Space and Space-Time Modeling using Process Convolutions

By D. Higdon. 2002

528 citations recorded by the source corpus.

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

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Citations in the corpus

Machine learning of linear differential equations using Gaussian processes (2017, background): “This particular instance corresponds to the well-known convolved Gaussian processes [21, 22] which are suitable for multi-output purposes [23].”
GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation (2014, background): “In total, there are 6 parameters θ = {P, ∂,N0, σd, σp, τ}.”
Multitask Gaussian Processes for Multivariate Physiological Time-Series Analysis (2015, background): “In [17], the notion of convolving two covariance functions has been presented, which has been further discussed in [18] for the case of MTGPs.”
THE COYOTE UNIVERSE. III. SIMULATION SUITE AND PRECISION EMULATOR FOR THE NONLINEAR MATTER POWER SPECTRUM (2009, methodology): “We choose a flexible class of smooth functions called a process convolution (Higdon 2002).”
A Case Study Competition Among Methods for Analyzing Large Spatial Data (2017, background): “Beginning in the late 2000’s, several approaches based on low-rank approximations to Gaussian processes were developed (or became popular) including discrete process convolutions (Higdon 2002; Lemos and Sansó 2009), fixed rank kriging (Cressie and Johannesson 2008; Kang andCressie 2011; Katzfuss and”
Mechanistic Hierarchical Gaussian Processes (2014, background): “One can alternatively look at (4) from a process-convolution perspective (Higdon 1998, 2002; Álvarez, Rosasco, and Lawrence 2012).”
Latent Force Models (2009, methodology): “We are not the first to suggest the use of convolution processes for multi-output regression, they were proposed by (Higdon, 2002) and built on by (Boyle and Frean, 2005) — the ideas in these papers have also recently been made more computationally practical through sparse approximations suggested b”
A Spatio-Temporal Model for Mean, Anomaly, and Trend Fields of North Atlantic Sea Surface Temperature (2009, methodology): “It is based on the representation of a Gaussian process as the convolution of a process with a kernel, as proposed in Higdon (2002).”
A Unified Framework for Fitting Bayesian Semiparametric Models to Arbitrarily Censored Survival Data, Including Spatially Referenced Data (2017, methodology): “Various approaches have been developed to overcome this computational issue such as process convolutions (Higdon 2002), fixed rank kriging (Cressie and Johannesson 2008), predictive process models (Banerjee et al. 2008), sparse approximations (Kaufman, Schervish, andNychka 2008), and the full-scale…”
Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing (2005, background): “These include spatially varying kernel convolution ideas as in Higdon, Swall and Kern (1999) and Higdon (2002) as well as a local stationarity approach as in Fuentes and Smith (2001).”
A full scale approximation of covariance functions for large spatial data sets (2012, background): “E-mail: huiyan@stat.tamu.edu example, Higdon (2002)), low rank splines or basis functions (e.g. Wikle and Cressie (1999), Ver Hoef et al. (2004), Kammann and Wand (2003) and Cressie and Johannesson (2008)) and predictive process models (Banerjee et al., 2008; Finley et al., 2009).”
Analyzing Nonstationary Spatial Data Using Piecewise Gaussian Processes (2005, methodology): “We adapted a simple one-dimensional example from Higdon (2001). In this example the sample size was 30, the spatial locations varied between 1 and 10, and the observations were created according to the formula”