Bayesian inference for non‐stationary spatial covariance structure via spatial deformations

By Alexandra M. Schmidt, Anthony OʼHagan. 2003

353 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence, Environmental Engineering

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Citations in the corpus

Manifold Gaussian Processes for regression (2014, background): “In a full Bayesian framework, the latent space L is integrated out to solve the regression task F , which is often analytically unfeasible (Schmidt and O’Hagan, 2003).”
Input Warping for Bayesian Optimization of Non-Stationary Functions (2014, methodology): “Schmidt and O’Hagan [2003] extended this warping approach for general GP regression problems using a ﬂexible GP mapping.”
Gaussian Process Regression Networks (2011, background): “…regression with non-stationary covariance function amplitudes (Turner and Sahani, 2008; Adams and Stegle, 2008) and length-scales (Gibbs, 1997; Schmidt and O’Hagan, 2003), and with heavy tailed predictive distributions (Neal, 1997; Vanhatalo et al., 2009) for outlier rejection (De Finetti,…”
Computational Phenotype Discovery Using Unsupervised Feature Learning over Noisy, Sparse, and Irregular Clinical Data (2013, background): “A warping approach has been previously described for spatial models [47], with the added complexity that the warping function was learned from the data.”
Nonstationary spatial covariance functions (2005, methodology): “varying geometric anisotropies is to use spatial deformations ( Sampson and Guttorp 1992, Perrin”
Modeling Nonstationary Processes Through Dimension Expansion (2010, methodology): “As the Sampson and Guttorp (1992) approach was set within a Bayesian framework by Damian et al. (2001) and Schmidt and O’Hagan (2003), setting the current algorithmic approach within such an inferential framework would allow the inherent uncertainty to be accurately reﬂected in resulting inferences…”
Heteroscedastic Treed Bayesian Optimisation (2014, background): “This approach was later extended by Schmidt and O’Hagan (2003).”
Generalized Spatial and Spatiotemporal Autoregressive Conditional Heteroscedasticity (2016, background): “Thus, Sampson & Guttorp (1992), Fuentes (2001), Fuentes (2002), and Schmidt & O’Hagan (2003), among others, have introduced various approaches to treat nonstationary spatial processes.”
Gaussian Processes for time-marked time-series data (2012, background): “These other works focus on inferring nonstationary warping/deformation mappings using splines and multidimensional scaling (Sampson and Guttorp, 1992) or with a GP mapping true space t to deformed space h(t) (Schmidt and O’Hagan, 2003).”
Nonstationary Covariance Functions for Gaussian Process Regression (2003, methodology): “the original input space to a new space in which stationarity is assumed, but research has focused on multiple noisy replicates of the regression func tio with no development nor assessment of the method in the standard regression setting [4, 5].”
Warped Gaussian Processes (2003, methodology): “In the context of geostatistics this has actually been dealt with by O’Hagan [12], where a transformation is made from an input space which can have non-stationary and non-isotropic covariance structure, to a latent space in which the usual conditions of stationarity and isotropy hold.”
Gaussian process product models for nonparametric nonstationarity (2008, methodology): “One of the first techniques was that of Sampson and Guttorp (1992) , who model a spline-based mapping to a latent input space in which the data are stationary.”
Modeling an augmented Lagrangian for improved blackbox constrained optimization (2014, methodology): “Modern GP methods accommodate nonstationarity (Schmidt and O’Hagan, 2003; Pa-ciorek and Schervish, 2006) and even regime-changing behavior (Gramacy and Lee, 2008).”
Basis-Function Models in Spatial Statistics (2021, background): “…of Zammit-Mangion et al. (2021b) circumvents this by forcing the mapping in each layer of the deep neural network to be injective, which precludes the possibility of ‘space-folding’, where space is mapped onto itself and can create undesirable spatial-prediction artefacts (Schmidt & O’Hagan, 2003).”
Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “Alternatively, Sampson and Guttorp (1992), Perrin and Monestiez (1999), Schmidt and O’Hagan (2003) and Anderes and Stein (2008) created nonstationary processes by smooth deformations of isotropic random fields.”
Estimating deformations of isotropic Gaussian random fields on the plane (2008, background): “Their work, as well as that of subsequent authors (see, e.g., [7, 11, 16, 19 ]) deals mostly with data from sparse observation locations with independent replicates of the random field.”