7~9月及12月河道生态流量大于RVA下限。可适量增大水库下泄水量,降低对下游河段生态系统的威胁。     

A Robust Multiquadric Method for Digital Elevation Model Construction

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.     

青藏高原多源雪深数据适用性综合评估北大核心CSCD

青藏高原积雪对区域气候及水循环有重要影响,现有积雪数据集在该区域存在很大不确定性,适用性评估工作不可或缺。基于气象站观测数据(OBS),采用秩评分方法对一套被动微波遥感(CHE)和两套再分析(ERA5-Land和MERRA2)积雪深度数据进行了多变量、多评价指标的综合定量评估。结果表明:从年平均积雪深度、年最大积雪深度、年积雪日数三个变量分别评价各数据,MERRA2对年最大积雪深度、年积雪日数模拟最好,CHE对年平均积雪深度描述最好;各数据在不同评价指标上的得分排名存在较大差异,CHE在描述线性变化趋势上具有优势,ERA5-Land在描述年际变化上具有优势,MERRA2在描述季节循环、多年平均值、极大值、标准差上具有优势;综合考虑,MERRA2在青藏高原适用性综合评分最高、ERA5-Land次之、CHE最低。三种数据均存在明显不足之处,MERRA2对积雪线性变化趋势的定性描述与OBS相反,对积雪年代际变化的模拟有待优化;ERA5-Land对各变量的多年平均值存在严重高估;CHE刻画积雪空间分布特征能力较差。由于青藏高原西部站点稀少,相关评估结论仅适用于高原中东部。基于遥感及再分析数据得到高原西部积雪变化趋势存在较大不确定性。     

滨海湿地物联网观测数据预处理方法

连续在线滨海湿地生态物联网观测系统,因传感器技术局限及环境干扰会产生异常观测数据,影响数据使用,有效的数据预处理极为重要。以上海崇明东滩国际重要湿地生态观测数据为研究对象,将异常数据分为数值异常、波动异常与异常事件3种类型,基于回归残差概率分布异常检测算法,使用查找表和多指标时间序列模型,综合多环境要素相互关系,构建针对滨海湿地生态观测的数据预处理方法。相比传统方法,该方法在保证异常数据检测精度的同时,更好地区分了异常事件与传感器异常,减少误判。通过分析9个指标5万余条数据,以10^-8~10^-20的阈值分别检测出0.18%~8.12%的数值异常和波动异常,以及2次异常事件。分析数据预处理结果,传感器的观测原理、观测季节等因素会影响传感器的稳定性,人类活动是造成观测区异常事件发生的主要因素。     

基于GF-2影像的离子吸附型稀土矿含量推断方法

寻找离子吸附型稀土矿床对保障我国关键矿产资源具有重要作用。综合利用广西崇左六汤矿区的基础地质、地球化学勘探、高分辨率遥感影像等多源地学数据,以已知矿床分布特征为约束,基于多项式回归及BP神经网络对该区进行建模,以决定系数R2及均方根误差（RMSE）为模型评价指标,对研究区离子吸附型稀土矿含量进行预测。研究结果表明,多项式回归模型检验R2=0.54,BP神经网络模型检验R2=0.64,剔除数据中高离群值后模型精度显著上升,多项式回归模型精度较好,但预测效果图与实测效果图差异较大。综上,数据中离群值的存在对模型的影响较大,模型拟合的好坏并非判断模型好坏的唯一标准,BP神经网络模型能较好预测研究区离子吸附型稀土矿含量。     

基于地下水多变量空间聚类分析的变异性评价

在现存地下水监测网站中,观测站点分布的任意性、随意性和层次不清以及观测数据的冗余性等问题普遍存在,应用空间聚类原理,对所选研究区域廊坊地下水的监测点位及监测指标分别进行了空间聚类分析,对原始数据和经聚类处理后的数据分别进行了空间变异性评价,结果显示空间聚类分析是有效合理的。试图将空间变异性和空间聚类方法结合起来,为环境监测点的重新布置提供了理论依据,使提高监测效率与监测点的代表性、优化监测网格成为了可能;了解监测指标及监测点位在空间上的相关程度,为环境监测指标的确定提供理论依据,进而为环境管理、污染物控制以及环境资源的综合利用提供基础依据。