Estimation of nonstationary spatial covariance structure

By David J. Nott, W. Dunsmuir. 2002

79 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/90cce30c6aeeab721ac8cb02ce4e1efa8b1b1149

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Citations in the corpus

Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies (2008, unknown): “For more details on estimation please refer to Nott and Dunsmuir (2002).”
Near-optimal sensor placements in Gaussian processes (2005, unknown): “We address this issue by exploiting locality in the kernel function: First, we note that, for many GPs, correlation decreases exponentially with the distance between points.”
Gaussian process product models for nonparametric nonstationarity (2008, background): “Other approaches involve Gaussian process mixtures (Rasmussen, 2000), augmentation of the input space (P.ngsten et al., 2006), and weighted sums of locally-stationary processes (Nott& Dunsmuir, 2002).”
Analyzing Nonstationary Spatial Data Using Piecewise Gaussian Processes (2005, background): “Other recent developments for modeling nonstationary processes include those of Nott and Dunsmuir (2002) and Fuentes and Smith (2001).”
A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components (2012, background): “Moreover, these models serve as building blocks for more sophisticated anisotropic and nonstationary covariances; for instance, see Mateu, Porcu, and Gregori ( 2008 ), Porcu, Mateu, and Bevilacqua ( 2007 ), and Nott and Dunsmuir ( 2002 ).”
Near-optimal sensor placements: maximizing information while minimizing communication cost (2006, methodology): “an approach to estimate nonstationarity proposed in [17].”
Nonstationary spatial covariance functions (2005, background): “Nott and Dunsmuir (2002) describe an approach to extending a covariance structure for a finite number of locations to a valid (generally) nonstationary covariance function on all of Rp that could also be combined with spatially varying spectra.”
Space–Time Covariance Functions (2005, background): “…as with many recent efforts to develop nonstationary spatial models (Sampson and Guttorp 1992; Higdon 1998; Fuentes 2002; Fuentes and Smith 2001; Nott and Dunsmuir 2002; Clerc and Mallat 2003), stationary space–time models should play a central role as a building block for nonstationary models.”
Gaussian Processes for time-marked time-series data (2012, background): “While other non-parametric Gaussian Processes have been studied (Sampson and Guttorp, 1992; Nott and Dunsmuir, 2002; Schmidt and O’Hagan, 2003; Murray-Smith and Pearlmutter, 2003; Paciorek and Schervish, 2006, 2003), we consider in depth the particular case of causal GPs.”
Nonmyopic active learning of Gaussian processes: an exploration-exploitation approach (2007, methodology): “An example of a parametric form for nonstationary is given by Nott and Dunsmuir (2002), who suggest to model nonstationarity by a spatially varying linear combination of isotropic processes.”