Nonstationary multivariate process modeling through spatially varying coregionalization

By Alan E. Gelfand, Alexandra M. Schmidt, S. Banerjee, C. F. Sirmans. 2004

366 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering

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Citations in the corpus

Kernels for Vector-Valued Functions: a Review (2011, background): “In [34], the authors introduced a nonstationary version of the LMC, in which the coregionalization matrices are allowed to vary as functions of the input variables.”
Gaussian Process Regression Networks (2011, methodology): “The GPRN framework extends and unifies the work of Journel & Huijbregts (1978), Neal (1996), Gelfand et al. (2004), Teh et al. (2005), Adams & Stegle (2008), Turner (2010), and Wilson & Ghahramani (2010b; 2011).”
Non‐stationary Cross‐Covariance Models for Multivariate Processes on a Globe (2011, methodology): “The variations of LMC models that give non-stationary covariance models such as in Gelfand et al. (2004) achieve the nonstationarity quite differently from the way the models in (8) achieve it.”
Matérn Cross-Covariance Functions for Multivariate Random Fields (2010, background): “…and Zidek 1994; Schmidt and Gelfand 2003) to weather forecasting (Rabier et al. 1998; Reich and Fuentes 2007), climate change (Jun, Knutti, and Nychka 2008), ecology (Royle and Berliner 1999), forestry (Finley et al. 2008), and economics (Gelfand et al. 2004; Sain and Cressie 2007), among others.”
Gaussian predictive process models for large spatial data sets (2008, methodology): “Here, we adopt a spatially adaptive version of the 'linear model of co-regionalization' (Wackernagel, 2006; Gelfand et al., 2004).”
Geostatistical estimation of forest biomass in interior Alaska combining Landsat-derived tree cover, sampled airborne lidar and field observations (2017, background): “, field AGB and airborne lidar samples (Gelfand et al., 2004).”
Probabilistic uncertainty analysis of an FRF of a structure using a Gaussian process emulator (2011, methodology): “Here, we use a method based on the linear model of coregionalization (LMC), a tool that is popular in geostatistics for modelling multivariate spatial processes (Journel and Huijbregts, 1978; Wackernagel, 1995; Goulard and Voltz, 1992; Gelfand et al., 2004).”
A MULTIVARIATE SEMIPARAMETRIC BAYESIAN SPATIAL MODELING FRAMEWORK FOR HURRICANE SURFACE WIND FIELDS (2007, methodology): “Variations of this linear model of coregionization (LMC) have been used by Grzebyk and Wackernagel (1994), Wackernagel (2003), Schmidt and Gelfand (2003), Banerjee, Carlin and Gelfand (2004) and Gelfand et al. (2004).”
Spatial Regression Modeling for Compositional Data With Many Zeros (2013, methodology): “independent univariate intrinsic CAR (1, σ(2)) models (Gelfand et al., 2004).”
Hierarchical modeling for extreme values observed over space and time (2009, methodology): “Here, we propose a coregionalization model in the spirit of Gelfand et al. (2004).”
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; Wackernagel, 2003; Schmidt and Gelfand, 2003; Gelfand et al., 2004; Zhang, 2007).”
Remarks on multi-output Gaussian process regression (2018, methodology): “There are some other extensions of typical LMC, for example, the nonstationary MOGP by using a spatially varying correlation matrix [50, 51], the combination of the LMC and the Bayesian treed Gaussian process [52, 53], and the self-measuring MTGP that uses the information of outputs to construct inf”
Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes (2012, background): “Some of the multivariate spatial models currently of interest in the statistics community may also be useful to this end [Apanasovich and Genton, 2010; Gelfand et al., 2004; Gneiting et al., 2010].”
Cross-covariance functions for multivariate random fields based on latent dimensions (2010, background): “The linear model of coregionalization for stationary processes (Goulard & Voltz, 1992; Wackernagel, 2003; Gelfand et al., 2004) implies that the cross-covariance function is Ci j (x1 − x2) = r∑ k=1 ρk(x1 − x2)aika jk, for an integer 1 r p, where A = {ai j } is a p × r full rank matrix and ρk(·) are…”
A Spatio-Temporal Downscaler for Output From Numerical Models (2010, methodology): “These are, in turn, modeled as correlated spatial Gaussian processes via the method of coregionalization (Schmidt and Gelfand 2003; Gelfand et al. 2004).”