Medical Geography: A Promising Field of Application for Geostatistics

The analysis of health data and putative covariates, such as environmental, socio-economic, behavioral or demographic factors, is a promising application for geostatistics. However, it presents several methodological challenges that arise from the fact that data is typically aggregated over irregular spatial supports and consists of a numerator and a denominator (e.g., population size). This paper presents an overview of recent developments in the field of health geostatistics, with an emphasis on three main steps in the analysis of areal health data: (1) estimation of the underlying disease risk, (2) detection of areas with significantly higher risk, and (3) analysis of relationships with putative risk factors. The analysis is illustrated by using age-adjusted cervix cancer mortality rates recorded from 1970 to 1994 of 118 counties in four Western USA states. Poisson kriging allows the filtering of noisy mortality rates computed from small population sizes, enhancing the correlation with two putative explanatory variables: percentage of habitants living below the federally defined poverty line, and percentage of Hispanic females. Area-to-point kriging formulation creates continuous maps of mortality risk, reducing the visual bias associated with the interpretation of choropleth maps. Stochastic simulation is used to generate realizations of cancer mortality maps, which allows one to quantify how uncertainty of the spatial distribution of health outcomes translates into uncertainty of the location of clusters of high values or the correlation with covariates. Finally, geographically-weighted regression highlights the non-stationarity in the explanatory power of covariates; the higher mortality values along the coast are better explained by the two covariates than the lower risk recorded in Utah.     

Downscaling in remote sensing

Downscaling has an important role to play in remote sensing. It allows prediction at a finer spatial resolution than that of the input imagery, based on either (i) assumptions or prior knowledge about the character of the target spatial variation coupled with spatial optimisation, (ii) spatial prediction through interpolation or (iii) direct information on the relation between spatial resolutions in the form of a regression model. Two classes of goal can be distinguished based on whether continua are predicted (through downscaling or area-to-point prediction) or categories are predicted (super-resolution mapping), in both cases from continuous input data. This paper reviews a range of techniques for both goals, focusing on area-to-point kriging and downscaling cokriging in the former case and spatial optimisation techniques and multiple point geostatistics in the latter case. Several issues are discussed including the information content of training data, including training images, the need for model-based uncertainty information to accompany downscaling predictions, and the fundamental limits on the representativeness of downscaling predictions. The paper ends with a look towards the grand challenge of downscaling in the context of time-series image stacks. The challenge here is to use all the available information to produce a downscaled series of images that is coherent between images and, thus, which helps to distinguish real changes (signal) from noise.     

Analysis of geographical disparities in temporal trends of health outcomes using space–time joinpoint regression

Analyzing temporal trends in health outcomes can provide a more comprehensive picture of the burden of a disease like cancer and generate new insights about the impact of various interventions. In the United States such an analysis is increasingly conducted using joinpoint regression outside a spatial framework, which overlooks the existence of significant variation among U.S. counties and states with regard to the incidence of cancer. This paper presents several innovative ways to account for space in joinpoint regression: (1) prior filtering of noise in the data by binomial kriging and use of the kriging variance as measure of reliability in weighted least-square regression, (2) detection of significant boundaries between adjacent counties based on tests of parallelism of time trends and confidence intervals of annual percent change of rates, and (3) creation of spatially compact groups of counties with similar temporal trends through the application of hierarchical cluster analysis to the results of boundary analysis. The approach is illustrated using time series of proportions of prostate cancer late-stage cases diagnosed yearly in every county of Florida since 1980s. The annual percent change (APC) in late-stage diagnosis and the onset years for significant declines vary greatly across Florida. Most counties with non-significant average APC are located in the north-western part of Florida, known as the Panhandle, which is more rural than other parts of Florida. The number of significant boundaries peaked in the early 1990s when prostate-specific antigen (PSA) test became widely available, a temporal trend that suggests the existence of geographical disparities in the implementation and/or impact of the new screening procedure, in particular as it began available.     

各向异性矿化特征的分析与模拟 及其在储量估算中的应用

矿化作用往往是地质事件及局部过程共同作用的结果,导致矿体空间形态复杂多变、矿石品位呈各向异性、尺度不一的非线性空间变异模式.传统方法无论是在矿石量的计算方面还是在矿块内平均品位的确定上都存在多种误差,并且无法实现信息的动态管理及直观表达.文章以安庆铜矿中心矿区为例,采用对数块kriging与三维地学模拟技术相结合的方法...     

不同采样点数量下土壤有机质含量空间预测方法对比

运用普通克里格、泛克里格、协同克里格和回归克里格4种方法,结合由DEM获取的高程因子以及土壤全氮和阳离子交换量（CEC）,预测了黑龙江省海伦市耕地有机质含量的空间分布。不同样点数量下海伦市土壤有机质含量的空间变异结构分析表明,样点数量多并不一定能够识别土壤有机质含量的结构性连续组分,最优化的布置采样点位置可能比单纯增加...     

空间分析中几种插值方法的比较研究

针对常用的空间插值方法在精度分析方面比较的不足,从地质统计学、数学函数和几何方法方面分别选取普通克里金插值法、三次样条函数法和距离权重倒数法进行插值精度的比较与分析。文章分析了各个方法的优缺点和局限性,选取疏密差异较大的均匀和不均匀离散点数据进行实验,利用三次趋势面模型和MATLAB,ArcGIS,GS+Version...     

Rainfall network design using kriging and entropy

The spatial distribution of rainfall is related to meteorological and topographical factors. An understanding of the weather and topography is required to select the locations of the rain gauge stations in the catchment to obtain the optimum information. In theory, a well‐designed rainfall network can accurately represent and provide the needed information of rainfall in the catchment. However, the available rainfall data are rarely adequate in the mountainous area of Taiwan. In order to provide enough rainfall data to assure the success of water projects, the rainfall network based on the existing rain gauge stations has to be redesigned. A method composed of kriging and entropy that can determine the optimum number and spatial distribution of rain gauge stations in catchments is proposed. Kriging as an interpolator, which performs linear averaging to reconstruct the rainfall over the catchment on the basis of the observed rainfall, is used to compute the spatial variations of rainfall. Thus, the rainfall data at the locations of the candidate rain gauge stations can be reconstructed. The information entropy reveals the rainfall information of the each rain gauge station in the catchment. By calculating the joint entropy and the transmitted information, the candidate rain gauge stations are prioritized. In addition, the saturation of rainfall information can be used to add or remove the rain gauge stations. Thus, the optimum spatial distribution and the minimum number of rain gauge stations in the network can be determined. The catchment of the Shimen Reservoir in Taiwan is used to illustrate the method. The result shows that only seven rain gauge stations are needed to provide the necessary information. Copyright © 2007 John Wiley & Sons, Ltd.     

The Bayesian maximum entropy method for lognormal variables

The Bayesian maximum entropy (BME) method can be used to predict the value of a spatial random field at an unsampled location given precise (hard) and imprecise (soft) data. It has mainly been used when the data are non-skewed. When the data are skewed, the method has been used by transforming the data (usually through the logarithmic transform) in order to remove the skew. The BME method is applied for the transformed variable, and the resulting posterior distribution transformed back to give a prediction of the primary variable. In this paper, we show how the implementation of the BME method that avoids the use of a transform, by including the logarithmic statistical moments in the general knowledge base, gives more appropriate results, as expected from the maximum entropy principle. We use a simple illustration to show this approach giving more intuitive results, and use simulations to compare the approaches in terms of the prediction errors. The simulations show that the BME method with the logarithmic moments in the general knowledge base reduces the errors, and we conclude that this approach is more suitable to incorporate soft data in a spatial analysis for lognormal data.     

空间软数据及其插值方法研究进展

由于对地观测技术的迅速发展,空间数据的种类和数量增长迅猛,由空间数据反演得到的各种信息日趋膨胀,这些反演结果中的信息不少以软数据的形式出现。在实际应用中,这些软数据往往与空间插值的目标变量具有一定的相关性,甚至成为控制目标变量空间分布特征的重要因素。然而,由于这些数据通常表示为非数值形式,在计算和处理上存在着一定困难,以致被传统的插值方法所忽视,从而造成信息浪费。近来出现的空间软插值方法是一种利用空间软数据作为辅助信息并以改善插值效果的方法,能够较好的处理并利用软数据所隐含的信息,具有较好的应用发展前景。本文根据空间软数据的特点及其分类,系统综述了空间软插值方法及其应用领域。首先分析了空间数据软硬性质的根本区别,论述了软数据的分类和“硬化”方法,然后介绍空间插值模型中对空间软数据的集成方法和原理,最后对空间软插值方法及其应用研究领域进行了展望。     

淮河流域水文随机方法的径流图化(英文)

Theoretical difficulties for mapping and for estimating river regime characteristics in a large-scale basin remain because of the nature of the variable under study: river flows are related to a specific area, i.e. the drainage basin, and are hierarchically organized in space through the river network with upstream-downstream dependencies. Another limitation is there are not enough gauge stations in developing countries. This presentation aims at de-veloping the hydro-stochastic approach for producing choropleth maps of average annual runoff and computing mean discharge along the main river network for a large-scale basin. The approach applied to mean annual runoff is based on geostatistical interpolation proce-dures coupled with water balance and data uncertainty analyses. It is proved by an applica-tion in the upstream at Bengbu in the Huaihe River Basin, a typical large-scale basin in China. Hydro-stochasitic approach in a first step interpolates to a regular grid net and in a second step the grid values are integrated along rivers. The interpolation scheme includes a con-straint to be able to account for the lateral water balance along the rivers. Grid runoff map with 10 km × 10 km resolution and the discharge map along the river with the 1 km basic length unit are the main results in this study. This kind of statistic approach can be widely used be-cause it avoids the complexity of hydrological models and does not depend on the meteoro-logical data.