A process-convolution approach to modelling temperatures in the North Atlantic Ocean

By D. Higdon. 1998

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Citations in the corpus

Nonstationary spatial covariance functions (2005, methodology): “Higdon (1998) and Fuentes (2002) describe methods for generating nonstationary covariance functions as integrals, but these integrals generally have to be carried out numerically.”
Second-order non-stationary modeling approaches for univariate geostatistical data (2017, methodology): “Convolution based non-stationary modeling approach introduced by Higdon (1998) and Higdon et al.”
Computationally Efficient Convolved Multiple Output Gaussian Processes (2011, methodology): “Applications include the construction of nonstationary covariances (Higdon, 1998; Higdon et al., 1998; Fuentes, 2002a,b; Pciorek and Schervish, 2004) and spatiotemporal covariances (Wikle et al., 1998; Wikle, 2002, 2003).”
Spatial modeling of extreme snow depth (2011, methodology): “be divided in three main families [Schabenberger and Gotway (2005)]. The moving window approach of Haas (1990) estimates a covariance function locally within a neighborhood. The convolution method of Higdon (1998) allows the construction of weakly nonstationary processes by convolving a zero-mean wh”
Some topics in convolution-based spatial modeling (2007, unknown): “Using a discretized version of (6), Higdon (1998) defines the spati ally referenced kernel k0s(� ) to be”
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (2011, background): “Many applications require non-stationarity in the correlation function and there is a vast literature on this subject (Sampson and Guttorp, 1992; Higdon, 1998; Hughes-Oliver et al., 1998; Cressie and Huang, 1999; Higdon et al., 1999; Fuentes, 2001; Gneiting, 2002; Stein, 2005; Paciorek and Schervish”
A kernel-based spectral model for non-Gaussian spatio-temporal processes (2002, methodology): “However, motivated by the non-stationary spatial modeling approach of Higdon (1998), Wikle (2001) showed that by considering spatially varying (heterogeneous) redistribution kernels in this framework, one can model very complicated dynamics, both diffusive and so-called ‘extra-diffusive’.”
Modeling Nonstationary Processes Through Dimension Expansion (2010, background): “The process–convolution approach (Higdon 1998; Higdon, Swall, and Kern 1999) relies on the notion that a wide range of stationary Gaussian processes may be expressed as a kernel convolved with a Gaussian white noise process, with the kernel being allowed to vary spatially to account for nonstationar”
Nonstationary covariance models for global data (2008, methodology): “Kernel convolution and its variants have been applied in several papers to create nonstationary covariance functions such as in Higdon (1998), Higdon, Swall and Kern (1999), Fuentes (2002) and Paciorek and Schervish (2006).”
Bayesian Solution Uncertainty Quantification for Differential Equations (2013, background): “The covariance structure is deﬁned as a ﬂexible convolution of kernels (see, e.g., Higdon, 1998, 2002).”
Space–Time Covariance Functions (2005, background): “Higdon 1998, Fuentes 2002, Fuentes and Smith 2001, Nott and Dunsmuir 2002, Clerc and Mallat”
A hierarchical model for the analysis of spatial rainfall extremes (2007, methodology): “As suggested by the approach of Higdon (1998), we approximate the random fields”
A Moving Average Approach for Spatial Statistical Models of Stream Networks (2010, background): “…construct valid autocovariances when confronted with new problems, such as flexible, nonparametric models (Barry and Ver Hoef 1996), multivariate models (Ver Hoef and Barry 1998; Ver Hoef, Cressie, and Barry 2004), and nonstationary models (Higdon 1998; Higdon, Swall, and Kern 1999; Fuentes 2002).”
Computer Model Calibration Using High-Dimensional Output (2008, background): “A spacing between kernels of about 1 standard deviation in the component directions is required to result in a satisfactory model for δ( x ) (Higdon 1998).”
A non‐stationary covariance‐based Kriging method for metamodelling in engineering design (2007, methodology): “Paciorek [12] used a process convolution approach extended from Higdon’s [21] method and Gibbs’ first method.”