Dynamic multi-resolution spatial models

Johannesson, Gardar; Cressie, Noel; Huang, Hsin‐Cheng

doi:10.1007/s10651-006-0005-9

Cited by 49 publications

(32 citation statements)

References 37 publications

(37 reference statements)

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“…This problem becomes even more profound when the data is collected in an ongoing manner. On the other hand, the spatio-temporal character of this remotely sensed data makes it suitable for application of dynamic multi-resolution spatial models [3] to estimate the missing data necessary for highresolution modeling and tracking of GHG emissions.…”

Section: Inference Methodsmentioning

confidence: 99%

“…This can be accomplished by making the distributions at the coarsest resolution change with time, forcing the distributions at higher resolutions to change as well [3]. Once dynamic factors are taken into account at the coarse resolution, predictions are made working down the tree structure, from the coarse resolution back to the finest resolution.…”

Section: Overviewmentioning

confidence: 99%

“…where Bj+1 is obtained from (3). Predictions are also made of the this coarse cell's variance based on one child…”

Section: Uptree Filteringmentioning

confidence: 99%

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Estimation of missing data points from remotely sensed datasets

Rodway

Musilek

2010

Ccece 2010

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This paper presents a method for estimation of missing data points in satellite measurements of CO2 concentrations. The spatiotemporal character of the data allows application of dynamic multiresolution spatial models, to obtain such estimates in an efficient way. Development of the model is described in detail, starting with its static variant that is later extended to use time series for further improvement of estimation accuracy. Static estimates have been tested using both synthetic and real satellite data, and compared to a simple prediction method. The presented results show that the developed model provides modest accuracy gains over the basic estimation method. Preliminary testing of the dynamic model shows the added value of including the time-shifted data in the estimation procedure, although a more rigorous quantification of the improvement still needs to be performed.

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Section: Inference Methodsmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

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Estimation of missing data points from remotely sensed datasets

Rodway

Musilek

2010

Ccece 2010

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“…One approach is to use covariance tapering [25,26], in which the correct covariance matrix is tapered using an appropriately chosen compactly supported radial basis function which results in a sparse approximation of the covariance matrix that can be solved using sparse matrix algorithms. Another approach is to choose classes of covariance functions for which kriging can be done exactly using a multiresolution spatial process [27][28][29]. Other approaches include fixed rank kriging [30] Before we proceed, we would like to clarify the notations.…”

Section: Introductionmentioning

confidence: 99%

Application of Hierarchical Matrices to Linear Inverse Problems in Geostatistics

Saibaba

Ambikasaran

et al. 2012

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Nous commençons par décrire brièvement l'approche géostatistique dans le contexte d'un problème inverse linéaire, puis discutons les difficultés rencontrées dans le cadre d'une implémentation à grande échelle. Ensuite, en utilisant une approche basée sur les matrices hiérarchiques, nous montrons comment réduire le coût de calcul d'un produit matrice-vecteur de O(m 2 ) à O(m log m) dans le cas de matrices de covariance denses ; m désignant ici le nombre d'inconnues. Combinée avec un solveur de Krylov, qui ne requiert pas la construction explicite de la matrice, cette méthode conduit à un algorithme beaucoup plus rapide pour résoudre le système d'équations associé à l'approche géostatistique. Nous illustrons enfin la performance de notre algorithme dans un situation spécifique, surveiller la concentration de CO 2 à l'aide de la tomographie sismique entre puits. Abstract -Application of Hierarchical Matrices to Linear Inverse Problems in Geostatistics -Characterizing the uncertainty in the subsurface is an important step for exploration and extraction of natural resources, the storage of nuclear material and gasses such as natural gas or CO 2 . Imaging the subsurface can be posed as an inverse problem and can be solved using the geostatistical approach [Kitanidis P.K. (2007) Geophys. Monogr. Ser. 171, 19-30, doi:10.1029/171GM04;Kitanidis (2011 Kitanidis ( ) doi: 10.1002

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“…Their structure allows accommodation of nonstationarities in the data and often permits fast computations, making them attractive for handling many large sets of data arising in practical situations, particularly in spatial and spatio-temporal contexts. See, for example, Huang et al (2002), Johannesson et al (2007), Patil and Taillie (2001) and references therein.…”

Section: Introductionmentioning

confidence: 99%

Inference on fractal processes using multiresolution approximation

Falconer

Fernández

2007

Biometrika

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We consider Bayesian inference via Markov chain Monte Carlo (MCMC) for a variety of fractal Gaussian processes on the real line. These models have unknown parameters in the covariance matrix, requiring inversion of a new covariance matrix at each MCMC iteration.The processes have no suitable independence properties so this becomes computationally prohibitive. We surmount these difficulties by developing a computational algorithm for likelihood evaluation based on a 'multiresolution approximation' to the original process. The method is computationally very efficient and widely applicable, making likelihood-based inference feasible for large datasets. A simulation study indicates that this approach leads to accurate estimates for underlying parameters in fractal models, including functional parameters in the recently introduced multifractional Brownian motion. We apply the method to a variety of real data sets and illustrate its application to prediction and to model selection.

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Dynamic multi-resolution spatial models

Cited by 49 publications

References 37 publications

Estimation of missing data points from remotely sensed datasets

Estimation of missing data points from remotely sensed datasets

Application of Hierarchical Matrices to Linear Inverse Problems in Geostatistics

Inference on fractal processes using multiresolution approximation

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