Second-order non-stationary modeling approaches for univariate geostatistical data

Fouedjio, Francky

doi:10.1007/s00477-016-1274-y

Cited by 39 publications

(21 citation statements)

References 86 publications

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“…Moreover, the features of the domain may even prevent the definition of a globally stationary model. Several approaches exist to handle non-stationary spatial fields (see Fouedjio, 2017, for a recent review). Of particular interest for the scope of this work are the methods based on local models which describe spatial dependence only within subregions of the spatial domain, where stationarity is taken to be a viable assumption (e.g., Fuentes, 2001Fuentes, , 2002Fouedjio et al, 2016;Heaton et al, 2015;Haas, 1990;Harris et al, 2010;.…”

Section: Introductionmentioning

confidence: 99%

Random domain decompositions for object-oriented Kriging over complex domains

Menafoglio

Gaetani

Secchi

2018

Stoch Environ Res Risk Assess

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We propose a new methodology for the analysis of spatial fields of object data distributed over complex domains. Our approach enables to jointly handle both data and domain complexities, through a divide et impera approach. As a key element of innovation, we propose to use a Random Domain Decomposition, whose realizations define sets of homogeneous sub-regions where to perform simple, independent, weak local analyses (divide), eventually aggregated into a final strong one (impera). In this broad framework, the complexity of the domain (e.g., strong concavities, holes or barriers) can be accounted for by defining its partitions on the basis of a suitable metric, which allows to properly represent the adjacency relationships among the complex data (such as scalar, functional or constrained data) over the domain. As an insightful illustration of the potential of the methodology, we consider the analysis and spatial prediction (Kriging) of the probability density function of dissolved oxygen in the Chesapeake Bay.

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Section: Introductionmentioning

confidence: 99%

Random domain decompositions for object-oriented Kriging over complex domains

Menafoglio

Gaetani

Secchi

2018

Stoch Environ Res Risk Assess

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“…It has been widely recognized that most processes manifest a spatially non-stationary covariance structure (Sampson, 2014). If the study domain is small in area or there is not enough data to justify more complicated non-stationary approaches, then stationarity may be assumed for the sake of mathematical convenience (Fouedjio, 2017). However, relationships between variables can vary significantly over space, and a 'global' estimate of the relationships may obscure interesting geographical phenomena (Brunsdon et al, 1996;Fouedjio, 2017;Sampson & Guttorp, 1992).…”

Section: Partitioned Geostatistical Models For Spatial and Spatio-temporal Datamentioning

confidence: 99%

“…If the study domain is small in area or there is not enough data to justify more complicated non-stationary approaches, then stationarity may be assumed for the sake of mathematical convenience (Fouedjio, 2017). However, relationships between variables can vary significantly over space, and a 'global' estimate of the relationships may obscure interesting geographical phenomena (Brunsdon et al, 1996;Fouedjio, 2017;Sampson & Guttorp, 1992). In Section 1.2 we described why it is important to carefully consider non-stationarity when estimating and making predictions from a modelled spatial or spatio-temporal process.…”

Section: Partitioned Geostatistical Models For Spatial and Spatio-temporal Datamentioning

confidence: 99%

Spatio-temporal modelling for non-stationary point referenced data

Morris¹

2021

Preprint

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Spatial and spatio-temporal phenomena are commonly modelled as Gaussian processes via the geostatistical model (Gelfand & Banerjee, 2017). In the geostatistical model the spatial dependence structure is modelled using covariance functions. Most commonly, the covariance functions impose an assumption of spatial stationarity on the process. That means the covariance between observations at particular locations depends only on the distance between the locations (Banerjee et al., 2014). It has been widely recognized that most, if not all, processes manifest spatially nonstationary covariance structure Sampson (2014). If the study domain is small in area or there is not enough data to justify more complicated nonstationary approaches, then stationarity may be assumed for the sake of mathematical convenience (Fouedjio, 2017). However, relationships between variables can vary significantly over space, and a ‘global’ estimate of the relationships may obscure interesting geographical phenomena (Brunsdon et al., 1996; Fouedjio, 2017; Sampson & Guttorp, 1992). In this thesis, we considered three non-parametric approaches to flexibly account for non-stationarity in both spatial and spatio-temporal processes. First, we proposed partitioning the spatial domain into sub-regions using the K-means clustering algorithm based on a set of appropriate geographic features. This allowed for fitting separate stationary covariance functions to the smaller sub-regions to account for local differences in covariance across the study region. Secondly, we extended the concept of covariance network regression to model the covariance matrix of both spatial and spatio-temporal processes. The resulting covariance estimates were found to be more flexible in accounting for spatial autocorrelation than standard stationary approaches. The third approach involved geographic random forest methodology using a neighbourhood structure for each location constructed through clustering. We found that clustering based on geographic measures such as longitude and latitude ensured that observations that were too far away to have any influence on the observations near the locations where a local random forest was fitted were not selected to form the neighbourhood. In addition to developing flexible methods to account for non-stationarity, we developed a pivotal discrepancy measure approach for goodness-of-fit testing of spatio-temporal geostatistical models. We found that partitioning the pivotal discrepancy measures increased the power of the test.

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“…Note that most of the existing clustering algorithms aim at clustering spatial observations based on similarity of the mean values. Furthermore, spatial processes from real applications are often second-order nonstationary (Fouedjio, 2017a;Schmidt and Guttorp, 2020).…”

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confidence: 99%

Collective spectral density estimation and clustering for spatially-correlated data

2020

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In this paper, we develop a method for estimating and clustering two-dimensional spectral density functions (2D-SDFs) for spatial data from multiple subregions. We use a common set of adaptive basis functions to explain the similarities among the 2D-SDFs in a low-dimensional space and estimate the basis coefficients by maximizing the Whittle likelihood with two penalties. We apply these penalties to impose the smoothness of the estimated 2D-SDFs and the spatial dependence of the spatially-correlated subregions. The proposed technique provides a score matrix, that is comprised of the estimated coefficients associated with the common set of basis functions representing the 2D-SDFs. Instead of clustering the estimated SDFs directly, we propose to employ the score matrix for clustering purposes, taking advantage of its low-dimensional property. In a simulation study, we demonstrate that our proposed method outperforms other competing estimation procedures used for clustering. Finally, to validate the described clustering method, we apply the procedure to soil moisture data from the Mississippi basin to produce homogeneous spatial clusters. We produce animations to dynamically show the estimation procedure, including the estimated 2D-SDFs and the score matrix, which provide an intuitive illustration of the proposed method.

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Second-order non-stationary modeling approaches for univariate geostatistical data

Cited by 39 publications

References 86 publications

Random domain decompositions for object-oriented Kriging over complex domains

Random domain decompositions for object-oriented Kriging over complex domains

Spatio-temporal modelling for non-stationary point referenced data

Collective spectral density estimation and clustering for spatially-correlated data

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