Conditional Simulation of Random Fields with Bivariate Gamma Isofactorial Distributions

This work focuses on a random function model with gamma marginal and bivariate isofactorial distributions, which has been applied in mining geostatistics for estimating recoverable reserves by disjunctive kriging. The objective is to widen its use to conditional simulation and further its application to the modeling of continuous attributes in geosciences. First, the main properties of the bivariate gamma isofactorial distributions are analyzed, with emphasis in the destructuring of the extreme values, the presence of a proportional effect (higher variability in high-valued areas), and the asymmetry in the spatial correlation of the indicator variables with respect to the median threshold. Then, we provide examples of stationary random functions with such bivariate distributions, for which the shape parameter of the marginal distribution is half an integer. These are defined as the sum of squared independent Gaussian random fields. An iterative algorithm based on the Gibbs sampler is proposed to perform the simulation conditional to a set of existing data. Such ‘multivariate chi-square’ model generalizes the well-known multigaussian model and is more flexible, since it allows defining a shape parameter which controls the asymmetry of the marginal and bivariate distributions.     

中国沿海多鳞四指马鲅(Eleutheronema rhadinum)与四指马鲅(E. tridactylum)形态与遗传位点差异分析

多鳞四指马鲅(Eleutheronema rhadinum)与四指马鲅(Eleutheronema tridactylum)是四指马鲅属(Eleutheronema)中的名贵经济鱼类,具有良好的养殖开发前景。本文对中国沿海多鳞四指马鲅与四指马鲅群体的26个形态特征值进行了多变量比较分析,提取了7个主成分,累计贡献率达到91.112%,前三个主成分贡献率分别为28.759%、21.467%、15.469%。多鳞四指马鲅与四指马鲅形态差异主要体现在头背部、尾柄部、背腹轴及头尾轴的特征。利用4个形态学参数建立了2群体判别公式,综合判别准确率高达100%,可作为多鳞四指马鲅与四指马鲅物种资源的初步判定方法。另外,利用简化基因组测序开发出多鳞四指马鲅与四指马鲅SNP标记69207个、In Del标记12884个,丰富了四指马鲅属鱼类遗传结构研究数据。本研究为进一步开展四指马鲅数属物种资源评估与保护、选育、功能基因研究提供基础资料。     

日本囊对虾(Marsupenaeus japonicus)秋繁仔虾形态表型与抗流性能间的相关性

于水温(18.0±1.0)°C、盐度20、pH 8.1±0.2条件下,以水流为胁迫因子(时长1min),以日本囊对虾秋繁同生群仔虾[总长(7.643±0.639)mm]为实验对象,以溢水口(实验初始时刻仔虾放置处)为起点,按等距离间距法将自制的水流测定装置(总长1m)依次划分为A(0—25cm)、B(25—50cm)、C(50—75cm)、D(75—100cm)和E(100cm)等五个区段,在确认实验终了时刻分布于A区段内仔虾数量占实验仔虾总数5%的水流速度为0.823cm/s后,以此为实验流速,借助显微扫描像素测量技术和多元分析方法定量研究了A、B、C、D、E实验群体(依次为实验终止时刻分布于A、B、C、D、E区段内的仔虾)个体间形态比例性状间的差异。结果表明:(1)在所涉15项形态测量指标中,各实验群体间均无显著差异(P0.05)的形态性状共计8项,依次为X_4(眼径)、X_5(头胸甲长)、X_6(头胸甲高)、X_7(第一腹节长)、X_8(第二腹节长)、X_9(第三腹节长)、X_~(10)(第四腹节长)和X_14(腹节高);(2)在所涉17项形态比例指标中,实验群体间均无显著差异(P0.05)的形态比例性状共计7项,依次为C_2(额剑长/总长)、C_9(第五腹节长/总长)、C_(10)(尾节长/总长)、C_(11)(尾扇长/总长)、C_(15)(头胸甲高/头胸甲长)、C_(16)(腹节高/第一腹节长)和C_(17)(尾节高/尾节长);(3)经主成分分析,提取到的5个特征值均大于1的主成分,累计贡献率达80.795%,其中第1主成分39.561%,其载荷绝对值大于0.5的主要影响变量占形态比例性状总数的47.059%;(4)将A实验群体定义为水流胁迫处理选留群,B、C、D、E实验群体统归为水流胁迫处理淘汰群。采用逐步判别法,以判别贡献率较大的C_1(第一触角柄长/总长)、C3(眼径/总长)、C7(第三腹节长/总长)、C13(额剑长/头胸甲长)为自变量,所建的Fisher分类函数方程组可较清晰地区分淘汰群和选留群个体,其中选留群的判别准确率P_1、P_2分别为98%和84.85%,淘汰群的判别准确率P_1、P_2分别为82.25%和97.63%,两者综合判别准确率为90.12%。综上可知,借助形态表型分型可实现日本囊对虾仔虾不同抗流性能群体间的筛选。     

Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula

The rainfall patterns of neighbouring meteorological subdivisions of India are similar because of similar climatological and geographical characteristics. Analysing the rainfall pattern separately for these meteorological subdivisions may not always capture the correlation and tail dependence. Furthermore, generating the multivariate rainfall data separately may not preserve the correlation. In this study, copula method is used to derive the bivariate distribution of monsoon rainfall in neighbouring meteorological subdivisions. Different Archimedean copulas are used for this purpose and the best copula is selected based on nonparametric test and tail dependence coefficient. The fitted copula is then applied to derive the bivariate distribution, joint return period and conditional distribution. Bivariate rainfall data is generated with the fitted copula and it is observed with the increase of sample size, the generated data is able to capture the correlation as well as tail dependence. The methodology is demonstrated with the case study of two neighbouring meteorological subdivisions of North‐East India: Assam and Meghalaya meteorological subdivision and Nagaland, Manipur, Mizoram and Tripura meteorological subdivision. Copyright © 2010 John Wiley & Sons, Ltd.     

The control of maturity and kerogen type on quantitative analytical pyrolysis data

Quantitative pyrolysis-gas chromatography has been performed on 96 kerogen samples isolated from 17 wells on the Norwegian Continental shelf. Petrographic and bulk geochemical measurements were also performed on the samples, and a combined data set of 117 variables for each sample was analysed using principal components analysis (PCA). This approach provides an objective and reproducible means of kerogen characterisation, which can be easily automated. In addition to objective kerogen characterisation and facile visualisation of facies and maturity related chemical trends, the method has the potential to allow objective prediction of key geochemical parameters such as maturity level from pyrogram data.     

An examination of the use of the logratio transformation for the testing of endmember hypotheses

Given a compositional dataset in the absence of any prior information on any mixing process which may have formed it, a complete analysis of mixtures determines three distinct types of estimates in order. These are: (i) the estimate of the number of endmembers or fixed source compositions, of which all the sample compositions of the dataset must be approximate mixtures; (ii) the estimated compositions for each of these chosen number of endmembers; and (iii) the estimated contributions of each of these endmember estimates to each sample. Traditionally, the estimate for the number of endmembers has been assessed either by mapping or by inspection of the coefficients of determination between the observed and estimated variables. Mapping entails the plotting on a map of the region from which the samples were taken, either the contours of the contributions of each endmember to each sample, or some other portrayal of the distribution of endmember abundances. Because it requires the complete analysis, assessment by this method is too elaborate except for final confirmation and display. Alternatively, choosing a number of endmembers, which result in suitability high coefficients of determination for all or most variables, may account for elements which are not part of the conjectured mixing process or, worse, may result in the identification of endmembers which may never in fact have existed. Such an error is similar to overspecifying a multiple regression model. So, the obvious starting point from which to assess the validity, or otherwise choice of endmember numbers, is to examine the matrix of residuals. The differences between the logratio-transformed observed and estimated data form an array of residual logratios. A linear combination of these may be formed for each sample, which, under a random perturbation assumption, should follow a univariate normal distribution. Whether or not this scalar is normal can be readily tested. It can also be examined graphically for such desirable qualities as symmetry when the test for normality may be too severe. This procedure is employed to assess the decompositions of the U.S.G.S. Mid-Pacific data and the Nazca Plate Surface sediments.This paper was presented at the 18th Geochautauqua, Newark, Delaware, 13–14 October 1989.     

多元门限回归模型的一种建模方法

本文根据门限自回归模型的基本思想[1]，提出一种多元门限回归模型的建模方法。其特点是充分考虑了预报系统中某些特殊预报因子突变点对预报关系的改变作用。数值实例表明，该模型在模拟和预报精度上比一般线性逐步回归模型有一定程度的提高。     

Estimation of a multidimensional covariance function in case of anisotropy

A model of a multivariate covariance function with an ellipsoidal directional correlation scale has been developed. The axes of the ellipsoidal scale are related to the eigenvalues and eigenvectors of a matrix B which characterizes the ellipsoid of the range of influence. The matrix B is found to be related to a matrix T which can be estimated directly from sparse sampling data and can be used to determine estimates of the matrix B. The method has been applied to both two-dimensional and three-dimensional cases. The numerical results show that the satisfactory accuracy is obtained with sparse sampling data from an anisotropic random function.     

矿化富集中心地质因素多元统计分析及应用

本文导出了通过控矿地质因素逻辑信息法的研究来建立矿化富集中心数学模型的公式,使矿化富集中心数学模型与控矿地质因素定量地联系起来。还给出了单个矿化富集中心趋势面分析的数学模型和矿床空间分布模型。在这基础上,以某锡-多金属成矿带中某远景区的研究为例说明怎样应用矿化富集中心地质因素多元统计分析（逻辑信息法、趋势面分析、逐步回归分析和聚类分析）进行矿床统计预测。     

小块体重的多元线性回归方程在锡铁山铅锌矿床储量计算中的应用

从锡铁山铅锌矿床小块体重样品原始测定数据入手，运用数学地质中的回归分析，建立了本矿床的小块体重多元线性回归方程，为矿床储量计算提供了科学参数。利用回归方程法计算小块体重进而可以推广到所有贱金属矿床的储量计算中。