Interpolation of spatial data

By Michael L. Stein. 1999

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Citations in the corpus

Objective Bayesian Analysis of Spatially Correlated Data (2001, background): “This was alluded to in De Oliveira et al. (1997) and stated, for particular models, in Stein (1999), but no systematic study of the phenomenon was undertaken.”
Non-Stationary Dependence Structures for Spatial Extremes (2014, methodology): “…Bessel function of second kind and ν > 0, model (9) yields a flexible non-stationary correlation based on the widely used Matérn model (Handcock and Stein, 1993; Stein, 1999; Guttorp and Gneiting, 2006), where the degree of differentiability of the associated Gaussian random field can be…”
INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018, background): “…by x ( s ) for simplicity, is assumed to be driven by a zero mean Gaussian process prior with precision τ s > 0 and Mat´ern correlation function (Stein, 1999; Lindgren et al. , 2011; Lindgren and Rue, 2015), i.e., cov { x ( s 1 ) , where K ν denotes the modiﬁed Bessel function of second…”
A Case Study Competition Among Methods for Analyzing Large Spatial Data (2017, methodology): “From a theoretical perspective, covariance tapering (in the framework of infill-asymptotics) is using the concept of Gaussian equivalent measures and mis-specified covariance functions (see, e.g., Stein 1999 and references therein).”
Intrinsic inference difficulties for trait evolution with Ornstein‐Uhlenbeck models (2014, background): “A requirement stronger than identifiability is needed instead, historically called microergodicity (Stein 1999).”
Testing environmental and genetic effects in the presence of spatial autocorrelation (2014, background): “The Matérn family is appropriate to fit autocorrelated processes with more or less rugged realizations, and is the most useful correlation model for a wide range of applications (Stein 1999, see also Minasny and McBratney 2005, Hoeting et al. 2006, Diggle and Ribeiro 2007).”
Multiresolution models for nonstationary spatial covariance functions (2002, methodology): “In this section we provide more deliberate comparisons for the Matern family (Stein, 1999).”
Learning soil parameters and updating geotechnical reliability estimates under spatial variability – theory and application to shallow foundations (2017, unknown): “…of lnw given the measurements is normal and its posterior mean function m′′lnw and auto-covariance function S′′lnw are given as follows (e.g. Stein 1999): m′′lnw(z) = m′lw + Slnw(z)S −1 m Dm, (32) S′′lnw(z1, z2) = S′lnw(z1 − z2) − Slnw(z1)S−1m STlnw(z2), (33) where Slnw(z) is an 1× 3…”
Sequential design of computer experiments for the estimation of a probability of failure (2010, methodology): “The parameters of the Matérn covariance functions are estimated on the initial design by REML (see, e.g. Stein, 1999).”
Convergence Types and Rates in Generic Karhunen-Loève Expansions with Applications to Sample Path Properties (2014, background): “l input spaces, which translates into general index sets T in our terminology. Similarly, certain spatial statistical methods require knowledge on the paths properties in terms of spaces, we refer to [64, 24, 60] and the references in these articles. Karhunen-Loe`ve expansions, their speed of conver”
A spatial zero-inflated poisson regression model for oak regeneration (2006, background): “The Matérn (1960) class of correlation functions ρ (r; γ , ν) = 2 (γ r/2) ν Kν (γ r) (ν) , (1) where Kν (·) is the modified Bessel function of the second kind (Abramowitz and Stegun 1965), includes a parameter ν that controls the smoothness of the realizations of the random filed ε (·) (Stein 1999).”
Nonstationary multivariate process modeling through spatially varying coregionalization (2004, methodology): “With regard to multivariate spatial process modeling using kernels, we were struck by the fact that the only readily-discovered work was that of Ver Hoef and Barry (1998) and Ver Hoef et al.”
Performance study of multi-fidelity gradient enhanced kriging (2015, methodology): “Various correlation functions, which can be different for each GEK model, can be employed (Näther and Šimák 2003; Rasmussen and Williams 2006; Stein 1999; Šimák 2002).”
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster (2012, unknown): “sian nonparametrics, Algorithms, Gaussian random ﬁeld, Bayesian inverse problems. 1. INTRODUCTION The use of Gaussian process (or ﬁeld) priors is widespread in statistical applications (geostatistics [60], nonparametric regression [31], Bayesian emulator modeling [45], density estimation [2] and inv”
Efficient methods for large‐scale linear inversion using a geostatistical approach (2012, methodology): “[14] Some possible choices for the Covariance Kernel Kð ; Þ arise from the Matérn family of covariance kernels [Stein, 1999], corresponding to isotropic, stationary stochastic process.”