Computationally Efficient Spatial Interpolators Based on Spartan Spatial Random Fields

Hristopulos, Dionissios T.; Elogne, S.N.

doi:10.1109/tsp.2009.2021450

Cited by 30 publications

(24 citation statements)

References 44 publications

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“…Improved representation of local properties also implies more accurate Kriging estimates, since the local properties of the field primarily determine the interpolation performance. For case studies that involve application of the FGC model in spatial interpolation see Hristopulos and Elogne 2009). We propose replacing n byñ ¼ n=A d to compare simulation results between random fields with the same covariance function but different coefficients.…”

Section: Discussionmentioning

confidence: 99%

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Relationships between correlation lengths and integral scales for covariance models with more than two parameters

Hristopulos

Žukovič

2010

Stoch Environ Res Risk Assess

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In geostatistical applications, the terms correlation length and range are often used interchangeably and refer to a characteristic covariance length n that normalizes the lag distance in the variogram or the covariance model. We present equations that strictly define the correlation length (r c ) and integral range (' c ). We derive analytical expressions for r c and ' c of the Whittle-Matérn, fluctuation gradient curvature and rational quadratic covariances. For these covariances, we show that the correlation length and integral range for a given model are not fully determined by n. We define non-trivial covariance functions, and we formulate an ergodicity index based on ' c . We propose using the ergodicity index to compare coarse-grained measures corresponding to non-trivial covariance functions with different parameters. Finally, we discuss potential applications of the proposed covariance models in stochastic subsurface hydrology.

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Section: Discussionmentioning

confidence: 99%

“…Connections between statistical field theories and geostatistics have been explored in a series of recent papers, e.g. (Hristopulos 2003b(Hristopulos , 2006Ž ukovič and Hristopulos 2008;Hristopulos and Elogne 2009).…”

Section: Introductionmentioning

confidence: 99%

Relationships between correlation lengths and integral scales for covariance models with more than two parameters

Hristopulos

Žukovič

2010

Stoch Environ Res Risk Assess

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“…Once the sparse precision matrix has been estimated, a number of efficient tools-mostly based on research in sparse numerical linear algebra-can be used to sample from the distribution, calculate conditional probabilities, calculate conditional statistics, and forecast [2,3]. GMRFs are of great importance in many applications spanning computer vision [4], sparse sensing [5], finance [6][7][8][9][10][11], gene expression [12][13][14]; biological neural networks [15], climate networks [16,17]; geostatistics and spatial statistics [18][19][20]. Almost universally, applications require modeling a large number of variables with a relatively small number of observations, and therefore the issue of the statistical significance of the model parameters is very important.…”

Section: Introductionmentioning

confidence: 99%

Parsimonious modeling with information filtering networks

et al. 2016

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We introduce a methodology to construct parsimonious probabilistic models. This method makes use of information filtering networks to produce a robust estimate of the global sparse inverse covariance from a simple sum of local inverse covariances computed on small subparts of the network. Being based on local and low-dimensional inversions, this method is computationally very efficient and statistically robust, even for the estimation of inverse covariance of high-dimensional, noisy, and short time series. Applied to financial data our method results are computationally more efficient than state-of-the-art methodologies such as Glasso producing, in a fraction of the computation time, models that can have equivalent or better performances but with a sparser inference structure. We also discuss performances with sparse factor models where we notice that relative performances decrease with the number of factors. The local nature of this approach allows us to perform computations in parallel and provides a tool for dynamical adaptation by partial updating when the properties of some variables change without the need of recomputing the whole model. This makes this approach particularly suitable to handle big data sets with large numbers of variables. Examples of practical application for forecasting, stress testing, and risk allocation in financial systems are also provided.

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“…Such data provide (1) frequent spatial estimates of major earth surface variables (Sellers 1997;Garrigues et al 2008) in a longrunning historical time-series; (2) a special resolution that is suitable for investigation of regional landscape changes; and (3) spectral coverage appropriate for studies of vegetation properties (Cohen and Goward 2004;Hayes and Cohen 2007;Tarnavsky et al 2008;Lin et al 2009). Therefore, in the analysis of remote-sensing images, interpolation of the sampled field is useful for contouring, re-sampling, normalizing, classifying, and estimating obscured or missing data (Hristopulos and Elogne 2009). Utilizing spatial interpolation methods to develop early warming systems for natural disasters is another interesting potential application of remote sensing analysis (Hristopulos and Elogne 2009).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, in the analysis of remote-sensing images, interpolation of the sampled field is useful for contouring, re-sampling, normalizing, classifying, and estimating obscured or missing data (Hristopulos and Elogne 2009). Utilizing spatial interpolation methods to develop early warming systems for natural disasters is another interesting potential application of remote sensing analysis (Hristopulos and Elogne 2009). Based on remote-sensing data, the normalized difference vegetation index (NDVI), a widely used vegetation index, is typically utilized to quantify landscape dynamics, including vegetation cover and landslides changes induced by disturbances (Cohen and Goward 2004;Hayes and Cohen 2007;Garrigues et al 2008;Lin et al 2008a).…”

Section: Introductionmentioning

confidence: 99%

Monitoring and identification of spatiotemporal landscape changes in multiple remote sensing images by using a stratified conditional Latin hypercube sampling approach and geostatistical simulation

Lin

Chu

Huang

et al. 2010

Environ Monit Assess

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This study develops a stratified conditional Latin hypercube sampling (scLHS) approach for multiple, remotely sensed, normalized difference vegetation index (NDVI) images. The objective is to sample, monitor, and delineate spatiotemporal landscape changes, including spatial heterogeneity and variability, in a given area. The scLHS approach, which is based on the variance quadtree technique (VQT) and the conditional Latin hypercube sampling (cLHS) method, selects samples in order to delineate landscape changes from multiple NDVI images. The images are then mapped for calibration and validation by using sequential Gaussian simulation (SGS) with the scLHS selected samples. Spatial statistical results indicate that in terms of their statistical distribution, spatial distribution, and spatial variation, the statistics and variograms of the scLHS samples resemble those of multiple NDVI images more closely than those of cLHS and VQT samples. Moreover, the accuracy of simulated NDVI images based on SGS with scLHS samples is significantly better than that of simulated NDVI images based on SGS with cLHS samples and VQT samples, respectively. However, the proposed approach efficiently monitors the spatial characteristics of landscape changes, including the statistics, spatial variability, and heterogeneity of NDVI images. In addition, SGS with the scLHS samples effectively reproduces spatial patterns and landscape changes in multiple NDVI images.

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Computationally Efficient Spatial Interpolators Based on Spartan Spatial Random Fields

Cited by 30 publications

References 44 publications

Relationships between correlation lengths and integral scales for covariance models with more than two parameters

Relationships between correlation lengths and integral scales for covariance models with more than two parameters

Parsimonious modeling with information filtering networks

Monitoring and identification of spatiotemporal landscape changes in multiple remote sensing images by using a stratified conditional Latin hypercube sampling approach and geostatistical simulation

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