Space–Time Covariance Functions

By Michael L. Stein. 2005

480 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/5424ee6239a747094db60fb0b2393c7329411eb0

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Citations in the corpus

Gaussian processes for time-series modelling (2013, background): “Fortunately, there exist a wide variety of functions that can serve in this purpose [3,4], which can then be combined and modified in a further multitude of ways.”
Statistical methods for regular monitoring data (2005, methodology): “…works such as Christakos (1992, 2000), Jones and Zhang (1997), Cressie and Huang (1999), Brown et al. (2000), de Iaco et al. (2001, 2002, 2003), Gneiting (2002), Hartfield and Gunst (2003), Ma (2003), Kolovos et al. (2004) and Stein (2005), or at least versions of these models adapted to S2r × R?”
A World Malaria Map: Plasmodium falciparum Endemicity in 2007 (2009, methodology): “The spatiotemporal component was represented by a stationary Gaussian process f(xi,ti) with mean l and covariance defined by a spatially anisotropic version of the space-time covariance function proposed by Stein [64].”
Spatio-temporal variograms and covariance models (2005, background): “This represents a rather limited description of space–time interaction, as pointed out by Cressie and Huang (1999), Kyriakidis and Journel (1999), and Stein (2005).”
Recent developments on the construction of spatio-temporal covariance models (2008, methodology): “Second, it is often desirable to have a covariance function that may take negative values or oscillate from positive to negative values (Shkarofsky 1968), but spatial or spatio-temporal covariance models frequently used in practice are nonnegative; see examples of Oliver (1995), Gneiting (2002), and”
Gaussian predictive process models for large spatial data sets (2008, background): “There has been recent discussion regarding valid non-separable space–time covariance functions; see, for example, Stein (2005) and discussion therein.”
A spatiotemporal precipitation generator based on a censored latent Gaussian field (2015, background): “For a collection of valid spatiotemporal covariances, see Cressie and Huang [1999], Ma [2003], and Stein [2005] among others.”
Continuous Spatial Process Models for Spatial Extreme Values (2010, methodology): “…be discretized to yield, e.g., annual maxima in which case we need only provide a dynamic Gaussian processmodel (see, Banerjee et al. (2004)) though we might view time as continuous in order to explicitly capture space-time interaction, using a valid spacetime covariance function, see Stein (2005).”
2010 Rietz lecture: When does the screening effect hold? (2011, background): “Stein (2005) shows that K(0, t) = 18π 2− 23π3/2|t|3/2+O(t2) as t→ 0 so that K(0, t) is not twice differentiable in t at t = 0, and the corresponding process is not mean square differentiable in time.”
Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry (2007, methodology): “We refer to Haslett and Raftery (1989) for background information and to Gneiting (2002a), Stein (2004, 2005) and de Luna and Genton (2005) for subsequent analyses of the Irish wind data.”
New classes of covariance and spectral density functions for spatio-temporal modelling (2008, methodology): “This confirms our initial feeling at the beginning of our analysis, in which a model taking into account the interaction between the marginal structures should outperform other types of models [as those used by Gneiting (2002) and Stein (2005) ].”
Geostatistical inference under preferential sampling (2010, background): “Another extension of this work would be in the understanding of preferential sampling for space–time models (Stein, 2005).”