Linear coregionalization model: Tools for estimation and choice of cross-variogram matrix

By Michel Goulard, M. Voltz. 1992

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Citations in the corpus

Kernels for Vector-Valued Functions: a Review (2011, methodology): “izing an objective function which involves some empirical measure of the correlation between the functions f d(x), Kb(x;x0), and the multivariate covariance obtained using a particular model, K(x;x0) [32, 47, 68]. Assuming stationary covariances, this criteria reduces to WSS = XN i=1 w(h i)trace ˆh ”
Automatic Variogram Modeling by Iterative Least Squares: Univariate and Multivariate Cases (2013, unknown): “For this purpose, there exists a numerical algorithm to ﬁnd the optimal matrix of sills for each basic structure, under the positive deﬁniteness constraint (Goulard and Voltz, 1992).”
Fusing point and areal level space–time data with application to wet deposition (2010, background): “Such specifications have a long history in geostatistics (see, for example, Goulard and Voltz (1992) and Gotway and Young (2002)).”
Multivariate Analysis and Spatial/Temporal Scales: Real and Complex Models (2007, background): “Goulard (1988, 1989), Goulard and Voltz (1992) have proposed several fitting procedures.”
Matérn Cross-Covariance Functions for Multivariate Random Fields (2010, methodology): “The prevalent way of guaranteeing this is to use the linear model of coregionalization (LMC), where each component is represented as a linear combination of latent, independent univariate spatial processes (Goulard and Voltz 1992; Wackernagel 2003).”
On the pseudo cross-variogram (1993, background): “Usually, however, too little is known to use such an approach, and multivariate spatial random processes are therefore modeled as linear coregionalizations (Joumel and Huijbregts, 1978; Wackernagel, 1988; Goulard and Voltz, 1992 ).”
Maximum‐likelihood estimation for multivariate spatial linear coregionalization models (2007, methodology): “Copyright # 2006 John Wiley & Sons, Ltd. Environmetrics 2007; 18: 125–139 DOI: 10.1002/env Due to the additive structure of LCM, we have EðYðsÞ jYÞ ¼ lþ XK k¼0 EðXkðsÞ jYÞ However, E(Xk(s)jY)¼ 0 due to independence.”
Remarks on multi-output Gaussian process regression (2018, methodology): “Linear model of coregionalization The most widely used generative approach for developing admissible multioutput covariance functions was pioneered in the geostatistics community, known as linear model of coregionalization (LMC) [36, 37, 38, 39].”
Nonstationary multivariate process modeling through spatially varying coregionalization (2004, background): “This specification for G is referred to as a nested cross covariogram model (Goulard and Voltz, 1992; Wackernagel, 2003) dating again to Matheron (1982).”
On digital soil mapping (2003, background): “In the early co-kriging studies (McBratney and Webster, 1983; Vauclin et al., 1983; Goulard and Voltz, 1992), these ancillary variables were other soil variables, indicating that other soil variables are themselves useful predictors of soil.”
Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification (2013, background): “Another more general model for the covariance function is the linear model of coregionalization (LMC) [24] [25] [26].”
A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components (2012, methodology): “A popular approach is to use a linear model of coregionalization (LMC) for stationary random fields (Goulard and Votz 1992 ; Schmidt and Gelfand 2003 ; Wackernagel 2003 ; Gelfand et al.”