Computational Issues in Fitting Spatial Deformation Models for Heterogeneous Spatial Correlation (original) (raw)
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1997
This paper presents the most recent methodological developments for an approachto modelling nonstationary spatial covariance structure through deformations ofthe geographic coordinate system that was first introduced in a technical report 10years ago (Sampson, 1986).We address primarily the problem of estimating the spatial covariance structurein levels of an environmental process at arbitrary locations (both monitored andunmonitored), based on records from N point monitoring sites x 1 ;...
Many environmental processes are heterogeneous in space (spatially non-stationary), due to factors such as topography, local pollutant emissions, and meteorology. Much of the commonly used spatial statistical methodology depends on simplifying assumptions such as spatial isotropy. Violations of these assumptions can cause problems, including incorrect error assessment of spatial estimates. This paper demonstrates important properties of the spatial deformation model of and for heterogeneous anisotropic spatial correlation structure.
20 Methods for estimating heterogeneous spatial covariance functions with environmental applications
Handbook of Statistics, 1994
Estimation of spatial covariance is important to many statistical problems in the analysis of environmental monitoring data. In this Chapter we review several difrerent methods for spati.al covariance estimation from monitoring data, with emphasis on methods for heterogeneous models. We briefly describe some applications, and outline how these methods can be extended to space-time and multivariate models.
How to Model the Covariance Structure in a Spatial Framework: Variogram or Correlation Function?
Data Analysis and Applications 4, 2020
The basic Kriging's model assumes a Gaussian distribution with stationary mean and stationary variance. In such a setting, the joint distribution of the spatial process is characterized by the common variance and the correlation matrix or, equivalently, by the common variance and the variogram matrix. We discuss in in detail the option to actually use the variogram as a parameterization.
Taking account of uncertainty in spatial covariance estimation
1997
In geostatistical analyses, variography and kriging depend crucially on the appropriate modeling of the variogram structure. We propose to model a whole class of plausible variogram functions instead of fitting a single variogram to empirical data and then assuming it to be the true underlying variogram. This way we can take account of various sources of uncertainty arising in variogram modeling and, on the other hand, we may include expert knowledge possibly conflicting with more or less reliable empirical variography. First, we present methods for the specification of a rich and flexible class of plausible variograms using spectral representations. Hereafter, we propose a new kriging method, minimax kriging, in order to find the linear spatial interpolator which minimizes the maximum possible kriging variance with respect to all plausible variograms.
Structuring Complex Correlations: An Overview of Multivariate Spatial Approaches
Multivariate spatial data are increasingly encountered in many disciplines, obvious examples being in geology, ecology, agriculture, epidemiology and in the environmental and atmospheric sciences. The defining feature of such data is the availability of measurements on a set of different and potentially related response variables at each spatial location in the region studied. Often, there is also an associated vector of potential explanatory variables measured at each of these sites. Such multivariate spatial data may exhibit not only correlations between variables at each site, but also spatial autocorrelation within each variable, and spatial cross-correlation between variables, at neighbouring sites. Any analysis or modelling must therefore allow for dependency structures that are both complex and inevitably confounded in the observed data. Moreover, if repeat observations are present on the response vector, they often refer to different points in time and add temporal autocorrelations or cross-correlations into the already complex mix of potential correlation structures.
Spatial models for spatial statistics: some unification
Journal of Vegetation Science, 1993
AbstracL A general statistical framework is proposed for comparing linear models of spatial process and pattern. A spatial linear model for nested analysis of variance can be based on either fixed effects or random effects. originally used a fixed effects model, but there are also examples of random effects models in Lhe soil science literature. Assuming imrinsic stationarity for a linear model, the expectations of a spatial nested ANOVA lllld (wo teon local variance (lTLV, Hill 1973) are funclions of the variogram, and several examples are given. Paired quadrat variance (PQV. Ludwig & Goodall 1978) is a variogram estimator which can be used 10 approximate TIl..V. and we provide an example from ecological data. BOIh nested ANOVA and TILV can be seen as weighted lag-I variogram estimators that are functions of support, rather than distance. We show that there are two unbiased estimators for the variogram under aggregation, and computer simulation shows that the estimator with smaller variance depends on Ihe process autocorrelation.
Analysis of spatial data with a nested correlation structure
Spatial statistical analyses are often used to study the link between environmental factors and the incidence of diseases. In modelling spatial data, the existence of spatial correlation between observations must be considered. However, in many situations, the exact form of the spatial correlation is unknown. This paper studies environmental factors that might influence the incidence of malaria in Afghanistan.We assume that spatial correlation may be induced by multiple latent sources. Our method is based on a generalized estimating equation of the marginal mean of disease incidence, as a function of the geographical factors and the spatial correlation. Instead of using one set of generalized estimating equations, we embed a series of generalized estimating equations, each reflecting a particular source of spatial correlation, into a larger system of estimating equations. To estimate the spatial correlation parameters, we set up a supplementary set of estimating equations based on the correlation structures that are induced from the various sources. Simultaneous estimation of the mean and correlation parameters is performed by alternating between the two systems of equations.