An Introduction to the Network Weight Matrix

This study introduces the network weight matrix as a replacement for the spatial weight matrix to measure the spatial dependence between links of a network. This matrix stems from the concepts of betweenness centrality and vulnerability in network science. The elements of the matrix are a function not simply of proximity, but of network topology, network structure, and demand configuration. The network weight matrix has distinctive characteristics, which are capable of reflecting spatial dependence between traffic links: (1) elements are allowed to have negative and positive values capturing the competitive and complementary nature of links, (2) diagonal elements are not fixed to zero, which takes the self‐dependence of a link upon itself into consideration, and (3) elements not only reflect the spatial dependence based on the network structure, but they acknowledge the demand configuration as well. We verify the network weight matrix by modeling traffic flows in a 3 × 3 grid test network with 9 nodes and 24 directed links connecting 72 origin‐destination (OD) pairs. Models encompassing the network weight matrix outperform both models without spatial components and models with the spatial weight matrix. The network weight matrix represents a more accurate and defensible spatial dependency between traffic links, and offers the potential to augment traffic flow prediction.     

Area‐to‐Point Prediction Under Boundary Conditions

This article proposes a geostatistical solution for area‐to‐point spatial prediction (downscaling) taking into account boundary effects. Such effects are often poorly considered in downscaling, even though they often have significant impact on the results. The geostatistical approach proposed in this article considers two types of boundary conditions (BC), that is, a Dirichlet‐type condition and a Neumann‐type condition, while satisfying several critical issues in downscaling: the coherence of predictions, the explicit consideration of support differences, and the assessment of uncertainty regarding the point predictions. An updating algorithm is used to reduce the computational cost of area‐to‐point prediction under a given BC. In a case study, area‐to‐point prediction under a Dirichlet‐type BC and a Neumann‐type BC is illustrated using simulated data, and the resulting predictions and error variances are compared with those obtained without considering such conditions.     

A Geostatistical Linear Regression Model for Small Area Data. 一种适用于小区域数据的地统计线性回归模型

We present a new linear regression model for use with aggregated, small area data that are spatially autocorrelated. Because these data are aggregates of individual‐level data, we choose to model the spatial autocorrelation using a geostatistical model specified at the scale of the individual. The autocovariance of observed small area data is determined via the natural aggregation over the population. Unlike lattice‐based autoregressive approaches, the geostatistical approach is invariant to the scale of data aggregation. We establish that this geostatistical approach also is a valid autoregressive model; thus, we call this approach the geostatistical autoregressive (GAR) model. An asymptotically consistent and efficient maximum likelihood estimator is derived for the GAR model. Finite sample evidence from simulation experiments demonstrates the relative efficiency properties of the GAR model. Furthermore, while aggregation results in less efficient estimates than disaggregated data, the GAR model provides the most efficient estimates from the data that are available. These results suggest that the GAR model should be considered as part of a spatial analyst's toolbox when aggregated, small area data are analyzed. More important, we believe that the GAR model's attention to the individual‐level scale allows for a more flexible and theory‐informed specification than the existing autoregressive approaches based on an area‐level spatial weights matrix. Because many spatial process models, both in geography and in other disciplines, are specified at the individual level, we hope that the GAR covariance specification will provide a vehicle for a better informed and more interdisciplinary use of spatial regression models with area‐aggregated data.     

A Geostatistical Framework for Area‐to‐Point Spatial Interpolation

The spatial prediction of point values from areal data of the same attribute is addressed within the general geostatistical framework of change of support; the term support refers to the domain informed by each datum or unknown value. It is demonstrated that the proposed geostatistical framework can explicitly and consistently account for the support differences between the available areal data and the sought‐after point predictions. In particular, it is proved that appropriate modeling of all area‐to‐area and area‐to‐point covariances required by the geostatistical frame‐work yields coherent (mass‐preserving or pycnophylactic) predictions. In other words, the areal average (or areal total) of point predictions within any arbitrary area informed by an areal‐average (or areal‐total) datum is equal to that particular datum. In addition, the proposed geostatistical framework offers the unique advantage of providing a measure of the reliability (standard error) of each point prediction. It is also demonstrated that several existing approaches for area‐to‐point interpolation can be viewed within this geostatistical framework. More precisely, it is shown that (i) the choropleth map case corresponds to the geostatistical solution under the assumption of spatial independence at the point support level; (ii) several forms of kernel smoothing can be regarded as alternative (albeit sometimes incoherent) implementations of the geostatistical approach; and (iii) Tobler's smooth pycnophylactic interpolation, on a quasi‐infinite domain without non‐negativity constraints, corresponds to the geostatistical solution when the semivariogram model adopted at the point support level is identified to the free‐space Green's functions (linear in 1‐D or logarithmic in 2‐D) of Poisson's partial differential equation. In lieu of a formal case study, several 1‐D examples are given to illustrate pertinent concepts.     

Model Uncertainty in Matrix Exponential Spatial Growth Regression Models

This article considers the most important aspects of model uncertainty for spatial regression models, namely, the appropriate spatial weight matrix to be employed and the appropriate explanatory variables. We focus on the spatial Durbin model (SDM) specification in this study that nests most models used in the regional growth literature, and develop a simple Bayesian model‐averaging approach that provides a unified and formal treatment of these aspects of model uncertainty for SDM growth models. The approach expands on previous work by reducing the computational costs through the use of Bayesian information criterion model weights and a matrix exponential specification of the SDM model. The spatial Durbin matrix exponential model has theoretical and computational advantages over the spatial autoregressive specification due to the ease of inversion, differentiation, and integration of the matrix exponential. In particular, the matrix exponential has a simple matrix determinant that vanishes for the case of a spatial weight matrix with a trace of zero. This allows for a larger domain of spatial growth regression models to be analyzed with this approach, including models based on different classes of spatial weight matrices. The working of the approach is illustrated for the case of 32 potential determinants and three classes of spatial weight matrices (contiguity‐based, k‐nearest neighbor, and distance‐based spatial weight matrices), using a data set of income per capita growth for 273 European regions.     

Geostatistical Prediction and Simulation of Point Values from Areal Data

The spatial prediction and simulation of point values from areal data are addressed within the general geostatistical framework of change of support (the term support referring to the domain informed by each measurement or unknown value). It is shown that the geostatistical framework (i) can explicitly and consistently account for the support differences between the available areal data and the sought-after point predictions, (ii) yields coherent (mass-preserving or pycnophylactic) predictions, and (iii) provides a measure of reliability (standard error) associated with each prediction. In the case of stochastic simulation, alternative point-support simulated realizations of a spatial attribute reproduce (i) a point-support histogram (Gaussian in this work), (ii) a point-support semivariogram model (possibly including anisotropic nested structures), and (iii) when upscaled, the available areal data. Such point-support-simulated realizations can be used in a Monte Carlo framework to assess the uncertainty in spatially distributed model outputs operating at a fine spatial resolution because of uncertain input parameters inferred from coarser spatial resolution data. Alternatively, such simulated realizations can be used in a model-based hypothesis-testing context to approximate the sampling distribution of, say, the correlation coefficient between two spatial data sets, when one is available at a point support and the other at an areal support. A case study using synthetic data illustrates the application of the proposed methodology in a remote sensing context, whereby areal data are available on a regular pixel support. It is demonstrated that point-support (sub-pixel scale) predictions and simulated realizations can be readily obtained, and that such predictions and realizations are consistent with the available information at the coarser (pixel-level) spatial resolution.     

Contouring the Cataclysm: A Geographical Analysis of the Effects of the Minoan Eruption of the Santorini Volcano

This study is a step forward in understanding the palaeoenvironmental effects of the Minoan eruption of Santorini (1627–1600 BCE). We employ geostatistics to produce a prediction map for the thickness of the tephra fallout over the Eastern Mediterranean, and we reconstruct the effects by comparisons with recent eruption analogues. Based on the geostatistical map, the amount of environmental disruption over so far undocumented areas is estimated by comparison with archaeological sites where emplaced Minoan tephra has been recorded before. Nevertheless, independent field evidence suggest that the environment responded differently in places, occasionally posing challenges to the presented interpolation. A second line of evidence coming from contemporaneous fluvial archives provides clues for a widespread ‘Minoan flood’ over a large part of the Eastern Mediterranean, associated with the eruption itself. This simultaneous hydrological event may have had a counterbalancing effect on the impacts of the Minoan tephra cover, and could explain the sporadic discrepancies between the predicted effects and the palaeoenvironmental evidence. Traces of the effects of this extraordinary volcanic event are also sought in the regional Late Bronze Age literature.     

Exploring scale-dependent correlations between cancer mortality rates using factorial kriging and population-weighted semivariograms

This article presents a geostatistical methodology that accounts for spatially varying population size in the processing of cancer mortality data. The approach proceeds in two steps: (1) spatial patterns are first described and modeled using population-weighted semivariogram estimators, (2) spatial components corresponding to nested structures identified on semivariograms are then estimated and mapped using a variant of factorial kriging. The main benefit over traditional spatial smoothers is that the pattern of spatial variability (i.e., direction-dependent variability, range of correlation, presence of nested scales of variability) is directly incorporated into the computation of weights assigned to surrounding observations. Moreover, besides filtering the noise in the data, the procedure allows the decomposition of the structured component into several spatial components (i.e., local versus regional variability) on the basis of semivariogram models. A simulation study demonstrates that maps of spatial components are closer to the underlying risk maps in terms of prediction errors and provide a better visualization of regional patterns than the original maps of mortality rates or the maps smoothed using weighted linear averages. The proposed approach also attenuates the underestimation of the magnitude of the correlation between various cancer rates resulting from noise attached to the data. This methodology has great potential to explore scale-dependent correlation between risks of developing cancers and to detect clusters at various spatial scales, which should lead to a more accurate representation of geographic variation in cancer risk, and ultimately to a better understanding of causative relationships.     

The Power of Models in Planning: The Case of DaisyGIS and Nitrate Leaching

Spatial deterministic simulation models such as DaisyGIS are increasingly being used for decision‐making in European planning. In Denmark specifically, there is an increasing interest at the regional level to use DaisyGIS as an administrative tool. There are, however, uncertainties associated with the use of these deterministic models, partly due to the spatial variation in input parametres. This study evaluates the use of DaisyGIS for nitrate leaching assessments based on nitrate leaching experiments carried out at the Marbjerg experimental site at Roskilde University. The study includes geostatistical analysis of soil and hydraulic variables and the use of remote sensing for deriving spatial information about the Leaf Area Index. It is found that the model predicts nitrate leaching well when using site‐specific input data but it is quite sensitive to the parameterization of carbon, the C/N ratio and variations in the Leaf Area Index (LAI). With the increasing use of Daisy in the counties, there is a need to find better ways of handling uncertainties in model output which can be used by decision‐makers and to study further the impact of spatial LAI assimilation on catchment scale nitrate leaching processes.     

Mapping the possible occurrence of archaeological sites by Bayesian inference

Regional archaeological prospections are often done by field walking, where the location of the sampled fields is often determined by factors like feared disturbance or recent plowing. The resulting data configuration can be suboptimal for spatial prediction of the archaeological potential by geostatistical methods like kriging. As an alternative, we propose a Bayesian method to map the possible occurrence of archaeological finds and compare this to indicator regression kriging. Three types of predictive models were implemented in the Bayesian context following deductive, inductive and mixed approaches to use auxiliary geographical information in the mapping. After prediction of a validation set, it was concluded that the mixed approach gave the best results in terms of map quality, and that the kriging method performed poorly. Usage of data on the presence and the absence of archaeological finds is to be preferred above usage of presence data only. Furthermore, a method is presented that filters those parts of a predictive map that are not strongly supported by evidence.     

Predicting Ductile Crack Initiation of Steel Bridge Structures Due to Extremely Low-Cycle Fatigue Using Local and Non-Local Models

The strain-based prediction model combining the Miner's rule and Manson-Coffin's relationship provides a local parameter for evaluating the ductile crack initiation of steel structures, and some modified models based on it were proposed to evaluate extremely low-cycle fatigue (ELCF) behaviors of steel structures. Previous research has confirmed these local models to be an accurate index for ductile crack initiation in steel bridge piers, however it is found to quite depend on the mesh size of the numerical model used. In this study, a non local damage parameter is presented and successfully applied to ductile crack initiation life assessment of steel bridge piers subjected to earthquake-type cyclic loading. The non local damage parameter is based on averaging the strains over the effective plane using a weight function in the exponential form, and introduces the non local damage parameter to replace the local state variable. Finite element analysis with three different mesh sizes is employed. Comparisons of the local and non local solutions with those of experiments indicate that the non local prediction model can predict the ductile crack initiation of steel bridge piers with good accuracy regardless of the specimen geometries and loading histories, meanwhile the mesh independent nature of the non local model is also demonstrated.     

Developing Geostatistical Space–Time Models to Predict Outpatient Treatment Burdens from Incomplete National Data

Basic health system data such as the number of patients utilizing different health facilities and the types of illness for which they are being treated are critical for managing service provision. These data requirements are generally addressed with some form of national Health Management Information System (HMIS), which coordinates the routine collection and compilation of data from national health facilities. HMIS in most developing countries are characterized by widespread underreporting. Here we present a method to adjust incomplete data to allow prediction of national outpatient treatment burdens. We demonstrate this method with the example of outpatient treatments for malaria within the Kenyan HMIS. Three alternative modeling frameworks were developed and tested in which space–time geostatistical prediction algorithms were used to predict the monthly tally of treatments for presumed malaria cases (MC) at facilities where such records were missing. Models were compared by a cross-validation exercise and the model found to most accurately predict MC incorporated available data on the total number of patients visiting each facility each month. A space–time stochastic simulation framework to accompany this model was developed and tested in order to provide estimates of both local and regional prediction uncertainty. The level of accuracy provided by the predictive model, and the accompanying estimates of uncertainty around the predictions, demonstrate how this tool can mitigate the uncertainties caused by missing data, substantially enhancing the utility of existing HMIS data to health-service decision makers.     

Reconstructing Population Density Surfaces from Areal Data: A Comparison of Tobler's Pycnophylactic Interpolation Method and Area-to-Point Kriging

We compare Tobler's pycnophylactic interpolation method with the geostatistical approach of area-to-point kriging for distributing population data collected by areal unit in 18 census tracts in Ann Arbor for 1970 to reconstruct a population density surface. In both methods, (1) the areal data are reproduced when the predicted population density is upscaled; (2) physical boundary conditions are accounted for, if they exist; and (3) inequality constraints, such as the requirement of non-negative point predictions, are satisfied. The results show that when a certain variogram model, that is, the de Wijsian model corresponding to the free-space Green's function of Laplace's equation, is used in the geostatistical approach under the same boundary condition and constraints with Tobler's approach, the predicted population density surfaces are almost identical (up to numerical errors and discretization discrepancies). The implications of these findings are twofold: (1) multiple attribute surfaces can be constructed from areal data using the geostatistical approach, depending on the particular point variogram model adopted—that variogram model need not be the one associated with Tobler's solution and (2) it is the analyst's responsibility to justify whether the smoothness criterion employed in Tobler's approach is relevant to the particular application at hand. A notable advantage of the geostatistical approach over Tobler's is that it allows reporting the uncertainty or reliability of the interpolated values, with critical implications for uncertainty propagation in spatial analysis operations.     

近红外光谱无损检测技术在古籍纸张性能分析中的可行性研究

为研究近红外光谱无损检测技术在古籍纸张分析检测中的可行性,采用近红外光谱分析方法,构建100个纸样的p H值、纤维聚合度、高锰酸钾值、碱储量4项指标的近红外光谱预测模型,并对模型的相关性进行验证。结果表明,近红外光谱分析模型对纸样p H值、纤维聚合度、高锰酸钾值的预测值跟实测值相关性较好,能够满足检测需求,对碱储量的预测值有一定误差,但能够满足参考性要求。实验结果证明了近红外光谱分析技术对珍贵文献纸张进行无损检测是可行的。     

基于GWR模型的合肥居住地价影响因素研究

以合肥市主城区为例,基于2010-2014年居住用地的出让数据,运用地统计法、GWR模型等方法,对合肥市居住地价的空间异质性及其影响因素进行研究。研究表明：①合肥市居住地价的空间分布呈现出显著的多中心的空间结构,地价的峰值区分别以老城区、政务区天鹅湖及滨湖新区塘西河公园为中心呈现圈层式分布;②不同的地价影响因素表现出不同的空间分布特征,其中容积率对居住地价的贡献度空间差异最大,其次是宗地面积,主干路次之,交通站点对居住地价的贡献度最小;③厘清各影响因素对地价的作用机制,建立动态的数字地价模型,不仅能促进土地资源的集约利用,重塑城市的空间结构,而且能为城市整体价值的发挥提供重要的理论支撑。     

Modeling fluid flow in a heterogeneous, fault-controlled hydrothermal system

Previous studies have shown that most hydrothermal systems discharging at the land surface are associated with faulting, and that the location, temperature and rate of discharge of these systems are controlled by the geometry and style of the controlling fault(s). Unfortunately, the transport of heat and fluid in fault-controlled hydrothermal systems is difficult to model realistically; although heterogeneity and anisotropy are assumed to place important controls on flow in faults, few data or observations are available to constrain the distribution of hydraulic properties within active faults. Here, analytical and numerical models are combined with geostatistical models of spatially varying hydraulic properties to model the flow of heat and fluid in the Borax Lake fault of south-east Oregon, USA. A geometric mean permeability within the fault of 7 × 10⁻¹⁴ m² with 2× vertical/horizontal anisotropy in correlation length scale is shown to give the closest match to field observations. Furthermore, the simulations demonstrate that continuity of flow paths is an important factor in reproducing the observed behavior. In addition to providing some insight into possible spatial distributions of hydraulic properties at the Borax Lake site, the study highlights one potential avenue for integrating field observations with simulation results in order to gain greater understanding of fluid flow in faults and fault-controlled hydrothermal and petroleum reservoirs.     

A Comparative Study on Ground Motion Attenuation in the 2012 Varzaghan-Ahar Doublet Event,Northwest of Iran

Predictive capabilities of the four updated NGA ground-motion models (NGA-WEST2) are evaluated in this study for acceleration response spectra using observed ground motions for August 11, 2012 Varzaghan-Ahar events in Iran. The predicted results were compared with those of regional attenuation equations and NGA08 models as well. The results of analyses revealed that the models of NGA-WEST2 improve prediction performance of NGA08 models for the two studied moderate events. All of models underestimate the recorded spectra of the second event for regionally significant period of 0.2 s at source distances below 50 km. For this distance range, almost all of the models underestimate the recorded spectra for periods larger than 1 s.     

文物裂隙趋势预测模型研究

露天不可移动文物常年遭受风化侵蚀和人为破坏,保存环境十分恶劣,掌握文物健康状况并进行趋势预测,是"预防性"文物保护工作的重要内容。文物健康监测数据具有不确定性和贫信息性,传统概率统计方法和模糊数学方法不能满足预测要求。针对文物裂隙数据的特点,以陕西唐顺陵天禄石刻为研究对象,提出了采用灰色系统理论来预测文物裂隙发展趋势,建立了裂隙GM((1,1)模型和Verhulst模型,分别确定了灰色模型的灰色作用量和发展系数,并且对唐顺陵石刻文物的裂隙进行了预测。实验用前12个月的裂隙月均值,对随后的7个月的裂隙进行了定量预测,发现天禄石刻的裂隙有缓慢增大的趋势。与同期真实裂隙监测值相比,GM((1,1)模型和Verhulst模型预测值的平均相对误差满足裂隙预测精度要求。研究结果为文物健康趋势研究提供了定量分析的理论依据。     

A Seismic Hazard Study through the Comparison of Ground Motion Prediction Equations Using the Weighting Factor of Logic Tree

Toward the assistance on selection of ground motion prediction models for seismic assessment, this article presents a seismic hazard study (compared to the viewpoint of attenuation equations), using a recent tool based on engineering judgment, called “weighting factor,” through a procedure similar to logic tree. For this purpose, the weighting factors were incorporated with a Venn diagram of attenuation models regarding experimenter’s concern and expert’s knowledge. It is found that the attenuation equations of the newer and intersection ones could be considered to estimate plausible and reasonable accelerations. The results indicate that the weighting factors could beneficially assist for suitability of attenuation models. This work is a novel for the region (Gaziantep, Turkey), thus it could complement expert’s knowledge about the attenuation models for future studies.     

The prediction of physique from the skeleton

This paper attempts to define the relation between (1) human skeletal measurements and (2) height, weight and physique indices. Admitted to the study were 686 men and women from five ethnic groups (White, Inuit, Gurkha, Bantu and San). In addition to height and weight, subjects had defined cranial and postcranial measurements taken using methods derived from clinical examination techniques. Measurements were checked for reliability. Skinfold callipers were used to allow for the thickness of soft‐tissues overlying bone widths. Adjustment factors were derived from radiological gold standards. Radiological measurements, adjusted for magnification, of the lumbar vertebrae from 42 subjects were also done. A correlation matrix was constructed for the complete study population and all variables to allow a preliminary assessment of useful predictive independent variables. Discriminant scores for classification by gender were calculated. Regression computations, using least square regression, were calculated for six defined reference populations. The regression residuals were examined to confirm fulfilment of assumptions. The results indicated that skull and dental arcade variables yield little information about the size and physique of an individual but have some relevance for group comparisons. Long bone widths are moderately and equally correlated with height and weight. Lower limb bone widths are better correlated with body weight than those of the upper limb. The best predictive variables for body weight are the minimal ‘area’ of the lumbar vertebrae (L1–L4) and regressions involving various bone widths. It is confirmed that height correlates well with the lengths of long bones, but the prediction is improved by the addition of a width from the same bone as a second independent variable. Lower limb long bones are not better predictors of height than upper limb ones. The body mass index is best predicted from the available measurements by a regression with the minimal ‘area’ of L1 and the tibial length as independent variables. A lumbar vertebra, particularly L1, yields important information about height, weight and the body mass index. The patella width is, in part, a marker for mesomorphy. Reconstruction of the ankle to enable the width across the malleoli to be measured would yield useful estimates of weight and height. The findings have been applied to the Paviland femur. A provisional male attribution has been made. The derived height is similar to that of tall modern White men. The physique was probably mesomorphic and ectopenic, the physique of strength rather than mobility, but the confidence intervals are very wide. To enable this sort of assessment to be made more confidently, the study requires replication substituting the precision of magnetic resonance imaging for the relative imprecision of skeletal measurements taken directly from the intact body. Copyright © 1999 John Wiley & Sons, Ltd.