Multivariate imputation in cross-sectional analysis of health effects associated with air pollution

We demonstrate a recently developed spatial interpolation methodology in a study of the chronic effects of air pollution on respiratory morbidity. Our study uses data from the Ontario Health Study, a large survey of households in Ontario conducted for the province by Statistics Canada. The interpolation procedure imputes unobserved vectors of air pollution concentrations for individual Public Health Units, from those observed at a few fixed air pollution monitoring sites. We use logistic regression methods to assess the significance of air pollution levels based on the imputed values after modelling the relationship between binary health responses and assorted covariates such as measures of life style. Our findings prove negative; no significant relationship between chronic respiratory morbidity and air pollution is found. The imputation methodology is seen to be promising and might well be used in other such analyses.     

A method to combine non-probability sample data with probability sample data in estimating spatial means of environmental variables

In estimating spatial means of environmental variables of a region from datacollected by convenience or purposive sampling, validity of the results canbe ensured by collecting additional data through probability sampling. Theprecision of the estimator that uses the probability sample can beincreased by interpolating the values at the nonprobability sample points tothe probability sample points, and using these interpolated values as anauxiliary variable in the difference or regression estimator. Theseestimators are (approximately) unbiased, even when the nonprobability sampleis severely biased such as in preferential samples. The gain in precisioncompared to the estimator in combination with Simple Random Samplingis controlled by the correlation between the target variable andinterpolated variable. This correlation is determined by the size (density)and spatial coverage of the nonprobability sample, and the spatialcontinuity of the target variable. In a case study the average ratio of thevariances of the simple regression estimator and estimator was 0.68for preferential samples of size 150 with moderate spatial clustering, and0.80 for preferential samples of similar size with strong spatialclustering. In the latter case the simple regression estimator wassubstantially more precise than the simple difference estimator.     

山东省典型工业城市土壤重金属来源、空间分布及潜在生态风险评价

选取山东省典型工业城市——莱芜市钢城区为研究区域,系统采集了106个表层土壤样品,测定了As、Cd、Co、Cr、Cu、Hg、Ni、Pb和Zn等9种重金属的含量,分别利用多元统计和地统计方法分析了重金属的来源和空间分布特征,最后对土壤重金属的潜在生态风险进行了评价.结果表明:1研究区9种重金属元素的平均含量均超过了山东省土壤背景值,其中Cd、Hg、Pb和Zn的平均值分别是背景值的2.42、4.69、1.74和1.54倍,在表层土壤中存在明显的富集.2Cd、Pb和Zn主要来源于工业"三废"、交通排放以及农药化肥的施用;Co、Cr和Ni为自然源因子,受到成土母质的控制;As和Hg来源于煤炭燃烧和钢铁冶炼,Cu受自然与人为因素共同影响.3研究区总体上处于中等与高生态风险的临界水平,其中Hg为高生态风险水平,Cd为中等生态风险水平,其他元素则均为低生态风险.     

北京东郊污灌土壤重金属含量的克立格插值及重金属污染评价

由于污灌方式、土壤质地等因素的影响,污灌土壤的污染程度可能具有较明显的空间差异。因此,传统的土壤环境质量评价方法难以准确反映土壤的环境质量。本文应用克立格方法对北京东郊污灌土壤表层重金属含量进行了分析,并在此基础上进行了单因子和多因子评价。结果显示,采样区的土壤属于轻度污染或无污染。由于污灌口分布、污泥施用等多种因素的影响,不同地块土壤受到的污染程度不同,形成一定的空间差异。     

Bayesian spatial prediction

This paper presents a complete Bayesian methodology for analyzing spatial data, one which employs proper priors and features diagnostic methods in the Bayesian spatial setting. The spatial covariance structure is modeled using a rich class of covariance functions for Gaussian random fields. A general class of priors for trend, scale, and structural covariance parameters is considered. In particular, we obtain analytic results that allow easy computation of the predictive distribution for an arbitrary prior on the parameters of the covariance function using importance sampling. The computations, as well as model diagnostics and sensitivity analysis, are illustrated with a set of precipitation data.     

Bayesian estimation of European sulphur emissions using monitoring data and an acid deposition model

A statistical method for estimating national emissions of acidifying air pollutants in Europe is presented. The method uses an acid deposition model to match official emissions data from European countries and measured depositions from a monitoring network. An application to 1990 sulphate data demonstrates the method and suggests some tendencies in the reported emissions. The proposed framework may prove useful for verifying national compliance with emissions standards, and the method should be applicable also to other substances than sulphur dioxide. The problem of designing an optimal monitoring network may also be assessed within the proposed statistical framework.     

禹城地区土壤铅含量空间分布的指示克里格估值

以鲁西北禹城地区土壤重金属Pb含量为例,针对其存在特异值与偏态分布的特点,利用指示克里格法研究了土壤Pb含量小于特定阈值的条件概率分布,分析了该地区土壤Pb含量的空间分布特征,并对普通克里格和指示克里格的估值效果进行交叉验证。结果表明：研究区土壤Pb含量总体较低,未超过国家标准的限值,但不同部位土壤Pb含量差异较大;普通克里格法和指示克里格法形成的土壤Pb含量空间分布格局相似,但普通克里格法的平滑效果强于指示克里格法;研究区域土壤环境质量总体良好,Pb含量高值区主要集中在各乡镇驻地附近的农田;指示克里格对土壤Pb含量空间估值的精度优于普通克里格,指示克里格法更适用于原始数据呈非正态分布且特异值对估值结果有较大影响的土壤属性。本研究结果为该地区土壤环境质量评价和重金属污染防控提供科学依据。     

山东省典型金矿区土壤重金属空间特征分析与环境风险评估

以山东省典型金矿区——焦家式金矿带为研究区,系统采集了77个表层土壤样品并对Cu、Pb、Zn和Cr的含量进行了测定;采用空间统计分析方法对重金属的空间变异结构、分布规律及潜在污染风险进行了研究.Cu、Pb、Zn和Cr的平均含量分别为19.41、27.32、49.81和39.27 mg·kg-1.半方差函数拟合表明Cu和Pb属于中等空间自相关,空间分布呈岛状;而Zn和Cr为结构性空间变异,受自然因素的控制,空间分布呈带状和岛状.热点分析与指示克里金插值结果表明,金城镇、辛庄镇与蚕庄镇的交界地带重金属环境风险较高,南部则为安全区,其中Pb的超标概率最大且中高风险区分布范围广泛.研究结果可为研究区土壤重金属污染评价和调控提供参考和依据.     

Use of best linear unbiased prediction for hot spot identification in two-way compositing

Compositing of individual samples is a cost-effective method for estimating a population mean, but at the expense of losing information about the individual sample values. The largest of these sample values (hotspot) is sometimes of particular interest. Sweep-out methods attempt to identify the hotspot and its value by quantifying a (hopefully, small) subset of individual values as well as the usual quantification of the composites. Sweep-out design is concerned with the sequential selection of individual samples for quantification on the basis of all earlier quantifications (both composite and individual). The design-goal is for the number of individual quantifications to be small (ideally, minimal). Previous sweep-out designs have applied to traditional (i.e., disjoint) compositing. This paper describes a sweep-out design suitable for two-way compositing. That is, the individual samples are arranged in a rectangular array and a composite is formed from each row and also from each column. At each step, the design employs all available measurements (composite and individual) to form the best linear unbiased predictions for the currently unquantified cells. The cell corresponding to the largest predicted value is chosen next for individual measurement. The procedure terminates when the hotspot has been identified with certainty.     

Space-time statistics for environmental and agricultural related phenomena

This paper presents an overview of space-time statistical procedures to analyse agricultural and environmental related phenomena. It starts with an application on root-rot development in cotton. Dependence modelling in space and time is done with the space-time variogram. Various kriging interpolators are presented for making predictions in space and time. Simulated annealing is used to design an optimal monitoring network for estimation of space-time variograms. In the application no clear indication was found for anisotropy, although strong evidence exists that the disease not only proceeds within rows but also jumps between rows. The optimal sampling scheme showed a spatial clustering of observations at the first and the last monitoring day and less observations at intermediate times.