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Areal Data (areal + data)

Distribution by Scientific Domains
Mathematics and Statistics42%

Selected Abstracts

Geostatistical Prediction and Simulation of Point Values from Areal Data

GEOGRAPHICAL ANALYSIS, Issue 2 2005
Phaedon C. Kyriakidis
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. [source]

Generalized Hierarchical Multivariate CAR Models for Areal Data

BIOMETRICS, Issue 4 2005
Xiaoping Jin
Summary In the fields of medicine and public health, a common application of areal data models is the study of geographical patterns of disease. When we have several measurements recorded at each spatial location (for example, information on p, 2 diseases from the same population groups or regions), we need to consider multivariate areal data models in order to handle the dependence among the multivariate components as well as the spatial dependence between sites. In this article, we propose a flexible new class of generalized multivariate conditionally autoregressive (GMCAR) models for areal data, and show how it enriches the MCAR class. Our approach differs from earlier ones in that it directly specifies the joint distribution for a multivariate Markov random field (MRF) through the specification of simpler conditional and marginal models. This in turn leads to a significant reduction in the computational burden in hierarchical spatial random effect modeling, where posterior summaries are computed using Markov chain Monte Carlo (MCMC). We compare our approach with existing MCAR models in the literature via simulation, using average mean square error (AMSE) and a convenient hierarchical model selection criterion, the deviance information criterion (DIC; Spiegelhalter et al., 2002, Journal of the Royal Statistical Society, Series B64, 583,639). Finally, we offer a real-data application of our proposed GMCAR approach that models lung and esophagus cancer death rates during 1991,1998 in Minnesota counties. [source]

Statistics for spatial functional data: some recent contributions

ENVIRONMETRICS, Issue 3-4 2010
P. Delicado
Abstract Functional data analysis (FDA) is a relatively new branch in statistics. Experiments where a complete function is observed for each individual give rise to functional data. In this work we focus on the case of functional data presenting spatial dependence. The three classic types of spatial data structures (geostatistical data, point patterns, and areal data) can be combined with functional data as it is shown in the examples of each situation provided here. We also review some contributions in the literature on spatial functional data. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Geostatistical Prediction and Simulation of Point Values from Areal Data

GEOGRAPHICAL ANALYSIS, Issue 2 2005
Phaedon C. Kyriakidis
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. [source]

Remotely sensed data used for modelling at different hydrological scales

HYDROLOGICAL PROCESSES, Issue 8 2002
Peter Droogers
Abstract There is a growing awareness that water will be one of the most critical natural resources and that there is a need for better management of the limited water resources. This paper reports on a study of a water-scarce river basin in western Turkey. Hydrological analyses, emphasizing water use for irrigation, are performed at three different spatial scales (field scale, irrigation scheme scale and basin scale) using two kind of model: a parametric basin-scale model and a physically based crop-scale model. Data accessibility for this basin, especially for areal data, was low. A combined use of public domain data sets and remotely sensed data was used to solve this problem. A public domain digital elevation model was used to generate the streamflow network and the distances and slopes to streams. Land-cover data and leaf area index data were derived from public domain NOAA,AVHRR images. For one irrigation scheme in the basin, detailed areal water balances were obtained from the simulation model and a comparison was made between a normal and a water-short year. At the basin scale, observed flows were compared with simulated flows. It is concluded that remotely sensed data and other public domain data can be used with simulation models at different scales to create a powerful tool to evaluate water resources in a basin context. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Generalized Hierarchical Multivariate CAR Models for Areal Data

BIOMETRICS, Issue 4 2005
Xiaoping Jin
Summary In the fields of medicine and public health, a common application of areal data models is the study of geographical patterns of disease. When we have several measurements recorded at each spatial location (for example, information on p, 2 diseases from the same population groups or regions), we need to consider multivariate areal data models in order to handle the dependence among the multivariate components as well as the spatial dependence between sites. In this article, we propose a flexible new class of generalized multivariate conditionally autoregressive (GMCAR) models for areal data, and show how it enriches the MCAR class. Our approach differs from earlier ones in that it directly specifies the joint distribution for a multivariate Markov random field (MRF) through the specification of simpler conditional and marginal models. This in turn leads to a significant reduction in the computational burden in hierarchical spatial random effect modeling, where posterior summaries are computed using Markov chain Monte Carlo (MCMC). We compare our approach with existing MCAR models in the literature via simulation, using average mean square error (AMSE) and a convenient hierarchical model selection criterion, the deviance information criterion (DIC; Spiegelhalter et al., 2002, Journal of the Royal Statistical Society, Series B64, 583,639). Finally, we offer a real-data application of our proposed GMCAR approach that models lung and esophagus cancer death rates during 1991,1998 in Minnesota counties. [source]