Some covariance models based on normal scale mixtures

Martin Schlather

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Spatial and Panel Data Analysis Point processes and geometric inequalities Gaussian Processes and Bayesian Inference

Abstract

Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new class is described that merges and generalizes various models presented in the literature, in particular models in Gneiting (J. Amer. Statist. Assoc. 97 (2002) 590–600) and Stein (Nonstationary spatial covariance functions (2005) Univ. Chicago). Furthermore, new models and a multivariate extension are introduced.

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References

1999Interpolation of Spatial Data 2002Nonseparable, Stationary Covariance Functions for Space–Time Data 1999Classes of Nonseparable, Spatio-Temporal Stationary Covariance Functions 2004Stochastic Models That Separate Fractal Dimension and the Hurst Effect 2005Space–Time Covariance Functions 2006Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry 2004Methods for generating non-separable spatiotemporal covariance models with potential environmental applications 2003Families of spatio-temporal stationary covariance models

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