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1.
Spatial statistics of clustered data 总被引：7，自引：7，他引：0
Modern spatial statistics techniques are widely used to make predictions for natural processes that are continuously distributed over some convex domain. Implementation of these techniques often relies on the adequate estimation of certain spatial correlation functions such as the covariance and the variogram from the data sets available. This work studies the practical estimation of such spatial correlation functions in the case of clustered data. The coefficient of variation of the dimensionless spatial density of the point pattern of sample locations is suggested as a useful metric for degree of clusteredness of the clustered data set. We show that the common variogram estimator becomes increasingly unreliable with increasing coefficient of variation of the dimensionless spatial density of the point pattern of sample locations. Moreover, we present a modified form of the variogram estimator that incorporates declustering weights, and propose a scheme for estimating the declustering weights based on zones of proximity. Finally, insight is gained in terms of a numerical application of the common and modified methods on piezometric head data collected over an irregular network.Acknowledgments. This work has been supported by grants from the National Institute of Environmental Health Sciences (P42 ES05948-02), the Army Research Office (DAAG55-98-1-0289), and the National Aeronautics and Space Administration (60-00RFQ041). Some of the calculations conducted in support of this work were done on the SGI Origin 2400 at the North Carolina Supercomputing Center, RTP, NC. 相似文献
2.
Precise estimation of covariance parameters in least-squares collocation by restricted maximum likelihood 总被引：1，自引：0，他引：1
Precise estimates of the covariance parameters are essential in least-squares collocation (LSC) in the case of increased accuracy requirements. This paper implements restricted maximum likelihood (REML) method for the estimation of three covariance parameters in LSC with the Gauss-Markov second-order function (GM2), which is often used in interpolation of gravity anomalies. The estimates are then validated with the use of an independent technique, which has been often omitted in the previous works that are confined to covariance parameters errors based on the information matrix. The crossvalidation of REML estimates with the use of hold-out method (HO) helps in understanding of REML estimation errors. We analyzed in detail the global minimum of negative log-likelihood function (NLLF) in the estimation of covariance parameters, as well, as the accuracy of the estimates. We found that the correlation between covariance parameters may critically contribute to the errors of their estimation. It was also found that knowing some intrinsic properties of the covariance function may help in the scoring process. 相似文献
3.
Z. T. Yucel R. H. Shumway 《Stochastic Environmental Research and Risk Assessment (SERRA)》1996,10(2):107-126
This paper is concerned with developing computational methods and approximations for maximum likelihood estimation and minimum mean square error smoothing of irregularly observed two-dimensional stationary spatial processes. The approximations are based on various Fourier expansions of the covariance function of the spatial process, expressed in terms of the inverse discrete Fourier transform of the spectral density function of the underlying spatial process. We assume that the underlying spatial process is governed by elliptic stochastic partial differential equations (SPDE's) driven by a Gaussian white noise process. SPDE's have often been used to model the underlying physical phenomenon and the elliptic SPDE's are generally associated with steady-state problems.A central problem in estimation of underlying model parameters is to identify the covariance function of the process. The cumbersome exact analytical calculation of the covariance function by inverting the spectral density function of the process, has commonly been used in the literature. The present work develops various Fourier approximations for the covariance function of the underlying process which are in easily computable form and allow easy application of Newton-type algorithms for maximum likelihood estimation of the model parameters. This work also develops an iterative search algorithm which combines the Gauss-Newton algorithm and a type of generalized expectation-maximization (EM) algorithm, namely expectation-conditional maximization (ECM) algorithm, for maximum likelihood estimation of the parameters.We analyze the accuracy of the covariance function approximations for the spatial autoregressive-moving average (ARMA) models analyzed in Vecchia (1988) and illustrate the performance of our iterative search algorithm in obtaining the maximum likelihood estimation of the model parameters on simulated and actual data. 相似文献
4.
Recent developments of 30 m global land characterization datasets(e.g., land cover, vegetation continues field) represent the finest spatial resolution inputs for global scale studies. Here, we present results from further improvement to land cover mapping and impact analysis of spatial resolution on area estimation for different land cover types. We proposed a set of methods to aggregate two existing 30 m resolution circa 2010 global land cover maps, namely FROM-GLC(Finer Resolution Observation and Monitoring-Global Land Cover) and FROM-GLC-seg(Segmentation), with two coarser resolution global maps on development, i.e., Nighttime Light Impervious Surface Area(NL-ISA) and MODIS urban extent(MODIS-urban), to produce an improved 30 m global land cover map—FROM-GLC-agg(Aggregation). It was post-processed using additional coarse resolution datasets(i.e., MCD12Q1, GlobCover2009, MOD44 W etc.) to reduce land cover type confusion. Around 98.9% pixels remain 30 m resolution after some post-processing to this dataset. Based on this map, majority aggregation and proportion aggregation approaches were employed to create a multi-resolution hierarchy(i.e., 250 m, 500 m, 1 km, 5 km, 10 km, 25 km, 50 km, 100 km) of land cover maps to meet requirements for different resolutions from different applications. Through accuracy assessment, we found that the best overall accuracies for the post-processed base map(at 30 m) and the three maps subsequently aggregated at 250 m, 500 m, 1 km resolutions are 69.50%, 76.65%, 74.65%, and 73.47%, respectively. Our analysis of area-estimation biases for different land cover types at different resolutions suggests that maps at coarser than 5 km resolution contain at least 5% area estimation error for most land cover types. Proportion layers, which contain precise information on land cover percentage, are suggested for use when coarser resolution land cover data are required. 相似文献
5.
New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity 总被引：2，自引：0，他引：2
Many heterogeneous media and environmental processes are statistically anisotropic. In this paper we focus on range anisotropy,
that is, stochastic processes with variograms that have direction dependent correlation lengths and direction independent
sill. We distinguish between two classes of anisotropic covariance models: Class (A) models are reducible to isotropic after
rotation and rescaling operations. Class (B) models can be separated into a product of one-dimensional functions oriented
along the principal axes. We propose a new Class (A) model with multiscale properties that has applications in subsurface
hydrology. We also present a family of Class (B) models based on non-Euclidean distance metrics that are generated by superellipsoidal
functions. Next, we propose a new method for determining the orientation of the principal axes and the degree of anisotropy,
i.e., the ratio(s) of the correlation lengths. This information reduces the degrees of freedom of anisotropic variograms and
thus simplifies the estimation procedure. In particular, Class (A) models are reduced to isotropic and Class (B) models to
one-dimensional functions. Our method is based on an explicit relation between the second-rank slope tensor (SRST), which
can be estimated from the data, and the covariance tensor. The procedure is conceptually simple and numerically efficient.
It is more accurate for regular (on-grid) data distributions, but it can also be used for sparse (off-grid) spatial distributions.
In the case of non-differentiable random fields the method can be extended using generalized derivatives. We illustrate its
implementation with numerical simulations. 相似文献
6.
G. Christakos V. Papanicolaou 《Stochastic Environmental Research and Risk Assessment (SERRA)》2000,14(6):471-478
Permissibility of a covariance function (in the sense of Bochner) depends on the norm (or metric) that determines spatial
distance in several dimensions. A covariance function that is permissible for one norm may not be so for another. We prove
that for a certain class of covariances of weakly homogeneous random fields, the spatial distance can be defined only in terms
of the Euclidean norm. This class includes commonly used covariance functions. Functions that do not belong to this class
may be permissible covariances for some non-Euclidean metric. Thus, a different class of covariances, for which non-Euclidean
norms are valid spatial distances, is also discussed. The choice of a coordinate system and associated norm to describe a
physical phenomenon depends on the nature of the properties being described. Norm-dependent permissibility analysis has important
consequences in spatial statistics applications (e.g., spatial estimation or mapping), in which one is concerned about the
validity of covariance functions associated with a physically meaningful norm (Euclidean or non-Euclidean). 相似文献
7.
J. A. Vargas-Guzmán T.-C. Jim Yeh 《Stochastic Environmental Research and Risk Assessment (SERRA)》1999,13(6):416-435
A sequential linear estimator is developed in this study to progressively incorporate new or different spatial data sets
into the estimation. It begins with a classical linear estimator (i.e., kriging or cokriging) to estimate means conditioned
to a given observed data set. When an additional data set becomes available, the sequential estimator improves the previous
estimate by using linearly weighted sums of differences between the new data set and previous estimates at sample locations.
Like the classical linear estimator, the weights used in the sequential linear estimator are derived from a system of equations
that contains covariances and cross-covariances between sample locations and the location where the estimate is to be made.
However, the covariances and cross-covariances are conditioned upon the previous data sets.
The sequential estimator is shown to produce the best, unbiased linear estimate, and to provide the same estimates and variances
as classic simple kriging or cokriging with the simultaneous use of the entire data set. However, by using data sets sequentially,
this new algorithm alleviates numerical difficulties associated with the classical kriging or cokriging techniques when a
large amount of data are used. It also provides a new way to incorporate additional information into a previous estimation. 相似文献
8.
《水文科学杂志》2013,58(2)
Abstract Methods were evaluated for interpolating precipitation (P), evapotranspiration (ET), and runoff (RO) at ungauged points on Shikoku Island, Japan, using data gathered from gauged stations on the same island. Two methods were examined: a “local” cubic spline interpolator, which, for a given point, fitted the function exactly to nearby gauged data points; and a “global” multivariate regression interpolator, which fitted the function to all gauged data points based on their topographic positions (i.e. latitude, longitude, altitude). Local and global interpolators did not generate similar results for P and temperature (T). The spatial density of gauged data points used in the interpolation affected the performance of the interpolators. With any given density of gauged data points included in the interpolation, the local interpolator outperformed the global interpolator. The findings indicate that local interpolators are more accurate predictors of the spatial distribution of water balance components in mountainous regions such as Shikoku Island. 相似文献
9.
《Journal of Atmospheric and Solar》1999,61(6):505-517
In Part 1 of this work (Akmaev, 1999), an overview of the theory of optimal interpolation (OI) (Gandin, 1963) and related techniques of data assimilation based on linear optimal estimation (Liebelt, 1967; Catlin, 1989; Mendel, 1995) is presented. The approach implies the use in data analysis of additional statistical information in the form of statistical moments, e.g., the mean and covariance (correlation). The a priori statistical characteristics, if available, make it possible to constrain expected errors and obtain optimal in some sense estimates of the true state from a set of observations in a given domain in space and/or time. The primary objective of OI is to provide estimates away from the observations, i.e., to fill in data voids in the domain under consideration. Additionally, OI performs smoothing suppressing the noise, i.e., the spectral components that are presumably not present in the true signal. Usually, the criterion of optimality is minimum variance of the expected errors and the whole approach may be considered constrained least squares or least squares with a priori information. Obviously, data assimilation techniques capable of incorporating any additional information are potentially superior to techniques that have no access to such information as, for example, the conventional least squares (e.g., Liebelt, 1967; Weisberg, 1985; Press et al., 1992; Mendel, 1995). 相似文献
10.
Estimating threshold-exceeding probability maps of environmental variables with Markov chain random fields 总被引：2，自引：2，他引：0
Weidong Li Chuanrong Zhang Dipak K. Dey Shanqin Wang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(8):1113-1126
Estimating and mapping spatial uncertainty of environmental variables is crucial for environmental evaluation and decision
making. For a continuous spatial variable, estimation of spatial uncertainty may be conducted in the form of estimating the
probability of (not) exceeding a threshold value. In this paper, we introduced a Markov chain geostatistical approach for
estimating threshold-exceeding probabilities. The differences of this approach compared to the conventional indicator approach
lie with its nonlinear estimators—Markov chain random field models and its incorporation of interclass dependencies through
transiograms. We estimated threshold-exceeding probability maps of clay layer thickness through simulation (i.e., using a
number of realizations simulated by Markov chain sequential simulation) and interpolation (i.e., direct conditional probability
estimation using only the indicator values of sample data), respectively. To evaluate the approach, we also estimated those
probability maps using sequential indicator simulation and indicator kriging interpolation. Our results show that (i) the
Markov chain approach provides an effective alternative for spatial uncertainty assessment of environmental spatial variables
and the probability maps from this approach are more reasonable than those from conventional indicator geostatistics, and
(ii) the probability maps estimated through sequential simulation are more realistic than those through interpolation because
the latter display some uneven transitions caused by spatial structures of the sample data. 相似文献
11.
J. Sénégas H. Wackernagel W. Rosenthal T. Wolf 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(1):65-86
The efficiency of a sequential data assimilation scheme relies on the capability to describe the error covariance. This aspect
is all the more relevant if one needs accurate statistics on the estimation error. Frequently an ad hoc function depending
on a few parameters is proposed, and these parameters are tuned, estimated or updated. This usually requires that the covariance
is second-order stationary (i.e. depends only on the distance between two points). In this paper, we discuss this feature
and show that even in simple applications (such as one-dimensional hydrodynamics), this assumption does not hold and may lead
to poorly described estimation errors. We propose a method relying on the analysis of the error term and the use of the hydrodynamical
model to generate one part of the covariance function, the other part being modeled using a second-order stationary approach.
This method is discussed using a twin experiment in the case where a physical parameter is erroneous, and improves significantly
the results: the model bias is strongly reduced and the estimation error is well described. Moreover, it enables a better
adaptation of the Kalman gain to the actual estimation error. 相似文献
12.
Compositional Bayesian indicator estimation 总被引：1，自引：1，他引：0
Carolina Guardiola-Albert Eulogio Pardo-Ig��zquiza 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(6):835-849
Indicator kriging is widely used for mapping spatial binary variables and for estimating the global and local spatial distributions
of variables in geosciences. For continuous random variables, indicator kriging gives an estimate of the cumulative distribution
function, for a given threshold, which is then the estimate of a probability. Like any other kriging procedure, indicator
kriging provides an estimation variance that, although not often used in applications, should be taken into account as it
assesses the uncertainty of the estimate. An alternative approach to indicator estimation is proposed in this paper. In this
alternative approach the complete probability density function of the indicator estimate is evaluated. The procedure is described
in a Bayesian framework, using a multivariate Gaussian likelihood and an a priori distribution which are both combined according
to Bayes theorem in order to obtain a posterior distribution for the indicator estimate. From this posterior distribution,
point estimates, interval estimates and uncertainty measures can be obtained. Among the point estimates, the median of the
posterior distribution is the maximum entropy estimate because there is a fifty-fifty chance of the unknown value of the estimate
being larger or smaller than the median; that is, there is maximum uncertainty in the choice between two alternatives. Thus
in some sense, the latter is an indicator estimator, alternative to the kriging estimator, that includes its own uncertainty.
On the other hand, the mode of the posterior distribution estimator, assuming a uniform prior, is coincidental with the simple
kriging estimator. Additionally, because the indicator estimate can be considered as a two-part composition which domain of
definition is the simplex, the method is extended to compositional Bayesian indicator estimation. Bayesian indicator estimation
and compositional Bayesian indicator estimation are illustrated with an environmental case study in which the probability
of the content of a geochemical element in soil being over a particular threshold is of interest. The computer codes and its
user guides are public domain and freely available. 相似文献
13.
This study investigates the correlation properties of integral ground-motion intensity measures (IMs) from Italian strong-motion records. The considered integral IMs include 5–95% significant duration, Housner intensity, cumulative absolute velocity, and Arias intensity. Both IM spatial correlation and the correlation between different integral and amplitude-based IMs (i.e., cross-IM correlation) are addressed in this study. To this aim, a new Italian ground-motion model (GMM) with spatial correlation for integral IMs is first introduced. Based on the newly developed GMM, the empirical correlation coefficients from interevent and intraevent residuals are investigated and various analytical correlation models between integral IMs and amplitude-based IMs are proposed. The effective range parameter representing spatial correlation properties and the trend in the cross-IM correlations are compared with existing models in the literature. The variability of the effective range parameters with respect to event-specific features is also discussed. Modeling ground-motion spatial and cross-IM correlations is an important step in seismic hazard and risk assessment of spatially distributed systems. Investigating region-specific correlation properties based on Italian strong-motion records is of special interest as several correlation models have been developed based on global datasets, often lacking earthquakes in extensional regions such as Italy. 相似文献
14.
Goodness-of-fit tests for the spatial spectral density 总被引：1，自引：1，他引：0
Rosa M. Crujeiras Rubén Fernández-Casal Wenceslao González-Manteiga 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(1):67-79
Detection and modeling the spatial correlation is an important issue in spatial data analysis. We extend in this work two
different goodness-of-fit testing techniques for the spatial spectral density. The first approach is based on a smoothed version
of the ratio between the periodogram and a parametric estimator of the spectral density. The second one is a generalized likelihood
ratio test statistic, based on the log-periodogram representation as the response variable in a regression model. As a particular
case, we provide tests for independence. Asymptotic normal distribution of both statistics is obtained, under the null hypothesis.
For the application in practice, a resampling procedure for calibrating these tests is also given. The performance of the
method is checked by a simulation study. Application to real data is also provided. 相似文献
15.
A latent class MDS model with spatial constraints for non-stationary spatial covariance estimation 总被引：3，自引：3，他引：0
J. F. Vera R. Macías J. M. Angulo 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(6):769-779
Multidimensional scaling (MDS) has played an important role in non-stationary spatial covariance structure estimation and
in analyzing the spatiotemporal processes underlying environmental studies. A combined cluster-MDS model, including geographical
spatial constraints, has been previously proposed by the authors to address the estimation problem in oversampled domains
in a least squares framework. In this paper is formulated a general latent class model with spatial constraints that, in a
maximum likelihood framework, allows to partition the sample stations into classes and simultaneously to represent the cluster
centers in a low-dimensional space, while the stations and clusters retain their spatial relationships. A model selection
strategy is proposed to determine the number of latent classes and the dimensionality of the problem. Real and artificial
data sets are analyzed to test the performance of the model. 相似文献
16.
— Velocity evaluation is a key step in seismic analysis. The covariance of the true velocity field must be known when interpolating or simulating velocities from well measurements using geostatistical methods. In addition, inversion procedures often require information pertaining to this covariance. Traditionally it has been taken to be the covariance of stacking velocities. We present a simple example to show that this approximation can lead to significant errors. Better methods, such as those of Touati (1996) and Iooss (1998), use the variance of prestack picked travel times as a function of offset to infer that of the velocities. In this paper we extend their results on the estimation of the covariance of the reflected traveltimes, and obtain an explicit expression for the covariance of the square of the stacking slowness as a function of the covariance of the velocities. Although we are not able to invert the formula analytically to yield an explicit estimator for these parameters, the results obtained using it furnish a good and quick estimation of the velocity's covariance. This is illustrated with synthetic examples. 相似文献
17.
A procedure is proposed for geochemical mapping of the water area bottom based on the subdivision of raw data into two components, i.e., systematic (regional) and random (local). The former is used to determine regional characteristic of the spatial radionuclide distributions in bottom sediments to be utilized to identify large radiogeochemical regions, while the latter is used to identify local anomalies and evaluate their characteristics. The systematic component of the radiogeochemical field is determined by trend analysis. Next, cluster analysis, i.e., hierarchic clusterization of the results of trend analysis followed by associative classification, is used for radiochemical zoning of the water area. After that, maps are constructed, showing contour lines of the local component of radiogeochemical fields, represented by deviations of the value in the given point from the trend. The result is a single map showing the radiogeochemical regions with contour lines of normalized anomalous activities of the radionuclides under study. The practical application of the method is illustrated by radiogeochemical mapping of the bed in the Eastern Gulf of Finland. 相似文献
18.
An empirical predictive relationship correlating significant duration to earthquake magnitude, site-to-source distance, and local site conditions (i.e., rock vs. stiff soil) for stable continental regions is presented herein. The correlations were developed from data derived from 620 horizontal motions for stable continental regions (e.g., central and eastern North America: CENA), consisting of 28 recorded motions and 592 scaled motions. The data set encompasses the earthquake magnitude from 4.5 to 7.6 and the distance from 0.1 to 199 km. The non-linear mixed-effects regression technique was used to fit a predictive model to the significant duration data. Similar to the trend observed from active shallow crustal region motions, significant durations predicted for stable continental region motions increased with increasing earthquake magnitude and increasing site-to-source distance. In comparing the predicted durations for CENA motions with those for motions from active shallow crustal regions (e.g., western North America: WNA), it is shown that the differences in significant durations for the two regions are relatively minor for site-to-source distances less than about 100 km. Lastly, the significant durations predicted by the proposed model are shown to be in good agreement with durations of the motions recorded during the Mineral, Virginia earthquake of August 23, 2011. 相似文献
19.
We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic
conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters
through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived
using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from
the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly
dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated
or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content
measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions. 相似文献
20.
Debra L. Hughson T.-C. Jim Yeh 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(5):285-298
We present a geostatistically based inverse model for characterizing heterogeneity in parameters of unsaturated hydraulic
conductivity for three-dimensional flow. Pressure and moisture content are related to perturbations in hydraulic parameters
through cross-covariances, which are calculated to first-order. Sensitivities needed for covariance calculations are derived
using the adjoint state sensitivity method. Approximations of the conditional mean parameter fields are then obtained from
the cokriging estimator. Correlation between parameters and pressure – moisture content perturbations is seen to be strongly
dependent on mean pressure or moisture content. High correlation between parameters and pressure data was obtained under saturated
or near saturated flow conditions, providing accurate estimation of saturated hydraulic conductivity, while moisture content
measurements provided accurate estimation of the pore size distribution parameter under unsaturated flow conditions. 相似文献